THE GRAVITY

  Version 2.0

 

ALFONSO LEON GUILLEN GOMEZ

All reserved rights

SANTAFE OF BOGOTA, COLOMBIA

 

AUGUST OF 1996

 

ABSTRACT

The thing this there is in front ours and we perceive it with all the power of our senses, but, its revelation to be conscious is arduous and late. We should encounter it, to throw us to the land one time and again, until by obstinacy we apprehend it.

The up to now impossible speed of gravity the humans we have had it in the constant of position of the stars and, during at least a century, it we have not recognized.

The obstinacy of the investigation that is repeated without giving to be twisted is the light that it permits the men to see in the cavern after the super dense darkness.

 

REGISTER OF THIS WORK

The present work is the version 2 of the scientific investigation that carries out during 1994-1995. This work, under the title "Proposed to measure the speed of the gravitation based on the Astronomy of Position" was registered in the Special Administrative Unit, National Direction of the Right of Author, Office of Registration, Book 10, Volume 30, Departure 414 dated 7 of September of 1995.

 

GRATEFULNESS

In the updating of this work I counted on the support of the doctor Juan José Salas, director of the Local Planetarium, and of the professors Benjamin Calvo and Gregorio Portilla, astronomers, that labor in the National University, who they supplied me excellent bibliography about the most recent advances achieved in the science of the Astronomy.

The doctor Carlos Lemoine had the graciousness to read the first version and to suggest me the change of presentation doing it clearer. In addition he observes that the graviton like the photon lack of mass then graviton can travel up c. Thus, he considers possible my theory about speed of gravity greater than c.

 

WORKS OF THE AUTHOR

1. A speed greater than the speed of light, 1969. The speed of light c does not limit, but is a constant of the nature. The speed of gravity is greater than c.

2. Proposed for to measure the speed of gravity according tides,1993.

3. Experiments of Tom Van Flandern indicate that the speed of gravity is minimum 20 billion times c, 2001.

4. Superluminary speed reached in experiment in Princenton, 2001.

5. The inertia of the energy and the speed of gravity, 2004.

6. The gravity truly is a force, 2004.

7. The concepts about of the speed of gravity, 2006.

8. The gravitational waves truly propagate in 5 dimensions, 2006.

 

ANTECEDENTS

 

Between 1969-1970, the author formulates the existence in the nature of speeds greater than c, in four articles, published in the newspaper "El Siglo". The originals are here.

 

 

 

In 1991-1993, the author proposed the accomplishment of several conducive experiments to the measurement of the speed of gravity from the static gravitational field, under the assumption that this field this constituted by virtual gravitons. These experiments were conceived from the perspective of the Astrophysics that studies the constitution and evolution of the celestial objects in special of the Sun and, later, of the Astronomical Geography, which it describes some phenomena which they happen in the Earth and they are related to the stars, referring me to most typical as they are the eclipses and the tides. The documents that credit these pioneering works of the author, in the 1990 principles, can be seen here.

 

TABLE OF CONTENT

 

INTRODUCTION

1 ANTECEDENT

1.1 Criticism of the theory of the Relativity

1.2 Quantum Theory of the gravitation

1.3 Speeds greater that speed of light

1.4 Experiments proposed

1.5 Conclusions

2 ASTRONOMY OF POSITION

2.1 The heavenly mechanics

2.2 The geometry of the space

2.3 Mechanical of Newton and Euclidean space

2.4 Relativist mechanic

2.5 The inadvertent key

2.6 Conclusions

3 TIME

3.1 Traditional system of fixation of the time

3.2 The expressions of the time

3.3 Differences and conversions

3.4 The Gregorian calendar

3.5 Julian Calendar

3.6 Besselian calendar

3.7 Conclusions

4 COORDINATES OF POSITION

4.1 Usual Framework

4.2 Units of measure

4.3 Heavenly Sphere

4.4 Land

4.5 Transformations among heavenly and terrestrial coordinates

4.6 Movements of the Land

4.7 Effects of the position and movement of the stars and the observer

4.7.1 Parallaxes

4.7.2 Aberration

4.7.3 Deflation of the light

4.7.4 Refraction of the light

4.8 Position of the planets

4.8.1 Orbital parameters

4.8.2 Daily Movement

4.8.3 Movement in systems of two bodies

4.8.4 Extension at more than two bodies

4.8.5 Additional Disruptions

4.8.6 Procedure shortened

4.8.7 Relativistic correction

4.8.8 Approach used in the calculation of the effects of the disruptions

4.8.9 Observations

4.9 Differential Corrections

4.10 Conclusions

5. MODEL PRESENT

5.1 Fundamental ephemeris

5.2 Framework of reference

5.3 Gravitational Model

Equation 1.

5.4 Evaluation of the model of force

5.5 Parameters

5.6 Observations

5.7 Corrections

5.7.1 Radar

5.7.2 Sond

5.7.3 Laser

5.7.4 Optics

5.8 Landslides in the positions of the planets

5.9 The precision reached

5.9.1 In keplerian astronomy of position

Table A. Orbital elements of the planets a, e, I according to the theory of classical Kepler

Table B. Orbital elements the planets W, w, L according to the keplerian classical theory

Table C. Most maximum errors from the formulae of classical Kepler

5.9.2 In astronomy of position based on DE200

5.10 Conclusions

6 PROPOSAL TO MEASURE THE SPEED OF GRAVITY

6.1 DE200-LE200 is partial

6.2 The landslide

Table 1. Landslide of the planets due to the speed of gravity

6.3 Characteristics of the landslide

Table 2. Factor distance

Table 3. Factor in inverse function to time that spends a planet in travelling through a second of arc

Table 4. Values of the function of correction of the landslide the planets (Pattern: Landslide Mercury)

6.4 Function of correction of the landslide

Table 5. Comparison of the landslide of the planets according to the position of perihelion

6.5 Comparison of the errors of Kepler and that of gravitation

Table 6. Most maximum errors from the keplerian classical formulae compared with the most maximum error attributable to effect of gravitation

6.6 Analysis of the results

6.7 Formula for to calculate the speed of gravity

6.8 Conclusions

APPEND

Table 1. Landslides of the planets

BIBLIOGRAFIA

 

Este trabajo también el lector puede verlo en español (This work also the reader can see it in Spanish).

 

 

INTRODUCTION

"The simple vision of something does not contribute nothing us. Each look carries us to a consideration, each consideration to a meaning, each meaning to a relation, and thus is able to be told that with each attentive look theorize us on the world"

W. Goethe

The phenomenon of the gravitation is the most studied phenomenon since the century XVII due its extraordinary significance in the comprehension of the Universe. Progressively it has developed three theories to interpret the gravitation. The first theory is that of Newton that permitted to explain the movements that are produced in the cosmos. Then, Einstein changes fantastically our conception about the time and the space. And the present theory that results of the integration of the two largest partial theories on the physics as are the Relativity and the Quantum theory, that have placed to scientific thought in the possibility to explain the origin of the Universe from the big-bang as well as to predict its future that can be big-crunch.

Nevertheless, we are far from understanding fully the gravitation. The most recent questioning about its origin, speed and nature quantum-wave do not count of final answers.

The theme of the gravitation as object of investigation is extensive and promissory for the physicists and astronomers that have the opportunity to develop spectacular theories and to carry out amazing discoveries that can change all our present conception   on the world and to give rise to a new physics.

Along a quarter of century, with several long interruptions, I have studied the theory of the Relativity and the Quantum Mechanics. This facts, early, conducted me to devise a theory about the existence, in the nature of speeds greater that speed of light. This speed Albert Einstein advanced it like the possible last speed in the Universe and impossible to infringe. Also, in the last five-year period, I have done, based on different approach astronomical, several proposals with the objective that experimentally the speed to the date unknown gravitation be measured, although, is believed is equal to speed of light. In my theory the speed of gravity belong the family of the super speeds and is one of the speeds greater than the speed of light.

In this work I develop the exposition of the results of the investigation that serves of backup to the proposal to measure the speed of gravity based on the astronomy of position.

The motives and the objective of the investigation are declared in the antecedents. The theoretical framework develops in the three following chapters that try the astronomy of position, about its conception and its structural elements of space, time and position. The procedure DE200/LE200 that it uses at present for the generation of the ephemeris of the planets is presented in the fifth chapter. The proposal for to measure the speed of gravity is exposed in the last chapter.

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1 ANTECEDENT

The theory of the General Relativity of the gravitation unifies the Special Relativity, formulated for systems in rest or in uniform rectilinear movement, with the geometry curve of Riemann and the mathematical tensor description of Grossman, with which is generalized the relativity to the systems subject to accelerations.

The general Relativity conceives the gravitation as the geometric field that results of the deformation curved of the spacetime introduced by the matter in the Universe. This field can suffer structural variations of nature purely undulatory and according to the Relativity the perturbation it propagates with a speed equal to speed of light (gravitational wave), since in this theory not greater speeds can exist.

The theory of the Quantum Gravity, that treats of unify the General Relativity with the Quantum Mechanics, adding it the aspect corpuscular to gravity relativist field, with what remains structurally similar to electromagnetic field, that is to say, as a graviton-wave duality and, besides, subject to principle of uncertainty. On the other hand, introduces new types of fields, one by each existing elementary particle.

In the nature two classes of phenomenas exist: the substance and the field. Both phenomenas are constituted by an even wave-particle or corpuscle-wave (1). The gravity field and the other existing fields in the nature, the same as the different states of the substance, are material form differentiated according to its magnitudes; one of them is its speed.

In the field the corpuscle is a state excited of the wave, for which do not exist corpuscles in rest neither animated to different speeds, in a same middle. The quantity of mass of the corpuscle differs of a type of field to another. The mass of the graviton is extraordinarily smaller relating to mass of the photon. Other fields can have corpuscles with still smaller mass of the graviton. The corpuscle represents the aspect inertial of the field that is to say that offers resistance to change in the movement (2).

In the substance, I maintain the law as much as less mass has one substantial structure and more energetic is one state then greater is its speed. This law I believe should be a law of the nature and to govern also in the field. The speed of propagation of a specific type of field should be greater when it is less massive and more energetic (3) with relation to another. The gravity field should have greater speed that the electromagnetic field and the most disintegrated fields that the gravitation should possess greater speeds.

The speed in the field only has been measured experimentally for the electromagnetic field. In the gravitation due to that its dimensions belong to the scale of Planck has not been possible to measure directly its speed.

Nevertheless, the possibility exists to establish the speed of gravity indirectly through the astronomical phenomenas where changes of the gravitation effect are produced. One of those effects is that of the change of the gravitation interaction in the different positions that the planets occupy in its orbits elliptic around the Sun.

(1) The author introduces the word of corpuscle to distinguish the components of the field, that lack mass according to the fourth moment, of the particles components of the structures of the substance that if possess mass.

(2) In last instance, to move it more speedy.

(3) Although the corpuscles not have mass according fourth moment they have mass in movement. Indeed, the corpuscles have mass according first moment. The mass graviton is less that mass photon. Either hand, the graviton precedes photon during quantum era. Therefore, graviton exists to temperatures greater than the temperatures of the photon. For these two reasons the author say that the graviton is less massive that photon and graviton is more energetic that photon.

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1.1 Criticism of the theory of the Relativity

Some people consider like the major merit of the theory of the Relativity of Einstein the to have applied the relativity of the geometry of the physical space to the description of the Universe with which is done relative the space and geometrically dependent of the bodies that build it to change that, as happens in the classical conception, be an absolute and independent of the bodies that move in it, being conceivable the disappearance of a body of a place but not the space that defines to that place. Einstein says that the geometric properties of the space are not independent, but are conditioned by the matter.

So much more occurs with relation to the time before of the Relativity also absolute. Einstein established that the time exists in the variation of physical something with a specific rhythm. If the variation refers to which it occurs in an atom, its rhythm is different according to the geometric nature of the space that occupies.

In the theory of the Relativity the spacetime is determined by the matter and at the same time this determines the movement of the matter. This fact enables the theory advanced that the spacetime, in its deeper structure, this subject to permanent variation as result of the permanent change that occurs in the matter. The permanent micro fluctuation of the spacetime is base of the quantum conception.

The laws of the mechanics of Newton are valid with relation to inertial reference systems, that is to say, systems in rest or in movement rectilinear uniform, not being valid for system with movement accelerated. In these systems in the mechanics of Newton is required for to describe them, to introduce complementary forces that serve for to pass from an inertial reference system to an accelerated system.

In the General Relativity of Einstein is possible to eliminate, in the description of the systems with movement accelerated, the forces by means of the establishment of an equivalent system of reference with an adequate geometric space.

That is to say, due to the relativity of the geometry of the physical space is possible to determine a geometric structure of the space, with relation to one reference system with movement accelerated, that permit to describe it without doing reference to forces. Particularly, the gravitation force can disappear when it passes to a system whose axes are accelerated conveniently.

The acceleration of a material body abandoned itself, in a position any of the Universe, equal can be attributed to the inertia or to the gravitation, resulting the same thing to affirm that it is accelerated or that its movement occurs in a gravity field. The possibility to conceive the things in this way, says Einstein, rests in the fundamental property of the gravity field to communicate to all the bodies the same acceleration, that is to say, in the principle of equality of the masses inertial and gravitatory. From this equivalence Einstein defines the gravitation based on the geometry of the spacetime.

In a space euclideo the bodies, not submit to external forces, move rectilinear uniform geodesic spacetime and the bodies submitted to the gravitation move continuing in curved paths. In a space of Riemann, these last bodies also move in a curved geodesic spacetime. A geodesic line is the most minimum distance among two points of a specific geometric space. In general, bodies travel through of geodesic spacetime when force external do not act on them. And forces disappear with the use of one adequate geometry.

In the theory of Einstein is affirmed that when a body is in liberty remains out of the action of every force and its express form of movement only properties of the spacetime in the places by where passes. Contrarily to the laws of the physical classic, the geometry of the universe is not euclidea, is a geometry curve that delimits a universe closed and finite, in the proximity of the bodies with mass.

The existing relation among quantity of matter and the value of the curvature of the spacetime in a point is defined by twenty functions of the coordinates of that point. Ten functions correspond to a part of the curvature that spreads freely in form of gravitation waves or, that is the same thing, undulations of the curvature (Weyl tensor). The ten remaining functions are determined by the distributions of the mass, energy, moment, angular moment, and internal tensions of the matter and by the constant G of gravitation of Newton (Metric tensor). All the mass of the Earth produces a curvature of the spacetime that is only of mil millionth splits of the curvature of the surface of the Earth.

The geometric configuration of the continuous spacetime possesses speed, that is to say, varies as a result of the modifications that occur in the matter. This disruption of the spacetime is the gravitation wave that for Einstein should be spread with a speed equal to speed of light.

Of the two types of modifications that occur in the physical bodies that Henry Poincare indicated, to know:

- Changes of state.

- Changes of position.

In the Relativity only has been considered the changes of position for the formation of the concepts of space and time. Einstein, in the Special Relativity considers the space built from rigid bodies, that is to say, without alteration of state also the time as the variation of something physical without change of state. Einstein says the fact that there are corporeal objects, lack of any alteration of state, inside specific sphere of perception, but only changes of position is of fundamental importance for the formation of the concept of space and, although, does not say it explicitly is understood the same thing for the concept of time. However, that Einstein in the General Relativity using Gaussian coordinates, which refer to non-rigid bodies (the famous mollusk), only mean that the standard measures changes of distances or time between coordinate values very close, it matches with rods or clocks, since the coordinates in themselves are meaningless. The gaussian coordinates do not concern to the changes of state or form of the reference bodies. Therefore, physics not included in the formulation of laws of nature, forward covariant Gaussian systems, the universal feature of the change in state or form. Provided that General Relativity is a theory of general covariance this omission is a fundamental lack.

Einstein in its conception about the Universe omitted that physically it exists in a multiplicity of states relating to the mass and to the energy, nevertheless Einstein discovered the connection among both. And its global solution is incomplete when only it refers to movement without considering the material states and forms that in last instance are the base of all the physical reality.

Each material form or state, considered structurally, constitutes a way of existence that possesses an impossible speed limit to infringe. Also one particular material form or state constitute a continuous definite spacetime building according one specific structural unit particle-wave or wave-corpuscle.

In the structures of the substance dominates the massive aspect on the energetic aspect. Indeed, in the substantial structures the wave is a perturbation of the particles. The substance exists in the material forms, super atom (4), molecules, and plasma. The molecular form adopts the states: Solid, liquid and gaseous. The plasma is an atomic state ionized. These forms and states present changes in its "lengths" and in the rhythm of its "clocks". This occurs when its structures are energetic excited, always inside the limits of magnitude that determine the form or state in question. By underneath or over of the limits the change of form or state is produced, save in the super atom that lacks lower limit by being the state terminal of the substance and of the matter.

In the forms of the field the main acquaintances are: weak nuclear field whose corpuscle is the boson. Strong nuclear field where is the gluon. Electromagnetic field where is the photon. And gravity field where is the graviton. In the phenomena of the field dominates the energy aspect in front of the massive aspect, resulting the corpuscles excitements of energy (5) inside the respective waves. In the general theory of the unification (TGU) joint with gravity quantum theory (TGU-Supergravity) in the highest energy level these four fields result "states" of one only call super gravitation.

Einstein recognizes in the matter the existence of the modification of its physical properties under specific gravitation conditions but Einstein do not refers like change of state or of material form. Einstein says that a clock situated in the Sun will have a different march to which possesses in the Land, therefore the gravity field is more intense in the Sun. The clock can be an incandescent atom of sodium and the length of wave emitted one of its possible rhythms. In the Sun the length of wave of light generated is greater to which the same atom radiates in the Land.

The time is conceived like speed confined in a gravity field and, although, Einstein it does not say explicitly the lengths in the Sun should be shortened for the same gravitation reason.

Einstein in its conception of space, without changes of state in the bodies and of form in the field and, additionally, giving for finished the material reality in the electromagnetic field, resolves the gravitation as geometric property of a spacetime not euclideo and determines the speed of light as cosmic final speed.

Einstein though explains by means of the geometry curve the gravitation did not develop a physical theory about the structure of the spacetime. Nevertheless, Einstein recognized its character undulatory that, necessarily, conducts to conceive the gravity field as energy phenomenon, but, for Einstein, lacking of excitations.

Einstein, with the aid of the mathematical Marcel Grossman, were limited to the mathematical formulation by means of one tensor of said structure curve that permitted some subsequent physicists, applying it to gravitation intense fields, to predict the existence of the graviton, that is to say, the existence in the gravity field of "excitements ". In this manner the structure wave-graviton was completed for gravity field. This structure combining with the quantum mechanics originate the gravity quantum theory, arose of the initial version. Though, Andrei Saharov, his progenitor, believed that gravitation is a Casimir effect of long range. Therefore, either scientific, mainly soviets, are the real authors of the la theory about of quantum gravitation. They proposed this theory by epoch of Saharov (6).

The processes predicted in the theory of the Relativity about as the phenomenon of the bodies occurs carried to a speed closed to speed of light are similar processes when a material change of form or of state occurs. Such processes in the Relativity are:

- Enlargement of the time by increase of the speed.

- Contraction of the length of the bodies during its movement.

- Increase of the mass by energy increment.

Such changes in the General Relativity are physicists not thus in the Special Relativity where are apparent effects by being referred to a specific chosen framework in rest that equivalent can be animated every framework of rectilinear uniform movement.

In the General Relativity due to the necessary accelerations-decelerations to pass a body of a system of reference to another the changes of time and length are physicists just as occurs with the paradox of the twins, although, only has been presented occurring in the time. But the effect of shortening real of the length should also be produced.

The equations of the Relativity of length, time, and mass for a body that is accelerated to the speed of light predict the collapse of the body in some moment when body reaches the speed c. In this moment the body will must to collapse in a plan of infinite density.

If it thinks about the physical transformation that owes the body to suffer when it grows continuously its mass and simultaneously to be contracted its length it so happens that the body should reach a density in “cold” sufficient so that the collapse be produced predicted by Chandrasekhar and Davidovich Landau once surpass the limits of density that they calculated. The addition of mass of the body should occur in the elementary form of particles that is to say, does not organize in a nuclear structure. It excludes that the body can suffer a nuclear combustion. By that reason, the body will remain "cold". The body will maintain its structure while the principle of exclusion of Pauli surpasses the gravitation effect (7). Nevertheless, to continue growing its mass and being reduced its length should be produced its gravitation collapse before that occur the predicted by the Relativity.

The shortening of the length has also to be given in the other two spatial dimensions of the body due to effect of gravitation that generates the additional mass. The body should acquire a spherical form caused by the phenomenon of the gravitation which possesses a center. The collapse of the body will be in a four dimensional point and not in a plan. The body collapsed constitutes a singularity where to stop being valid the laws of the physical acquaintance. Einstein when exposed its conception about the deformation spacetime, of the body accelerated to the speed of light, did not keep in mind the forecasts of Chandrasekhar and Davidovich Landau that, although, formulated for stars, I consider necessarily should be applied to a body in that relativistic condition. I think that the effect of gravitation by the growth of the mass of the body accelerated cannot be ignored (8). Chandrasekhar obtained the Novel by this forecast. Although, He advances this limit in the terms of one minimum mass, equivalent to one and half time the mass of the Sun, also he relates this limit with a volume of radio of a few thousands of kilometres that permits to express this limit in the notion of density as I said (That is, the Schwarzschild radius).

With relation to if is possible or not to be able to carry a body so closed c, for that its mass reaches similar value, is not prominent since is a matter of the forecast of what will occur in an experiment thought.

It is had present that the present physics this based on the experiments thought.

In my opinion the effects that are produced when it accelerates a body to the speed of light are those of change of material form. To high energy levels, in the unified general theory, TGU, is established that the quanta of the weak nuclear field, that is to say, the bosones W+, W- and Z0 possess the same behavior that the photon, quanta of the electromagnetic field. Also, it foresees the same thing with the strong nuclear field. This fact, verified recently, I predicted it in 1970 when present the convertibility among the different types of field, according to M. Vasiliev and K. Staniukovich. Though, then I conceive it like change of state more than of material form.

The difference among one and another is that in the change of state the granular component is conserved structurally, for example, when is passed from the solid state to liquid the molecule is conserved, while, that in the material change of form there is change in the structure composition of this. Thus, in the step of the substance to electromagnetic field is passed from the particle (molecule) to photon (corpuscle). The particle possesses intrinsic mass while the corpuscle only mass in movement. Though, both have granular composition.

A change of transition among state and material form is the change occurred in the substantial molecular form when passes to form of plasma, in which the atomic structure is lost remaining one “soup" of particles components of the atom. A material change of form occurs in the conversion of the nuclear particles and electrons in photons or other corpuscles.

In the nuclear phenomena of fission-fusion by excellence conversions occurs among mass-energy.

Einstein in its intent of unification of the physics in around to field conceives the gravitation as an energy phenomenon, contradicting its orthodox geometric theory and, indirectly, as material form. Einstein says: "we have two realities: matter and field (substance and field). There is not doubt that currently cannot be conceived all the physics built on the concept of matter as the physicists believed in the last century principles. By the moment we have to accept both concepts. But we can think that the matter and the field are completely different realities? In a way simplistic, it given a small particle of matter we would be able, to form us the image of the same one, supposing it exists a surface well defined where the particle ceases of existing and where their gravitational field appears.

In this image, the region in which are valid the laws of the field is separated abruptly of the region in which been present the matter. But, the field represents energy and the matter represents mass and since the theory of the Relativity knows that the mass possesses energy and this mass.

The matter (9) is, with a great deal, the major deposit of energy; but the field that wraps the particle represents also energy, although in an incomparably smaller quantity". Besides, Einstein formulates, in last instance that the speed of light depend of the gravitation. Indeed, the speed of light can surpass c, in the empty spacetime, if a negative(10) gravity field acts on the light. This, indirectly, is attributing to that energy form of the gravitation a greater speed that speed of light. Even the equations of Einstein permit the possibility of the existence of a type of corpuscle named tachyon (physically packet of negative energy), whose mass in rest would be imaginary mass (space-like 4 momentum, proper imaginary time), with always greater speeds that speed of light. The tachyon predicted mathematically, with posterity to the death of Einstein, to ends of the sixty when, coincidentally, I exposed my theory on the existence in the greater nature of speeds to the light based on my philosophical reflection about the physical connection among the substance and the field.

The find, in the equations of Einstein, of the possibility of tachyons, carried out at that time, did mathematically viable the formulation of my theory and, although, coinciding in the time, went to backs so much of its discoverers as mine.

The tachyon is adjusted perfectly to graviton and to all quanta of the different fields exist, since only exist in movement and to one unique and constant speed. But, the tachyon exists disconnected of the physics of the particles and of the corpuscles without traffic can exist among them. Of such way in the theory of the tachyon the superluminal speed cannot be reached since subluminal or luminal speed. In the meantime in my theory if.

In my theory when one for of the field is the result of a subsequent disintegration of the substance more there of the generating of the electromagnetic field, that is to say, when the field is a form of existence of the energy subsequent to electromagnetic field then  its speed is greater than speed of the light.

Einstein, extraordinary genius, inexplicably did not give the following step in the structural formulation of the gravitation that it would have permitted him to develop a quantum theory of the gravity field. That is to say, Einstein would have discovered the double character wave-quanta of the gravitation. Einstein repeated the error of the physicists that formulated the theory about the electromagnetism as phenomenon of the space that surrounded to the electric loads. They understand it like energy phenomenon, although without coming to discover it as material structure, question that if resolved Einstein. This discovers conducting Einstein to photoelectric effect, with that he gained the Novel prize. Also, it conduced Einstein to rediscovery of the mutual conversion among mass and energy.

Becquerel and subsequently the husbands Curie when discovered the radioactivity indirectly they established the conversion among mass and energy.

In the modern theory of the quantum gravitation it is expected that in the distances of Planck, that is to say, 1.61 * 10 -33 centimeters of length, speeds appear over speed of light, it become blurry the real distinction among past and future. Additionally, it is now almost accepted that virtual particles traveling above c, thanks to the experiments of the Dr. Nimtz on the evanescent waves (1992) and of the Dr. Walker in the near field of the electromagnetic wave (1999) and the reflections of the author (1969) and Dr. Tom Van Flander (1998) on the speed of the graviton. FAQ while until the 1990s denied such possibility, from the 2000s accept it. Currently about virtual particles of the photon and graviton it says they can not carry information since not passing the lapse of incertidummbre, but the author replies that in the electromagnetic and gravitational static fields is well established that the scope tends to infinity. Then, through, an chain the virtual photons and virtual gravitons go in the direction of the infinite (the chain can not be anything other than a chain links creation- annihilation of virtual particles, occurring in a vacuum, through which they pass the lapse of uncertainty. This chain according to Dr. Tom Van Flander is a wave, or Dr. Nimtz is the evanescent wave or Dr. Walker is the preformation of the wave in the near field). Therefore, the energy of the potential energy of static fields was transported and represents information.

Einstein in the conceptual development of the gravitation "skates" among conceiving it like geometric or material phenomenon, the correlation among spacetime and matter is ambiguous with relation to their conception of gravitation that, defined in some phrases, appears like a determinant phenomenon of the spacetime, that is to say, as material.

(4) Very near the absolute zero of Kelvin exists the state condensed of Bose-Einstein. In this state not molecular structure exists but the formation of a big super atom, with all the nuclei and electrons of the atoms that usually appear in the molecular structures of the bodies.

(5) Packages of energy.

(6) Einstein in the concept of matter only includes the substantial phenomenon, that is to say, the material phenomenon of electronic and nuclear composition. Therefore, for Einstein exists in the nature two phenomenon, matter, and energy. The energy is the phenomenon undulatory composed by photons, in the electromagnetic field.  

(7) In the orthodox contemplation the body closed c not collapse because the growth of mass is in kinetic energy form and not exist particles, therefore, not is submit to Pauli exclusion but if to Bose-Einstein statistic that permit infinite energy superposition. However, there is one threshold up where not is possible with additional energy continuing augment kinetic energy being as bodies would overpasses c. Author believes that more there of this threshold the addition of energy must to unchain process of generation of particles.

(8) Universe Today published the following article: Does Gravity Increase With Speed? Question - (Apr 13, 2004) My question about Relativity is fairly straightforward. I know about time dialation, length contraction, and mass increase as you approach the speed of light. My question is: since your mass increases as you approach the speed of light, would that also translate into a gravatational increase as well? Because if it would, wouldn't it be possible to theoretically travel fast enough that your mass would increase to the point where the spaceship would collapse into a black hole? - AstroWannabe Answer by Dr. Paul Francis - In principle, the answer is yes, but it depends crucially on exactly how you accelerated the spacecraft to such a ridiculous speed. Consider a 100 metre sized spacecraft, for example. To collapse into a black hole, it would need a mass 35 times larger than Jupiter. How much energy would you need to apply to the spacecraft to accelerate it enough to acquire this mass? This is easily computed using E=mc2 - ie. multiply the mass (in kilograms) by the speed of light (in metres per second) squared. The answer is 6 times 10 to the power 45 Joules, which is roughly the combined energy output of all the hundred billion stars in the Milky Way since the Big Bang. So - if you could focus all this energy in some way on one little spacecraft, you could accelerate it up to fast enough to become a black hole. But if you focussed all this energy on anything small, it would probably become a black hole, whether or not it were moving! If, for example, you zapped a stationary peanut with this sort of energy, it would collapse to form a black hole! Dr. Paul Francis received his PhD in astrophysics at the University of Cambridge, and worked at Steward Observatory, with NASA and at the University of Melbourne before getting tenure at Mt Stromlo Observatory (part of the Australian National University).

I immediately wrote to Dr Paul Francis and other scientists about of this thesis and her relation with my theory about speeds greater than c. This letter is: In August of 1995, in Bogota, Colombia, I published my work “Proposal for measure the speed of gravity according with Position Astronomy”. In August of 1996, also in Bogota, Colombia, I published my work “The Gravity”. This work is second version of previous play. In “The Gravity” I formulate the following theory: In the nature exist speeds greater than speed of light in vacuum, one is speed of gravity according with following theses: 1. The best interpretation of the equations of Einstein of the Relativity about time dilation, length contraction, and mass increase when a substantial body accelerates and body successively approach to the speed of light is the interpretation of that body changes of physical form. This interpretation is result of to revise Relativity with the collapse Chandrasekhar y Landau theories and the Pound-Rebka experiments. The substantial body very, very closed to speed of light would collapse to a black hole form. Sure the transformation of one substantial body in black hole using the mechanism of successive acceleration until very, very closed speed of light only it reaches inside of the frame of one thinking experiment. In this form of black hole one substantial body is not controlled by physical rules known. One substantial body has atomic structure like atoms or plasma. In nature the either category body is transmitting force such like virtual photon, virtual graviton, W+, W-, Z0, or gluon. The acceleration of one substantial body is caused by addition of energy in the form of kinetic energy. 2. In general the addition of energy to bodies with atomic structure is the cause of the transformation of physical form or physical state of the matter. Thus the matter in the state condensed of Bose-Einstein is passed to molecular form and molecular form is passed to plasma form. Or in molecular form the state solid is passed liquid and state liquid is passed gaseous. Also, substance to very high energy is passed to energy forms such like the transformation of nuclear mass to real and virtual photons during the nuclear process observed in the Sun of the atomic combustion of hydrogen in helium. 3. The best interpretation of the theory of the quantum era drives to transformations of the forms of energy according with the high energies. These transformations are the cause of the successive unifications such like weak energy and electromagnetic energy is unified in electroweak energy form, reached in laboratory in 1983, and strong energy and electroweak energy is unified in TGU and all energy forms are unified in one only form in the highest energy, in supergravity theory. 4. Each form and state of the substance has one limit speed for his elementary compounds, more there the form or state it transforms in either. The limit speed of one form or state is the limit speed for the signals modulates in elementary compound of that form or state. Thus, for example, the possible highest speed of molecules of the state gaseous is the limit speed of all signals that it can modular in the molecules in the forms molecular and state condensed of Einstein-Bose. The limit speed for substantial bodies is the speed of light in the vacuum, named c. Because the substantial bodies it would transform in black holies if they will reach the speed c. 5. But the speed of light in vacuum is not final limit speed of Universe. Because: A) In the General Relativity theory the speed of light in the vacuum depending of density of energy of vacuum. This speed is c for density of energy of vacuum closed to density 0. This density 0 is one relative value that corresponding to density of density of energy of vacuum observed near to Land. Vacuum with absolute density energy 0 corresponding to one absolute empty space, this space no exists. For vacuum with relative negative density of energy, < 0 , speed of light must over passes c. B) The speed c is over passed for the same electromagnetic waves for one vacuum of negative of energy like is observed with evanescent waves in the experiments realized by Dr Gunter Nimtz. C) The non locality principle observed in the quantum systems proved in Alain Aspect experiment. This principle suggests the existence of signals with speed closed to infinite speed. D) The theory of Big-Bang requires of one speed at moment of explosion closed to infinite speed. Einstein was aware of this requirement but he explains that it does not violates limit speed c because is the speed of expansive explosion of spacetime. Indeed I say “spacetime” does not exist empty. Then what was the speed of material content of spacetime during Big-Bang?. And which was the material content of spacetime at moment Big-Bang?. I respond the speed of material was closed to infinite speed and material was supergravity according with Big-Bang and quantum era theories. 6. Gravity is not substance and gravity equal to electromagnetism lack of four moment mass. Then speed of gravity can to be greater than speed of c. If gravity is not a Cassimere effect of long reach then his speed must to be different to speed of c because is universal the principle of quantitative difference between qualitative different material things and gravity and electromagnetism would be different things. Now according quantum era theory supergravity generates first gravity and after electromagnetism. Indeed the speed of gravity must to be near to speed of supergravity. Thus speed of gravity is greater than speed of electromagnetism. If a body very closed to speed of light it would collapse in a black hole then we have one clues thesis that drives to my formulate theory of existence of speeds greater than c. My theory about of existence of speed greater than c was for first time published in 1969-1970 in the newspaper “El Siglo” in four articles.

(9) In 1968, the author, of this work, read a book about popular version, of M. Vasiliev and K. Staniukovich, of thru quantum gravitation theory, of the group of scientific soviets. He used quantum gravitation theory for to do the criticism of the Relativity of Einstein. Thus, the author originates the theory about existence of superluminal speeds in nature. This theory was published in the paper “El Siglo“ in 1969-1970.

(10) A positive potential gravity reduces the speed of photons opposite to particles. This action of gravity on light violates conservation of the momentum-energy, according Paul Marmet.

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1.2 Quantum Theory of the gravitation

In 1967, Andrei Sakharov formulated the theory that the gravitation would be a purely quantum phenomenon originating from the energy of the vacuum. Einstein had also considered the gravitation as energy, but, without needing its nature.

According mainly to Dr De Witt (1984) the ideas about quantum gravity are:

In the physical Newton flat vacuum is the idle spacetime. In the physical curve einsteniana the vacuum is full of electromagnetic fields free. In the quantum physics the vacuum is been of fields of any class also free, that is to say, far away of its sources.

A free electromagnetic field mathematically is equivalent to an infinite collection of harmonic oscillators. In the vacuum each oscillator is found in fundamental state that is the lowest energy state. The relativist oscillator remains quiet in a definite position.

The quantum oscillator is subject to aleatory fluctuations due to that in the quantum mechanics the electromagnetic field equal than all another field fluctuates, although, all satisfy the principle of relativity, so that an observer cannot determine his speed through the fluctuations of a field. This result implies that the field is zero on the average and that the amplitude of the fluctuations enlarges when diminishes the length of wave.

But in 1976 William Unurh showed that the fluctuations of the field serve to determine the acceleration. A detector of particles, submitted to a constant acceleration, that can be that of the gravitation, and inside a plot encapsulate of the vacuum whose borders went totally waterproof to the electromagnetic radiation, would react set against the fluctuations of the vacuum as if was quiet inside a gas of photons that had a proportional temperature to the acceleration. These photons would be able to be eliminated giving rise to a new vacuum. The first vacuum would be of density of energy null and the second vacuum of negative energy since there would be necessary to add it photons thermal for to causing to rise to zero. A case exists known as effect Casimir in which, in 1948, the negative energy of the vacuum was detected indirectly that is something less than! Nothing!

The vacuum of energy null is the quantum equivalent of the empty and flat spacetime. This vacuum possesses inflexibility that it expresses in the constant G of Newton.

In the curved spacetime the vacuum is of negative or positive energy. These energy variations of the vacuum are due to the variations, of a point to another, that are produced in the curvature. The source of that energy is the own spacetime. Due of inflexibility of the vacuum, the curvature requires energy that is taken of the vacuum. Therefore, the curvature represents energy that can return to vacuum.

The variations of the curvature of the spacetime can arrive at "to excite" the fields of the vacuum until producing aleatory particles, being that maximum production where the curvature is maximum and where changes more quickly. This mechanism, in the big-bang, can that originated all the existing matter in the Universe. Another phenomenon that generates a great flow of particles is the step of a star to black hole, that is to say, when the star suffers the collapse gravitation predicted by Chandrasekhar and Landau.

Due to that the spacetime acts on the particles is deduced that the particles have retroaction on the spacetime what becomes an object it quantum that should satisfy the demand of the phenomenon that the own gravity field be quantified in the sense that acquire a composition formed by corpuscles that is also phenomenon of the own spacetime. The fluctuations of the gravity field produce corpuscles in small quantities when correspond to long waves, compared with the length of Planck.

The corpuscle of the gravity field is the graviton. This interacts in an appreciable way with the matter and induces curvatures on the order of Planck in the spacetime when reaches the energy of Planck. For long lengths of wave the energy that carries the graviton distorts the geometry of fund; for short lengths of wave, distorts even the associated waves with the graviton. In the ordinary quantum theory from fields the spacetime is a fixed background. In the quantum gravitation the background only is not affected for the fluctuations of the field but the same background fluctuates.

The quantum gravitation, since the point of view of its physics, remains confined to the dimensions of Planck that are extremely small. The unit of length of Planck is 1.61 * 10 -33 centimeters that is to say, 1021 smaller times than the diameter of an atomic nucleus. The unit of time of Planck is 5.36 * 10-44 seconds, that is to say, fantastically more small.

A special difficulty represents the comprehension of the gravitation quantified field since to stop being a purely geometric phenomenon passes to be material.

The idea about the graviton, of the first generation of physicists, is that possesses mass and the possibility to be transmuted in particles. The collision of two gravitons can originate two particles, for example, an electron and a positron that at the same time can be can become gravitons, as D. Ivanenko showed in that epoch.

In a field the mass of the corpuscle is proportional to number of oscillations by second of the waves. The physical M. Vasiliev and K. Staniukovich estimated the mass of the graviton, toward ends of the decade of the sixty, in 0.5 * 10 -65 grams, extraordinarily small magnitude as corresponds to every magnitude in the scale of Planck.

Due that the gravity field possess mass should have weight and to occupy a place in the spacetime another of the incomprehensible questions if, on the one hand, is the cause that the mass has weight and, on the other side, constitute the own spacetime.

The serious problems that present the quantum theory of the gravitation are a consequence of the theory of the Relativity, of which inevitably is removed, to be combined with the quantum theory introduced in 1925 by Werner Heisenberg and Erwin Schrondiger. The solutions presented to those problems without experimental guide are supported in the imagination.

But the forecasts that result of the meeting of the Relativity and the Quantum Mechanics have been confirmed repeatedly in the last 50 years. And, though, the quantum mechanics still has not been incorporated adequately to the gravitation the quantum theory is the base of almost all the science and modern technology.

Another completely new consequence of the meeting of the Relativity and the Quantum Mechanics is that each particle, existing in the substance, remains associated with a type of field and each field associated with a class of indistinguishable particles. The weak and strong nuclear fields, and electromagnetic and gravity fields are not the only fields of the nature, can to exist many other more.

Hawking when he refers to the modern version of the theory of the quantum gravitation exposes a theory about the elementary particles and the existing forces in the nature that changes the conception on the graviton of the first epoch, returning it imponderable.

Such theory has like base some discoveries carried out to ends of the decade of the sixty that to their authors deserved the Nobel prizes in 1969 and 1980. One of those discoveries established experimentally, is that the neutron and the proton are not elementary particles since they are composed by other smaller particles named quarks.

Another great discovery is that the particles, in the substance, and the corpuscles, in the field, possess a property named spin. This property refers to the conservation or not of the form of the particle or corpuscle with relation to the different directions of the space that occupies. The states of the spin are:

- 0 when corpuscle is like a point that the same thing seems since all the directions.

- 1 when the corpuscle is like an arrow that different corpuscles seem from different directions. Only, if the corpuscle rotes 360 degrees, corpuscle seems the same.

- 2 when the corpuscle is like an arrow with two heads that from different directions different corpuscles seems. Only, if the corpuscle rotes 180 degrees, corpuscle seems the same.

- Higher values for corpuscles that require successively rotating a smaller fraction for corpuscle seems the same.

- ½ when the particle by means of a double rotation particle seems the same.

All known corpuscles and particles in the Universe belong to the two following groups:

- The particles of spin ½ which are constituents of the substance.

- The corpuscles of spin among 0-2 that are the generators of the forces among the particles.

The spins greater to 2 can correspond to corpuscles not yet discovered.

The particles hold principle of exclusion discovered by Wolfgang Pauli, in 1925, consistent in which two similar particles cannot exist in the same quantum state, that is to say, to have equal speed and to occupy the same position, inside the limits set by the principle of uncertainty. In contrary case the particles would collapse to high density due to the forces exercised by the corpuscles.

The corpuscles are not submitted to principle of exclusion for which can generate very intense forces. The mechanism of those forces is that the particles exchange corpuscles, emitting them some and absorbing them other. All the particles that interact, of that way, suffer changes of speed, varying their rapidity and/or the direction of their movement, as if forces acted among them.

The corpuscles that intervene in the forces are the virtual corpuscles due to that them cannot be discovered through detectors as if occurs with the particles or real photons that if are detected. Nevertheless the effects of the corpuscles virtual can measure. The graviton real although not yet discovered, says Hawking, is call gravitation wave by physicists of the first post-einstenian generation.

The explanation of the existing forces in the nature according to the quantum theory is as continues:

- The strong nuclear force occurs in the atom and is caused for the exchange of virtual gluones of spin 1, that maintain to quarks united in the proton and in the neutron and to protons and neutrons united in the nucleus of the atom.

- The weak nuclear force also occurs in the atom and is produced by the exchange of virtual bosones of spin 1 that act on all the nuclear particles and are which originate the radioactivity.

- The electromagnetic force acts on the electrically charge particles as the electrons and the quarks and is proper exchange of virtual photons among those particles. In the atom does that the electrons orbit around of the nucleus.

- The gravity force is attributed to exchange of virtual gravitons of spin 2 among the particles and corpuscles that form the nature. This force is the only universal force since affects all the particles and still other real corpuscles. In the solar system is the cause that the planets orbit around Sun.

The gravity and electric forces are forces that work to large distances while the weak and strong forces are of short reach. The main reason is that the corpuscles of weak an strong forces possess a great mass in comparison to graviton and photon masses.

Two bodies approach because the emission of gravitons in all the directions produces that among them a high field of depression arise which does that they precipitate one on the other.

The depression among the two bodies occurs in the spacetime that the surrounds them. This depression curves the spacetime according relativistic forecast.

The gravitation interaction would be annulled if for some unknown circumstance the emission of gravitons cease. The emission of gravitons occurs as has said in form aleatory and variable for which the interaction this submit continuously changes that in the effect of gravitation are not instantaneous but communicated according to the speed of gravity.

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1.3 Speeds greater that speed of light

In the years of 1969 and 1970, in a series of four articles, published in the Sunday Weekly, of the newspaper "El Siglo", of Bogota, I exposed my theory about the existence of speeds greater than speed of light, one of which would be speed of gravity, basing on:

- The quantum theory of the gravitation that in that epoch the physical Andrei Saharov recently had proposed. This theory, in its contemporary version, is the especially accepted.

- In my interpretation of the phenomenon of the constancy of the speed of light with respect to system of reference where the same speed be measured, which I conceive like the general situation of the speeds limits, that correspond about change in the diverse forms and states of existence of the matter.

In such limit points one maximum speed exists for the communication of signs inside of the state o form. This limit speed is own to each material state or form. These speeds play equal role, in each state and forms to speed of light in our Universe. Similarly for the settings building with various states or forms also exits one limit speed for the communication of signs inside of the setting that is equal to limit speed of the state or form whose structural elemental particle o corpuscle the merest and energetic one(11) according all quanta of the setting.

- In the law, that I advance, on the greater speeds that correspond to the material states and forms when are less inertial. This is the case of the gravitation, whose corpuscle, the graviton, must to have fantastically lower magnitude inertial in front of photon, corpuscle, of the electromagnetic field inside which the phenomenon of light is given.

As opposed to Einstein in my theory any field, even the gravitation, is a material phenomenon, that is to say, that possesses mass and exists in the spacetime. The matter, in physics, is really the substance that equal to field has a structure granular-wave, although, is declared mainly as composed phenomenon of particles. Einstein knew about the behavior undulatory of the electron that named waves of the matter and, nowadays, the physicist no ignores that even the stars, with his enormous masses, possess an associated wave.

The difference among the substance and the field is that the first it structures from the particle and the second from the wave. In the substance the wave is a disruption caused by the particle in the middle, while, the corpuscle in the field is an excitement of the wave.

All the forms and states of the field and substance are executions in the time, differentiated qualitatively, of the possibilities of existence of one original material structure according to different levels of temperature. All forms and states of field and substance are mutually possible of transformation and are submit to same laws that are the most general physical laws of the matter.

One of those laws, to which I referred in 1969, is la united of the various forms, and states of the substance and multiplicity of forms of the field that result of the sweeping that occurred in the time, of the different possible organizations of one original material structure. The states of the substance result of the different energy levels in which organizations of the molecules can exist stables, while that the different forms of the substance are result of different level of temperature in which organizations of nucleus and electrons can exist stables.

In the field my forecast about material united coincidentally was developed from the discovery of the quarks continued by the theory of Abdus Salam and Steven Weinberg, proposed in 1967, about united of the weak nuclear field and the electromagnetic force, confirmed experimentally in 1983 by the Central European for the Nuclear Investigation, CERN.

To high energies the bosons and the photon behave in a similar way. The bosones, W+, W-, and W0, are the particles transmitters of the weak nuclear force. It is foreseen that equal occurs with the strong nuclear field.

The resultant idea that is known as the base of the general theory of unification, TGU, is that to high energies is produced the decay of the strong nuclear interaction and the intensification of the weak nuclear interactions and the electromagnetism. To very high energies, call of the great one unification, these three types of interactions should have a same intensity and only to be different aspects from an only interaction. The TGU predicts, also, that to this energy the different particles of spin ½, as the quarks and the electrons, are essentially equal, reaching new unification.

In February of 1970, when still I did not know the theory of Salam and Weinberg, in the last article on " Speeds greater that speed of light", I exposed the central idea of the discovery that the CERN carried out in 1983. In 1979 Salam and Weinberg in company of Sheldon Glashow, simultaneous authors of said theory, gained the Novel. In 1983 Carlos Rubbia and Simon Van der Meer, that went experimental discoverers, also gained the Novel. This idea is:

"The existence of the matter covers the form with a greater complication of the vinculums, of the forms of movement and of the structure of the material objects. But does not it cover all the process of the existence, but alone is a part.

The processes of complication are compulsorily substituted for other of disintegration, disorder. This material movement in two regular senses in each moment of its development by the degree of development in which is found the two tendencies that govern the matter in movement: tendency of transformation of the mass in energy and tendency of transformation of the energy in mass. When it dominates the first tendency on the opposite tendency the matter occurs in processes of disintegration: The molecules break down in atoms, the atoms in elementary particles, the mesons in photons, the photons in gravitons, the gravitons in..."

Another great law of the physics that advanced in 1969 is law of the greater speed that corresponds to a form or state when is more energetic and less inertial than another. The inertia is the property of the particle and of the corpuscle to be opposed to suffer changes in its movement, that is to say, to suffer accelerations and is directly proportional to the quantity of mass of the particle or the corpuscle in a specific state or form. In the solid state, closed to temperature absolute zero, the speed of molecules is zero. In the gaseous state the molecules move to a speed of near ,5 kilometers by second. It plasma the elementary particles move to speeds that surpass the 24 thousand kilometers by second. The photon that does not exist in rest moves in the vacuum to a speed close to the 300 thousand kilometers by second. The graviton that exists in the scale of Plank should move to an immensely large speed.

The proposal of speeds greater that speed of light I formulated it conserving the effect discovered by Michelson-Morley, that is to say, of the constancy of the speed of light in front of any system inertial of reference in rest or animated of movement that, in the scale of our measurements, also should be produced in front of the super speeds. Superluminal speed is possible mathematically according to the formulae of the Relativity as scientist shown for the tachyon in the decade of the sixty.

The equations of Einstein about the mass, length, and time maintain its validity for to express the speed of light as the limit in that the material change of substantial forms will be produced to singularity form.

The main objection contra possibility of speeds greater than speed of light originates in the breaking law of the causality. Nevertheless, in the different forms and states of the nature exist limit speeds for the broadcast of signs, inside the corresponding form or state, without that they constitute limits in the sense of the speed of light according Special Relativity.

If we consider a physics of the liquid state it can describes presenting the phenomenon of the contraction of the time and the enlargement of the length when this state is excited with energy and approach its conversion to state gaseous. In that physics the speeds in different systems of reference will not be able to be transformed according to the sum of vectors of Newton and a conversion of the type of Lorentz should be used. But, contrary conversion of speeds according speed of electromagnetic field, the time is shorting, and the length is dilating. The molecules moving with a greater speed generate a "time" that elapses more quickly in comparison to when molecules possessed less energy and they had a smaller speed. The molecules moving a greater distance nevertheless inside of the respective topologic pattern of the liquid state cause a widened space.

In general when a state or form gain or lose energy modifies the continuous proper spacetime that will be of topology curve for every state or form that co exists in various levels of energy among the minimum and the maximum possible measures. But meters and clocks will conserve its capacities of measurement in the usual units since all in that "universes" is subject to the same deformation.

In the liquid state when the molecules reach the speed of gaseous state ceases the liquid state. Therefore, in that physic, the speed of near ,5 kilometers by second is an impossible speed of to surpass. These facts occur in any physics referred to a material form or state. For the states of the substance, when the process is progressive in energy, the time and length effects occur in reverse with respect process to carry bodies to the speed of light. But this is similar when the process is regressive, that is to say, for example, if is passed from the gaseous state to liquid state.

It does little time I have thought about the weak nuclear forces and strong, the electromagnetic and gravity force and its effects some attractive times and repulsive others based on:

- The model of the photon real that to be generated by the atom causes the step of the electron, that the photon causes, of a orbit over a lower one and when a photon interacts with an electron causes the complementary step, that is to say, of that electron of a lower orbit to another superior. In both cases, an effect of force is produced, in the first attractive effect and in the second repulsive effect.

- The property of the spin that understand like developer that the particles with spin ½ and the corpuscles with spin 1 and 2 do not possess a spherical or almost-spherical form that is the acquaintance more frequently for the structures of the atom and the molecular, as well as that of the stars and the planets, in the macrocosm, that are own forms of the inanimate nature.

The effect of force in its repulsive and attractive modalities I believe is a consequence so much of the energy, mass, speed etc. as of the as form and size of the particles and corpuscles than interact. Two electrons or protons when it interacts it repulses due also to their size and form, an electron, and a proton are attracted for the same reason. That is to say, two particles self attract when their forms and size of some manner are complementary and they self repulse when not.

(11) According size of particle and level of temperature, the ascendant order of the forms of the substance is: condensed state de Einstein-Bose, molecules and plasma. Similarly the ascendant order of the states of the molecules is: solid, liquid, and gaseous.

According size of quanta and level of energy ascendant order of the forms of the field is: Gravitation, electromagnetism, weak, and strong. Similarly according lowest size of corpuscle and lowest level of energy of the wave the ascendant order of the states of the electromagnetism is: evanescent waves, long waves, microwaves, light waves, ultraviolet waves, rays x, and rays gamma. Evanescent waves have a speed superluminal, light waves have speed c. Author do not know experiments of measure of speed of either electromagnetic waves. However those experiments maybe have realized. But, according Maxwell, also, is c.

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1.4 Experiments proposed

Among 1991-1993 I have proposed the execution of experiments lead to establishment of the speed of propagation of the gravitation. First since the perspective of the Astrophysics that studies the physical constitution and evolution of the heavenly objects. And, with posterity, of the Astronomical Geography, that describes some phenomena that occur in the Land and that are related to the stars, referring me to the most typical as are the eclipses and the tides.

The base of the experiments proposed is the horary difference, that should exist, among the occurrence of the heavenly phenomenon in which a change in the gravitation is produced and its planetary effects, especially, on the Land, under the supposed that the gravitation is of dynamic nature and it spreads to a finite speed.

The conception about the gravitation adopted is the quantum gravity theory and its speed analyzed inside the context of the gravitation interaction among stars.

The cosmic phenomena, in which changes in the gravitation are produced, that in the past I have studied, are the following:

- Decrease of the mass of the Sun, in near four million tons by second, and its effect of diminish the magnitude of gravity force, as consequence of the loss of solar mass accumulated during the lapse in which this phenomenon communicates to the planets. The decrease of the force of gravitation of the Sun must cause secularly the decrease of the speed of translation of the planets and the angular displacement of its orbits.

In the theory of the General Relativity is necessary to notify that the spacetime deformation pre exists of such way that the demonstration of the speed of gravity is given in the slow undulations that suffers said curvature and not in the interaction among the bodies subjects to phenomenon of gravitation.

The study of the previous phenomenon can carry out through radio astronomy, especially when is more intense which happens in cyclic periods, approximately of some 11 years. The disintegration can assumed of discrete magnitude, taking like unit the effect expected in the lapse that spends the light in travelling through the 69.82 million kilometers among the Sun and the position of perihelion of Mercury. In this lapse an angular displacement should be produced of the orbit of Mercury close to 3.19 millionth of second arc if the speed of gravity is equal to speed of light.

- Step of the Sun and the Moon of quadrature to sicigias. In quadrature the gravity forces of the Sun and the Moon operate in straight angles among themselves and their resultant is minimum force on the Land. In sicigias, moments of conjunction and opposition, such forces operate on the same straight line and the resultant is maximum force on the Land. The effect of quadrature or sicigia causes changes in the marc of the time, measured with clocks of pendulum. These changes should be produced with a difference with relation instant in which the quadrature or sicigia occurs, equal to lapse that the phenomenon spends in being communicated to respective clock of pendulum.

- Variation of the effect semi annual solar on the terrestrial tides, that is consequence of the orbit elliptic of the Land around the Sun, which is represented like the long harmonic of period L2, and whose extreme values occur in the perihelion, 31 of December, maximum value, and in the aphelion, 1 of July, minimum value. The retard among the instants in which occurs the perihelion or the aphelion and their effect on the terrestrial tide is equal to interim that spends the change of gravitation in being communicated to the tide.

The great difficulty that exists for the execution of the experiments proposed is that the effects correspond to infinitesimal variations that require of extraordinary procedures and instruments of measurement.

Nevertheless, the effects of the eclipses in the pendulum and of the short harmonics of period, especially, the lunar semi diurnal M2, in the terrestrial tides has been studied experimentally by the physicists, although, they have not done in order to measuring the speed of gravity.

The scientists investigated in various eclipses the attraction of the Land by the Sun. In one of them the French M. Alle observed the variation of the behavior of the movement of the pendulum of clock. But, under observation repeated carried out in 1961, during an eclipse in the Soviet Union, that threw, in some, increase of the force of gravitation and, in, other, its decrease was not possible to conclude to favor or against the theory of Alle, since the effects could be explained for other indirect causes of the eclipse.

The terrestrial tides, differently of the oceanic tides, can be explained more adequate with the astronomical theory of the tides, call theory of the equilibrium.

The terrestrial tides have been investigated in the United States, Japan, Russia, and Germany. In this last country, in Hesse, in the mine Reichenberg the experiment that was there carried out reveal eight of the partial tides in short period of astronomical origin; the relations of amplitude and phase agree with the theoretical predictions. In another experiment carried out in Marburgo was measured the changes in magnitude and direction of the lunar tide semidiurnal M2. Such changes should correspond to changes occurred in the force of gravitation that the cause.

The proposals that have formulated about the execution of experiments for to measure the speed of gravity I have presented them to Colombian and international agencies, among which are found COLCIENCIAS and the International Center of Physics. Some of this agencies have answered, such is case of the doctor Joost Kircz of ELSEVIER, Science Publishers B.V., Amsterdam, who in October of 1992, considered the valuable project and encouraged me to persist, as in effect I have done.

Currently I have abandoned the approach of the Astrophysics and the Astronomical Geography as base of the experiments for to measure the speed of gravity by the technical difficulties already mentioned and I have take the focusing of the Astronomy of Position.

The finds of the investigation that have carried out are surprising and I can notify that without proposing them, neither to know it the astronomers, of the previous discipline, have met some necessary elements for to measure the speed of gravity that can be taken advantage of establishing it. The bases in which is based me theory and the new proposal of measurement of the speed of gravity are presented in this work.

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1.5 Conclusions

- For the General Relativity the gravitation is a field that results of the deformation curved of the spacetime introduced by the matter in the Universe.

- Gravitation according General Relativity pre exists own gravity effect. But gravitation is submitted to variation by the changes, during immense lapse, that occur in the matter to great scale. In the solar system the gravitation configures almost-static elliptic runners by where the planets orbit freely in around Sun. The rotation in rosette of the orbit of Mercury that is in the solar system the orbit that more quickly changes delays three million years.

- According to Einstein, the variations of the gravity field is a phenomenon purely undulatory lacking of the aspect corpuscular characteristic of the other fields, totally foretell it and spreads with a speed equal than speed of light.

- The General Relativity of the two change types that occur in the material bodies only considers the change of position for the formation of the concept of spacetime. Einstein considers the spacetime built from stiff bodies, that is to say, without alteration of state or form that is the other change type that occurs in the nature. Einstein excludes of the movement the diverse material forms and states that are the base of the physical existence.

- In my theory maintains that each material state or form possesses an existing topology in a continuous proper spacetime with an impossible speed to infringe. The speed in the states of the substance varies among a minimum value and another maximum. The speed in the forms of the field is unique for a same medium, although I consider the possibility that be also of lapse but infinitesimal.

- In the theory of the General Relativity the bodies carried much closed speed of light physically suffer the enlargement of the time, the contraction of their length and the increase of their mass. Phenomenon I observe similar change of state o form that can also be given in the inverse sense in which the time contracts and the length dilates.

- Since the perspective of the equations of the Relativity of length, time and mass in some moment the body collapses in the proximity to reach the speed of light in an plan of infinite density. But according to it predicted by the theory of the singularity of Chandrasekhar and Davidovich Landau that was not considered by Einstein, the collapse that will occur will be in a four dimensional point.

- In my opinion the effects that are produced when it accelerate a body to the speed of light are the effects of change of material form. Which it implies that the speed of light do not be the last possible speed in the Universe as in general is not the speed of none of the material forms of existence. Save if the matter has one last form with one maximum speed. The group of soviet scientist believed that are infinites the material forms. I believe that speeds exist greater than speed of light when the field corresponding is the result of one combustion of the substance subsequent to which generates the electromagnetic field, case that occurs with the gravity field.

- Einstein did not discover the structure quanta-wave of the gravitation. This could him permitted to develop a quantum theory of the gravity field and to recognize it as a way of material existence instead of conceiving it like phenomenon of the spacetime.

- The quantum theory of the gravitation, based in Saharov, considers that is a phenomenon of the energy of the vacuum that is full free fields, that is to say, fields far away of its sources. The vacuum of energy null is the quantum equivalent of the vacuum and flat spacetime. In the curved spacetime the vacuum is of negative or positive energy. In average the vacuum has energy zero.

- The energy variations of the vacuum are due to the variations that are produced in the curvature of the spacetime. The inflexibility curved requires energy that is taken of the vacuum. Therefore the curvature represents energy that can return to vacuum.

- The variations of the curvature of the spacetime can arrive at "to excite" the fields of the vacuum until producing aleatory particles named gravitons.

- Due to that the spacetime acts on the particles is deduced that the particles have retroaction on the spacetime for which should satisfy the demand that the own gravity field be quantified in the sense that acquire a composition formed by corpuscles that is also phenomenon of the own spacetime.

- The quantum gravitation, from the point of view of its physics, remains confined to the dimensions of Planck that are extremely small. Its unit of length is 1.61 * 10-33 centimeters, that is to say, 10 21 smaller times than the diameter of an atomic nucleus. The unit of time of Planck is 5.36 * 10-44 seconds, that is to say, fantastically more small.

- The graviton interacts in an appreciable way with the matter and induces curvatures on the order of Planck in the spacetime when reaches the energy of Planck.

- The gravitation force, according group soviet scientist, is attributed to exchange of gravitons among the bodies that form the nature. This force is universal. In the solar system is the cause that the planets orbit in around Sun. If that exchange hypothetically came to cease the gravitation would be annulled. The exchange of gravitons varies in a permanent way causing that the gravitation force, that is to say, the interaction change of intensity continuously inverse with square of the distance according the relative position of the Sun and planets. These changes are not instantly but according to the speed of gravity.

- In the quantum gravitation the orbital paths are dynamic paths. Permanently the paths are redone.

- Two bodies approach because the emission of gravitons in all the directions produces that among the bodies a high field of depression arise which does that bodies precipitate one on the other. The depression among the two bodies occurs in the spacetime around them. This local spacetime is curved according to the relativistic forecast.

- Another completely new consequence of the quantum theory is that each particle, existing in the substance, remains associated with a type of field and each field associates with a class of particles indistinguishable. The electromagnetic, nuclear fields and gravitation are not the unique of the nature, exist many other more. According group soviet scientist exist infinite fields.

- The phenomenon of the constancy of the speed of light with respect to system of reference where the same speed be measured I believe that can be the general situation of the limit speeds, according points of change in the diverse forms and states of existence of the matter. In such points exist maximum speeds for the communication of signs, pertaining to the speeds that are own to each material state or form.

- I believe that is a law of the nature the law that the material states and forms when are less inertials and more energetics, they have greater speeds. In the solid state, to a near temperature to absolute zero, the speed of molecules is zero. In the liquid state the molecules vibrate. In the gaseous state the molecules move to a speed of near ,5 kilometers by second. In the plasma the elementary particles move to speeds that surpass the 24 thousand kilometers by second. The photon that does not exist in rest moves in the vacuum to a speed close to the 300 thousand kilometers by second. The graviton, that exists in the scale of Plank, can be that move to an immensely large speed.

- The proposal that I do of speeds greater than speed of light conserves the effect of Michelson-Morley that, in the scale of our measurements, should be produced in front of the super speeds.

- The main objection contra the possibility of speeds greater than speed of light originates of the supposed law break of the causality. Nevertheless, in the different states and forms of the nature speeds are given that are limits for the broadcast of signs, inside a specific state or form, without these speeds constitute limits in the sense of the advanced of the Relativity with relation to the speed of light.

- In a physics of the liquid state the phenomenon of the contraction of the time occurs and also the enlargement of the length when the state is excited adds energy closed at the moment approach its conversion to state gaseous. In that physics the speeds in different systems of reference will not be able to be transformed according to the sum of vectors of Newton and a conversion of the type of Lorentz should be used. Besides, the speed of .5 kilometers by second will be impossible to infringe. These facts occur in any physics when is referred to a determined material state or form.

- I have proposed to measure the speed of gravity based on the horary difference, that should exist, among the occurrence of a heavenly phenomenon in which a change in the gravitation is produced and its planetary effects, especially, on the Land.

- A first phenomenon is that of the decrease of the mass of the Sun, in near four million tons by second that causes secularly the decrease of the speed of translation of the planets and the angular displacement of its orbits.

- A second phenomenon is the step of the Sun and the Moon of quadrature to sicigias. In quadrature the gravitation forces of the Sun and the Moon operate in straight angles among themselves and their resultant force is minimum on the Land. In sicigias, moments of conjunction and opposition, such forces operate on the same straight line and the resultant is maximum force on the Land. The effect of quadrature or sicigia causes changes in the marc of the time, measured with clocks of pendulum.

- A third phenomenon is the variation of the semi annual solar effect on the terrestrial tides, that is consequence of the orbit elliptic of the Land around the Sun, which is represented like the long harmonic of period L2, and whose extreme values occur in the perihelion, 31 of December, maximum value, and in the aphelion, 1 of July, minimum value.

- A fourth phenomenon is the constant change of the gravitation action of the Sun on the planets what causes describes them their orbits elliptic. This phenomenon is studied for the astronomy of position and adopted in this study as the base to measure the speed of gravity.

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2 ASTRONOMY OF POSITION

The astronomy of position tries the description and prediction of the positions and movements of the heavenly bodies.

The astronomy of position covers two different aspects narrowly related. These are:

- The mechanical theory of the positions of the stars.

- The astronomical observations that measure such positions and movements with relation to specific systems of reference.

The astronomical observation serves so much of empirical base of the theory that does the physical-mathematics description of such observations as of verification of its predictions.

The mechanical theory, in its splits cinematic, makes use of diverse spatial systems of coordinates referred to a specific scale of time. In its dynamic splits is supported mainly in the heavenly Newton mechanics.

The position of a material body is defined for its spatial relation with relation to a physical system of reference that permits to determine univocally the place that occupies the body inside the space and the time with the geometric configuration of that system of reference. The position is essentially relating to a system of reference in the space and to a scale of time.

By excellence the astronomy of position studies the stars in the solar system.

The solar system is a practically remote physical system in the space, whose dynamic structure depends only of the interior system forces.

The solar system, with exception of the comets whose total mass is very small, is content in a spherical volume of near 6000 million kilometers of radio, approximately 6 ten thousandth of year light, while the most nearby star, the Next Centauri, is found to 4 years and 3 months distance light.

The Solar system behaves mechanically as a punctual system of free masses, submitted by well determined force and free practically of external disruptions. This is due to that the Sun and the planets move as if the total mass of each one of these stars was concentrated on its centers of masses. On the other hand the 99,86 percent of the total mass of the solar system is found concentrated on the Sun; the 0,135 percent in the planets and the 0,00004 percent in the satellites.

The remainder of the bodies that compose the system, that is to say, comets, asteroids, meteorites and medium interplanetary represent a despicable mass that does not have sensitive effects in the movements of the Sun and the planets.

The solar system has been historically the ideal laboratory where has been able to establish the principles and laws of the Newton mechanic. Also to control its accuracy by means of observations very to be exact, since the experiments that are carried out in the Land are always affected by difficult strange forces to determine, such as frictions and external fields of force.

The astronomy of position requires assuming a topology for the solar system inside the several possible. Of the topology chooses the geometric properties of the systems of reference depend that they serve of representation to movement of the stars. Also, of the topology choose the nature of the force that serves for to explain the stars movements. The force, as happens in the geometry of Riemann, can be the simple demonstration of the curvature of that topology.

Although since the theory of the Relativity is considered the topology of the spacetime curve, corresponding to solar system, not way exists to test it experimentally.

For the majority of the calculations of the astronomy of position the Euclidean geometry is used based on plans where the angles of a triangle add 180 degrees. The use of the Newton mechanic this united to geometry euclidea, since by that epoch it did not know another.

But for very exact calculations of the positions of the stars the corrections are used based on the theory of the Relativity that results to apply the named parameterized post-Newton equations.

For practical use to the astronomer turns out to be better to continue using the Newton mechanic due to that by its antiquity a cultural predisposition exists to understanding it more easily than the einstenian mechanic. This attach to the tradition is a ballast that has maintained hidden a great difference among both mechanics. This difference is that while for Newton the gravitation is supposed of instant action to distance for Einstein not exist instant action to distance, then the gravitation must spreads with the speed of light. Similar change with relation to the gravitation itself has not been incorporated in the calculations due to that still for the relativists have remained ignored.

I believe that this is a fundamental key to clarify certain inaccuracy in the calculations of the position of the planets that today is corrected by means of empirical constant and, besides, for to establish experimentally the true speed of gravity.

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2.1 The heavenly mechanics

The description cinematic, that is to say, the description that refers to the purely geometric part of the movement, was established from observations done about the positions of the planets by Tycho Brahe to ends of century XVI, what permitted to Johannes Kepler to formulate, in 1619, the laws of the movement of the planets around the Sun in a Euclidean space and in an absolute time. These laws are the following:

- The orbit of each planet is an ellipse with the Sun in one of its focus.

- The radio vector, that unites the Sun with the planet, sweeps equal areas in equal times.

- The buckets of major semi axis of the orbits planetary are proportional to the squares of the periods of revolution.

The dynamic description, that is to say the description that refers by force that the elliptic path of the planets around the Sun, cause was formulated for Isaac Newton, in 1687, deducing him of the laws of Kepler and of the dynamic laws of the fall of the bodies that at the same time Newton deduced of the mechanical laws of Galileo.

The axioms of the dynamic of Newton are:

- An absolute three-dimensional Euclidean metric space exists.

- The space is homogeneous and, consequently, isotropy in infinite extension.

- An absolute time exists really uniform.

- A remote material body remains in rest or movement rectilinear uniform. This principle is named inertia.

- The resultant force that acts on a material body is equal to product of its mass by the acceleration. This statement is named fundamental law.

- All action exercised by a force on a remote particle corresponds in every single moment a reaction produced by an equal force of contrary sense. This principle is named action-reaction.

- Two material particles are attracted with a proportional force to their masses and inversely proportional to square of the distance that separates them. This is the law of the universal gravitation.

The force among the planets and the Sun is a particular case of the universal law of gravitation. This law is enunciated mathematically thus: The force F exercised among two punctual bodies of masses M and m is proportional to M and m and inversely proportional to square of the distance d that separates them:

F = G M. m / d 2

G is a constant value that has been determined experimentally with great accuracy and its value is:

G = (6,6742 ± 0,0031) . 10-11 m3 kg-1 s-2

The results of all the experiments carried out have established that this constant value is independent of the chemical and physical properties of the bodies that are attracted or of the medium among them. In the quantum theory of the gravitation is considered that this constant express the inflexibility of the spacetime.

Although the law of Newton was formulated for the ideal case of punctual masses, is shown that the bodies of symmetry spherical are attracted as if its total mass was concentrated on its centers of masses. The Sun and the planets to certain degree of approximation possess spherical symmetry.

The laws of Kepler serve for a first approximation in the description of the orbits and movements of the planets.

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2.2 The geometry of the space

In 1832 Bolyal and in 1835 Lobatchevski created a geometry not euclidea, named hyperbolical or pseudo spherical geometry, from denying the fifth postulate, of the Euclidean geometry, relating to that by an exterior point to a straight only can pass an and alone a parallel to the same line. The new postulate establishes that infinite parallels can pass. The properties of the pseudo spherical geometry result in contradiction with the geometric common ideas but, although, different is likewise valid. In the pseudo spherical geometry the sum of the angles of a triangle is smaller than 180 degrees.

In 1854 Riemann makes another not Euclidean geometry named spherical geometry by being base on the sphere for a two-dimensional space. In this geometry the sum of the angles of a triangle is greater than 180 degrees, with a proportional excess to area.

Poincare did the exercise with a geometry in which a straight can be perpendicular itself, although, the notion of perpendicular is defined differently to the Euclidean geometry.

Infinity geometries exist possible of spaces all mathematically valid.

Nevertheless, the scientists have experienced with such spaces in search of which of them corresponds to Universe thinking about that Universe has an unique proper geometric structure.

Gauss tried to determine the metric structure of the space measuring with theodolite the angles of a very large geodesic triangle, formed by the tops of three mountains. He obtained the value of 179 degrees, 59 minutes, 59 seconds, 320 for the sum of the interior angles of the triangle which differs alone in 0 seconds, 680 of the value euclideo of the 180 degrees, lower discrepancy to margin of error of the measures. Therefore, the space resulted, in this measurement, is Euclid.

Equal conclusion results of the measures of the distances and positions in the solar system, as well as of its triangulations performed to determine the distances or geometric parallaxes of the stars. Up to now not any test originating from the observations exists that indicates different angular values to them required by the Euclidean geometry.

In the space that surrounds us to distances on the order of 1023 cm and inside the errors of the measures, the observations indicate a Euclidean geometric structure.

Nevertheless, to discover by means of experiments the geometry that to Universe corresponds is useless Thus Poincare established him at the beginning of this century and to date has not been refuted.

It can be elected for arbitrary convention a geometry Euclid or not Euclid and utilizing it to describe the Universe observable defining a operator method of measure of distances among bodies.

This does not it mean the not existence of evidence with relation to the curvature of the spacetime which is obtained when we launch an object up, where remains during a brief time. Its movement of ascent and descent shows said curvature near the surface of the Land. Although the curvature of the path of the object is appreciated, with every clarity, certain are that it turns out to be very small.

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2.3 Mechanical of Newton and Euclidean space

The formulae of the dynamics of Newton, referred to a Euclidean space, serve to predict theoretically the movement of the stars and the astronomical observations   of position permit to verify empirical the accuracy of the movements foretold by the theoretical calculations.

The dynamics of Newton possesses a high degree of accuracy and turns out to be sufficient for almost all the theoretical studies and practical applications of the astronomy.

The positions and movements the planets predicted by the theory of the dynamic of Newton coincide with all observed to a high degree of precision, inside the errors that are assignments in the observations. The movements of Mercury and the Moon are excepted by that present discrepancies over the errors of observation.

In the case of Mercury is due to deficiencies of the Newton´s theory on the gravitation that are corrected with the theory of the Relativity of Einstein. And, in the case of the Moon is on account of the secular variation of the speed of rotation of the Land.

In 1845, before to the exposition of the theory of the Relativity, but, very subsequently to theory of Newton, the astronomer Le Verier discovered that the perihelion of the elliptic orbit that describes Mercury around the Sun displaces itself for a circle.

This displacement is very small; only 43.2 angular seconds in the course of 100 years. According to the theory of Newton this displacement should not exist. It was supposed that the force of gravitation it diminishes not as r-2, but as r -2,00000016 that contradicted the universal law of gravitation.

Einstein was who formulated that the relativist equations are reduced to the law of gravitation of Newton for weak fields; so that discrepancies with the classical laws appear should be considered very intense gravitational fields.

In our planetary system the attraction among the Sun and Mercury is greater that the existing among the Sun and any another planet, therefore Mercury is the most nearby planet. The General Relativity predicts that the elliptic path of Mercury, that constitutes its Newton path, should rotate slowly with respect to Sun generating a rosette. The ellipse of Mercury performs a revolution or complete rotation in three million years.

It is seen that the effect is very weak and few hopes to discover it in more far away planets of the Sun that Mercury. This effect that is universal is caused for the character undulatory of the gravity field.

The dynamics of Newton fails in some extreme cases of speeds or very large or very small dimensions, as well as in the opinion of the astronomers Krasinsky and Chunayeva fails completely in the adjustment of the data obtained by means of satellites of probe as Mariner and Vikingo. Besides, its axioms do not satisfy the conditions of an axiomatic modern.

The relativity mechanic describes exactly all the cases of movement. But, in practice the theory of the Relativity is added only, when is necessary, in the form of small corrections of the results obtained previously with the Newton dynamic.

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2.4 Relativist mechanic

In the Special Relativity an inertial system is defined, in gravity field absence, in a continuous spacetime, in exchange for the absolute Newton space. The transformation of spacetime coordinates among inertial systems is carried out by means of the formulae of Lorentz.

In the General Relativity an inertial system is defined as a infinitesimal lapse inside of the spacetime of a system in free fall according to the local gravitational field that is due to all the matter of the Universe.

There are finite regions with relation to a chosen system of reference where the material particles move freely without accelerations and in which the laws of the Special Relativity are notably exact, such systems are considered almost-inertials.

One of such finite regions is that of the Land-Moon masses center falling in the orbit elliptic around the Sun in a relatively weak gravitational field.

The speeds of the stars in the solar system, of this in the galaxy and still of the own galaxy are also relatively small speeds compared with speed of light.

The effects of the Special Relativity for a system being moved with the Land around the Sun are on the order of 10-8; also the effects of the General Relativity are on the order of 10-8.

The main relativistic correction that is done in astronomical measurements of distances using the radio wave technique or detecting with telescopes the heavenly position of bodies is the correction due to the deflexion of the electromagnetic waves that the gravitation causes. This deflexion is the curvature that the waves suffer.

In the model more exact mathematician used for the calculation of the acceleration of the point of mass of a planet, in the solar system, it includes the relativistic parameters named PPN ß, that measures the not linear superimposition of the gravitation, and PPN α that measures the curvature of the space produced by the mass of the remainder of the solar system.

The possible deviations in the accuracy reached in the calculations with the relativistic correction yet cannot be evaluated because there are not a sufficient lapse of data counts on.

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2.5 The inadvertent key

Nevertheless, one postulate exists in both mechanics that differs fundamentally in the astronomical results, although has remained inadvertent: for Newton according to its law of the universal gravitation when one of the bodies changes the position with relation to either body, varies instantly the force that acts on the second body, which spreads with an infinite speed.

Nowadays, of the scientific is one conviction that not instantaneous actions exist, of the type of the Newton gravitation. First, Faraday and Maxwell established that the action electrodynamics is through intermediate processes with finite speed of propagation and, then, Einstein, in the Relativity, the action to distance with infinite speed replaced it for the action to distance with the speed of light (12).

In my theory I adopt a variant of the postulate about not action to distance of Einstein. I modify this postulate based in Faraday-Maxwell thus:

The action among the different phenomena of the nature always occurs with a finite speed. Particularly, with maximum speed permitted inside of a determined material state or material form. That maximum speed is the speed corresponds at state or material form according to its own nature.

(12) The postulate of Einstein about not instantaneous action to distance but action with speed of light necessarily oblige to assign speed to gravitation, because one body can not instantaneous exert his gravitation on either body. In last instance, the theory of Einstein about of gravity, is simply the theory of the inertia in one curve geometry of 4-dimensions de Riemann, then like curve gravity does not has speed; but this really is physically unsustainable. The fact that, according Einstein, the bodies exert gravitation through spacetime curved no is excuse for to violate the postulate of the action to distance with finite speed. ¿How, this occurs? Einstein did not explain. Einstein doubted about spacetime nature between geometric pure and energetic medium. ¿Which is speed of that gravitation action? Einstein never said it. But the most reasonable speed would be c. In terms of the General Relativity the author assumes the speed c for the one body gravitation action on either body. By this reason, following to Einstein, the author considers, in this work, that speed c of gravitation would must to be included in the procedures of ephemeredes.

The reader must to distinguish the speed of gravity according to the bodies exert their gravitation of the speed of gravity wave that Einstein if define. The speed of gravity wave is the speed of propagation of a perturbation of the spacetime caused by not uniform acceleration of a source of gravitation. This speed is c.

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2.6 Conclusions

- The description cinematic that refers to the geometric description of the movement was established from observations that permitted to Johannes Kepler to formulate the laws of the movement of the planets around the Sun.

Those laws serve at present for a first approximation in the description of the orbits and movements of the planets.

- The dynamic part that refers to the cause of the planetary movement the force among the planets is bases on and the Sun that is a particular case of the universal law of gravitation of Newton.

- To describe the movement of the stars in the observable Universe can be elected arbitrarily a geometry Euclid or not Euclid. This does not it mean that do not exist evidence with relation to the curvature of the spacetime which is obtained when we launch an object up. Its movement of ascent and descent shows said curvature.

- The formulae of the dynamics of Newton, referred to a Euclidean space, serve to predict theoretically with a high degree of accuracy the movement of the stars since coincide with the positions observed to a high degree of precision. The movements of Mercury and the Moon are excepted because they present greater errors. In the case of Mercury owes to deficiencies of the Newton´s theory on the gravitation that are corrected with the theory of the Relativity of Einstein, and in case of the Moon on account of the secular variation of the speed of rotation of the Land.

- The mechanics of the Relativity describes exactly all the cases of movement. But, in practice the theory of the Relativity is added only, when is necessary, in the form of small corrections of the results obtained previously with the dynamic of Newton.

- The effects of the Special Relativity for a system being moved with the Land around the Sun are on the order of 10-8; also the effects of the General Relativity are on the order of 10-8.

- The main relativistic correction that is done in astronomical measurements of distances using the radio wave technique or detecting with telescopes the heavenly position of bodies is the proper correction to curvature of the electromagnetic waves caused by the gravitation.

- In the model more exact mathematician used for the calculation of the acceleration of the point of mass of a planet is included two relativistic parameters named PPN ó that measure the curvature in the superimposition of the gravitation, and PPN α that measures the curvature of the space.

- According with the conception of Einstein about that not instantaneous action to distance exists; one body can not instantaneously exert your gravitation on either. This is a fundamentally differentia in the mechanics of Newton and Einstein, although it has remained inadvertent. For Newton the gravitation acts to distance instantly. For Einstein the gravitation possesses a speed equal to speed of light.

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3 TIME

The time is considered absolute. Along many years were measured using astronomical techniques that refer the movement of the Land with relation to the stars, that by its distance, turn out to be practically motionless and this stars are named fixed stars.

In the past the terrestrial movement of rotation was used, more recently the movement of translation of the Land around the Sun.

But the normalization of the measurement of the time has been reached utilizing quartz and atomic clocks.

The time measured astronomically has three expressions that are:

- Sidereal.

- Solar true.

- Solar middle.

The time that is taken like civilian is derived from the solar middle and is known like the universal time that governs everywhere.

These three types of measurement of the time are convertible through formulae and data that appear in astronomical yearbooks.

With the astronomical time various calendars were built that permit to express the time in a continuous way. The calendars most used, in different astronomical applications, are Gregorian, Julian and Besselian.

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3.1 Traditional system of fixation of the time

In astronomy the chosen physical system traditionally for the measure of the time is formed by the stars of the solar system, whose movement is defined with relation to some practically motionless axes of coordinates with relation to the stars, of such way that a system results one inertial system. The equations that are utilized are equations of the physical Newton dynamics that for some very precise calculations add relativist corrections and a small correction for to include the rotation of the solar system in the Galaxy. But, these corrections are very small and few times are used.

The method, to determine and to compare successive positions of the stars of the solar system, is reduced to measures of angles with rays of light, that permit to determine the astronomical coordinates in function of the time that by hypothesis is considered uniform. The relation of the coordinates of the star, that is to say its position, in function of the time, is named ephemeris of the star.

The coordinates are obtained mathematically by means of the integration of the dynamic equations in function of the time and of the constant of integration whose numerical value is fixed from the observations. By consequence the ephemeris depends essentially of the observations and is affected of the errors of the same.

The astronomical observations of the coordinates of a star conduct for inverse interpolation in the ephemeris to the determination of the time. The method used in practice to measure astronomically the time is that of interpolation in the tables of ephemeris published annually by some observatories.

The astronomical measure of the time implies the three following steps:

- To establish the dynamic theory of the planetary system.

- To obtain the ephemeris of the stars of that system.

- Interpolate in the ephemeris the position observed of said stars to obtain the time.

To 1950 the astronomical time was determined, exclusively, from the ephemeris of the movement of rotation of the Land. Recently, the ephemeris, with greater precision, is obtained by means of the movement of translation of the terrestrial axis in around to the Sun.

The movement of the stars, although, is perennial does not indicate directly the time, for which, nowadays, electronic clocks of precision are used and growing stability. Currently in the astronomical observatories have clocks of quartz, with a precision even in 10 nano seconds.

The maximum uniformity has been reached with atomic cesium clocks that have a relative variation of the march on the order of 10-12.

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3.2 The expressions of the time

In astronomy the time, in a specific moment, is equal to horary angle that forms a definite point as zero with a determined meridian, generally, the local. The election of the point zero gives rise to three different expressions of the time. These expressions are:

- Sidereal when the equinox of spring is taken or vernal point that is almost fixed with relation to the stars, for which is the adequate point to measure the movement of these.

- Solar true when the point is the center of the Sun. This position changes with relation to the stars from a day to another, due to annual movement of the Land in its orbit.

Besides, this change is not uniform by being carried out the movement of translation in a plan inclined on the Equator and to be the elliptic path what gives rise to days of different duration, since the movement of the Sun is quicker when moves near to the Land and slower when moves away. This path is known as the ecliptic.

- Solar middle when the point is the center of the middle Sun, that is a fictitious Sun that describes the same path of the true Sun but so that travels through the plan of the Equator with a path to circulate and a uniform movement.

The origin of the time, in the previous systems, is the instant of the upper step of the point zero, by a determined meridian and the unit of time is the day, that is to say, the interval among two consecutive steps of such point by that meridian. A day sidereal is the interim among two consecutive steps of the equinox of spring, point Aries, by a meridian, generally, that of the place, exactly, in a turn of the Land of 360 degrees. Due to the precession annual, in sense retrograde, of the point Aries, the day sidereal is smaller in .009 second to the another sidereal that is defined with relation to the fixed stars, that is to say, interval of time among two consecutive steps of a fixed star by the meridian of the place. Besides, is a little less than the solar day, step of the Sun two consecutive times by the meridian localities, on account of that the year tropic, that is the interval among two consecutive steps of the Sun by the equinox of spring, has 366.242197 days sidereal and only 365.242197 solar. This difference it owes to that while the solar time is measured taking the center of the Sun as reference, the sidereal time is measured with relation to the stars that remain almost fixed relating to the Land. A true solar day is on the average, three minutes fifty-six seconds, and longer fraction than the sidereal day.

The solar day middle, that corresponds to two consecutive steps of the middle Sun by a determined meridian, approximately, in a turn of the Land of 361 degrees, is equal to average of the duration of every day solar true of the year and corresponds to 24 hours, 0 minutes, 0 seconds while in sidereal hours to 24 hours, 3 minutes, 56,5553 seconds. The difference is close to the 4 minutes mentioned previously.

As civil time the solar middle is taken, but, in agreement to the lower step of the Sun with relation to a meridian, for which the astronomical time and the civilian differ in the hours of the morning and are equalized in the hours of the afternoon. The astronomical time is measured with reference to the upper step of the Sun. The meridian taken for the civil time is that of Greenwich and the horary angle is the formed by the center of the middle Sun with the meridian of Greenwich, this time is named Universal.

The time differs in all the positions on the Land that do not be in the same meridian, and the difference in the times is named difference of lengths among the respective places. The time from a place with relation to another will be equal to the time in one of them more or minus the difference of length among them, according to that the last place is found eastward or western of the first place. Based on the time of the meridian that is taken like official for a country is that the Legal time is defined that unifies the hour in all the territory of a nation, extensive territories are excepted that have different hour as in the United States or Russia.

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3.3 Differences and conversions

The existing differences among the three expressions of the time are known as:

- Acceleration of the fixed stars when the difference is among the solar day middle and the sidereal day.

- Equation of the time when the difference is among the true solar time and solar middle time.

The value of the equation of the time is positive of December 24 to the 15 of April and of June 16 to the 31 of August. In the other dates is negative. Four days are excepted in the year in which both times coincide and the equation of the time is equal to zero. Such days are:

. December 24

. April 15

. June 14 and

. September 1

The conversion among the different expressions with which is measured the astronomical time is carried out utilizing data that appear tabulates in astronomical yearbooks and the corresponding relations and equations that have defined for that application.

The middle solar local time, Hm, in every single moment is determined from the middle sidereal local time, Tm, observed, directly, in that instant, that is the true time, Tv, subtracted the equation of the equinoxes. Consequently, the numerical relation among the two scales is determined from the instant in which know simultaneously the values of Hm and Tm referred to a same meridian, that generally, is that of Greenwich adopted conventionally to define a half unique solar time, that enlarged in 12 hours, to become time civil, serves like universal time, TU, everywhere.

TU by not being rigorously uniform is named like TUO to distinguish it of the universal time TU1 and TU2, corrected partially of that lack of uniformity, which is due to variations of the meridian and to irregularities of the terrestrial rotation and, although, are very small should be included in long lapse, not thus, in short, for example, of a day.

The scale TU2, by international agreement, is transmitted for all the practical uses and is conserved in the observatories and horary central by means of clocks of high precision, whose correction and march is determined in the observatories from the astronomical observations. But on account of its incomplete uniformity is not, this scale, adequate for the heavenly mechanics.

The distribution in the world of TU2 is carried out, currently, almost exclusively, by means of horary signs transmitted by radio which are:

- Local, of low precision, with an error over several tenths of second, sufficient for the ordinary needs civilians.

- They retransmitted since diverse radio stations distributed in different countries. These are signs of high precision, with an error on the order of the ten thousandths of second, and occasionally to the micro second by means of special procedures as are the satellite connection way, with very long lengths of wave or by air transportation of clocks. This it is the time used for the remainder of the civil needs, navigation, and astronomical observation.

The relation of the day sidereal middle to the solar day middle is of. .997269566414 and the reciprocal one of 1.002737909265.

The time TUO in any instant is obtained multiplying the time sidereal of Greenwich, since 0 hours of TUO, by the first factor, that is to say, by the relation among the day sidereal middle with respect to solar day middle.

The middle sidereal local time is obtained subtract of sidereal true time, Tv, the equation of the equinoxes, EE, whose value is found tabulate in the ephemeris astronomical for the 0 hours of TUO of each day.EE varies little in a day.

The sidereal local time, Tm, is converted to sidereal time in the meridian of Greenwich, Tm (Gr), subtract, if is eastward of Greenwich, or adding, if is western of Greenwich, the length among the local meridian of Tm and the meridian of Greenwich.

The transformation of TUO to time sidereal is performed continuing the same previous steps but in invested order.

The universal time TUO, or civil local time in the meridian of Greenwich, can become civil local time in a meridian any, TC, of a specific length adding, if is to the western of Greenwich, or subtract, if is eastward of Greenwich, such length to TUO.

The previous equivalences permit to calculate numerical tables of more detailed conversion that are included, in the astronomical yearbooks. When precision is required more the equations of conversion are used.

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3.4 The Gregorian calendar

The time elapsed among two consecutive projections of the Sun on a same star is the sidereal year that has a duration of 365 days solar medias, 6 hours, 9 minutes, 10 seconds, that is to say, 365,256361 days solar medias.

The time elapsed among two consecutive steps of the Sun by the equinox of spring, point Aries; that is to say, among two consecutive beginnings of the spring is the year tropic. Its duration is of 365 days solar medias, 5 hours, 48 minutes, 50 seconds, that is to say, 365,2422 days of time solar medias. In this is based the construction of the Calendar that corresponds to catalogue divided into months, weeks and days of the named civil year, similar lapse to tropic year but composed of a whole number during the day media, 365, that differ in .2422 days medias of the tropic year. To compensate the mismatch a day enlarges it each 4 years to the calendar, being obtained the year leap.

Due to that a day is added instead of .9688 is generated an error that in 400 years equals to 3.12 days, for which in such interim 3 years are omitted leaps, and as, still, subsists an error of .12 days gives rise to an advancement in the year tropic of 1.2 days each 4000 years that to stop declaring it leap, as would correspond, the day is eliminated. Nevertheless, difference subsists of .2 days that gives rise to a mismatch of a day in 20 thousand years.

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3.5 Julian Calendar

For many astronomical purposes is more convenient to use the Julian calendar that is a continuous account during the day referred to instant of Greenwich corresponding to noon. This calendar is identified with the prefix JD. The Julian hour for 0 UT always finishes in. 5. The time inside the day it express as a fraction decimal of the day. The Julian date current requires of 7 digits. The Julian date can be used with UTC or other scales as the TAI or TDT.

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3.6 Besselian calendar

For some astronomical purposes such as the specification of the epoch in the heavenly system of coordinates, is convenient to measure the time in years and to define an instant of time to express it like fraction of the year. This calendar is identified with the prefix B. due to that the instant in which begins the year (.0) does not correspond to Julian was introduced a modification replacing it for the new version in which 100 years are exactly 36525 days, that is to say, a Julian century and B1900.0 corresponds exactly to the date 1900 January. 5. The new version is indicated with the suffix J. The standard epoch recommended for the use in the catalogues of stars and in the theories of the movement of the planets:

J2000.0 = 2000 January 1.5 = JD 2451545.0 TDB.

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3.7 Conclusions

- In astronomy the traditional system for the measure of the time is formed by the stars of the solar system, whose movement is defined with relation to some practically motionless axes of coordinates with relation to the stars. The equations used are those of the Newton dynamic that for some very precise calculations add relativist corrections and a small correction for to include the rotation of the solar system in the Galaxy.

- The position of the star in function of the time is named ephemeris of the star.

- The astronomical time was determined from the ephemeris of the movement of rotation of the Land. Recently, also by means of the ephemeris determine by the movement of translation of the terrestrial axis in around to the Sun.

- The movement of the stars does not indicate directly the time for which nowadays electronic clocks are used. In the astronomical observatories have clocks of quartz, with a precision even in 10 nanoseconds. The maximum uniformity has been reached with atomic clocks.

- In astronomy the time is equal to the horary angle that forms a definite point as zero with a determined meridian. The election of the point zero gives rise to three different expressions of the time. Sidereal when the equinox of spring is taken. Solar true when it takes the point of the center of the Sun. Solar middle when the point is the center of the middle Sun.

- The civil time is measured with respect to the solar middle enlarged in 12 hours in agreement to the lower step of the Sun relation meridian of Greenwich. This time is named Universal. By not being rigorously uniform is named like TUO to distinguish it of the universal time TU1 and TU2, corrected partially of that lack of uniformity.

- The Gregorian calendar is a catalogue of the civil year divided into months, weeks, and days. The civil year is bases on tropic year that is the time elapsed among two consecutive steps of the Sun by the equinox of spring. This composed of a whole number of 365 day middle, that differ in .2422 days of the tropic year. The mismatch is corrected enlarging a day each 4 years, being obtained the year leap.

- Julian Calendar is a continuous account during the day referred to instant of Greenwich corresponding to noon. This calendar is identified with the prefix JD. The Julian hour for 0 UT always finishes in .5. The time inside the day it express as a fraction decimal during the day.

- Besselian calendar measures the time as fraction of the year. It is identified with the prefix B. due to that the instant in which begins the year (.0) does not correspond to Julian was introduced a modification that gave rise to a new version in which 100 years are exactly 36525 days, that is to say, a Julian century and B1900.0 corresponds exactly to the date 1900 January .5. The new version is indicated with the suffix J.

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4 COORDINATES OF POSITION

For the purposes of the astronomy of position is necessary to understand the three following aspects:

- The Land to which are referred the positions of the stars.

- The heavenly sphere where for a terrestrial observer are supposed placed the stars.

- The movements of the Land that affect the direction in which the stars are observed, being especially important the precession and nutation. Also other astronomical phenomena as are the parallaxes and the aberration, deflation and refraction of light.

The heavenly sphere and the ellipsoid, that is an approximation to the figure of the Land, are the two ideal bodies that mainly are used in Astronomy of position.

So much for the heavenly sphere as for the ellipsoid various systems of reference are utilized. The firsts are heavenly astronomical coordinate systems. And, the seconds are geographical coordinates systems.

A system of reference is defined by a framework and a system of coordinates.

The position of the stars is necessary representing it in different frameworks of reference and in various systems of coordinates, in agreement to context in which the position will be used. Often the framework with relation observations are facts it differs of the most convenient framework for the comparison of the data observed with the theory.

The frameworks are of two classes: Some frameworks are defined as not rotary with relation to the Land or to another star, generally, referred to the stars calls "fixed” that change of position very slowly with time, these belong to the heavenly astronomical systems of coordinates. The other, frameworks rotate with the Land or another star and when refer to the ellipsoid are geographical systems of coordinates.

The same denomination can be used for a heavenly system of coordinates and another geographical of coordinates, for example, the position of an observer placed in the surface of the Land is specified in geocentric coordinates referred to ellipsoid, that rotes with the Land, and also in heavenly geocentric coordinates relating to the stars "fixed". The specification of a rotative system of coordinates or no, depend if is qualify with "heavenly" that is the denominative of framework inertial.

Each system of coordinates corresponds an individual forms to express the position of a star with relation to a specific framework, just as the rectangular system of axes, generally, three-dimensional. Although, two coordinates are sufficient to represent the direction of the star. Since his distance provided that radial remaining constant. Another usual system is polar coordinates.

The units of measure used are referred to the circumference and are expressed in radians, degrees, and hours.

The transformation among different systems of coordinates is geometric and is carried out utilizing the techniques of the trigonometry spherical or of the algebra of matrix and vectors.

The geographical systems of coordinates permit to set the position of the stars with relation to the Land and, by means of the adequate transformations, to refer said positions to the heavenly astronomical systems, used to relate to the position of the stars "fixed".

In general, the stars move with relation to the frameworks. And frameworks with relation to "space". Therefore, it is necessary to specify the time to that the systems of coordinates refer and the time to that the framework is defined. These two times often are different and can be expressed in the different scales of time previously views.

The position of the planets is set in ecliptic heliocentric coordinates and defined by means of 6 parameters named orbital parameters.

The position of the planets can be calculated for any instant. The theory of the movement in a system of two bodies is used. One body is the Sun and the other body is the planet and the position is calculated using the formulae of Newton.

The general theory, developed by Sundman for more than two bodies, covers a great mathematical complexity by including the effect of all the planets in the orbit that is foretold. A procedure simplified is calculating the orbits resolving the problems of two bodies and including the effect of the other planets as disruptions.

For the estimation of the disruptions two approaches exist, the numerical integration and the general theories. The first method this based on to perform an adjustment to the observations of the positions of the planets that historically are arranged. The other method is supported in the analysis that is carried out for the movement of a specific heavenly body.

For very exact calculations of the orbits are included the relativistic effects treating them as if were also disruptions.

The observations about the positions of the stars correspond to done registrations the majority by means of telescopes. Over the sixty years exists very exact observations taken with techniques of radio astronomy, laser and by means of satellites.

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4.1 Usual Framework

Each system of reference depends on the election of a framework and the form to specify the coordinates with relation to that framework. Among the main frameworks are the following:

- Topocentric referred or measured with relation to the surface of the Land.

- Geocentric referred or measured with relation to center of the Land.

- Selenocentric referred or measured with relation to center of the Moon.

- Planet centric referred or measured respect to center of any of the planets.

- Heliocentric referred or measured with respect to center of the Sun.

- Barycentric referred or measured with respect to center of masses of the solar system or of the Sun and a specified sub conjunct of planets.

These frameworks can be heavenly or rotary.

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4.2 Units of measure

The units of measure used in astronomy are referred to the circumference and are:

- The radian that is the arc of circumference of length equal to one radio. The length of the circumference is of 6,28319 radians.

- The degree is the three hundred sixtieth splits of the circumference. The degree is subdivided in 60 minutes and the minute in 60 seconds of arc, being the subdivisions of the second decimals.

- The hour is the twenty-fourth splits of the circumference. The hour is subdivided in 60 minutes and the minute in 60 seconds of arc, being the subdivisions of the second decimals.

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4.3 Heavenly Sphere

For an observer situated on the surface of the Land, the firmament appears as an immense semi spherical vault, in the night sprinkled of stars and stars and in the day with clouds, limited by the topographical irregularities of the terrestrial surface or by the surface of the sea. This is due to that the observer constitutes a center of vision. The observer for any direction to which rotate has a visual one of equal radio, distinguishing only the apparent directions in which the stars are found, when them perceives.

If the observer is an astronaut, placed in orbit, he will see a sphere on which appear placed the stars due to that his vision not this hindered by the Land and extends in all the directions of the surrounding space. Such sphere is named heavenly sphere, that can have like center any arbitrary point in the space.

The position, in which a star is observed, is determined by means of polar coordinates with respect to the surface of the heavenly sphere that has like reference the globe of the earth and a determined plan referred with respect to this sphere. The coordinates are defined in a Euclidean space by means of two angles, measured in degrees, minutes and second of arc, that refer to the latitude, coordinate y, and to the length, coordinate x.

The latitude is the angle formed among the parallel that coincides with the plan of reference and that parallel in which the star is found. It is measured from 0 to 90 degrees North or South. The parallels are parallel circles according circle equatorial of the heavenly sphere.

The length is the angle on the plan formed among a meridian chosen like origin and that meridian of the star. It is measured from 0 to 360 degrees in the direction or against the movement of the needles of the clock. The meridians are vertical circles according circle equatorial.

The real distance of the stars is stranger and their position is considered projected on the heavenly sphere that by convention is supposed of radio unit. This causes what the distance disappears of the equations of position.

The heavenly sphere is an ideal body, built to resemblance of the globe of the earth, where are supposed placed the stars, with center in the terrestrial observer. This is the case topocentric, nevertheless the center can be in the Land, case geocentric, or in the Sun, case heliocentric.

It serves to establish a simple image of the sky with stars and permits to set positions and to draw movements by means of the adoption of systems of coordinates appropriate, whose purpose is to set the direction of the heavenly bodies, not its distance, representing it for points on designed circles of reference on the surface of the sphere and with respect to its center. The heavenly sphere as the globe of the earth possesses:

- Axis of the world or polar axis, around which seems to rotate the entire firmament in direction east-west.

- Heavenly equator that is the circumference specific on the heavenly sphere by the intersection with the perpendicular plan to axis of the world that passes for the center of the Land.

- Heavenly parallels that are the parallel to heavenly Equator.

- Heavenly meridians that are perpendiculars to heavenly Equator and pass for the heavenly poles.

These lines can be considered like projections on the heavenly sphere of the corresponding designed lines on the terrestrial surface (to See Graphic 1).  

Four main systems of coordinates exist that depend on the plan chosen like reference. The planes can be:

- Horizon that is the normal plan to the vertical localities, or apparent direction of the gravitation, and passes through the position of an observer. It is tangent to an observer placed on the terrestrial surface, but, with respect to the heavenly sphere passes for its center.

- Equator is the plan that passes for the equatorial heavenly circle, which is parallel to terrestrial equator and forms an angle with the horizon equal to horizon with the terrestrial equator.

- Ecliptic is the plan on which the apparent path of the Sun with respect to heavenly sphere in the course of the year is produced. This plan has an inclination of 23 degrees and 27 minutes with relation to plan of the Equator. The upper intersection of the ecliptic with the Equator is named point Aries or vernal point. The lower intersection is named Pound.

The coordinates are:

- Horizontal system when refer to horizon.

In the horizontal system of coordinates the length is named azimuth; the point of origin of the angle, that is to say 0 degrees, corresponds to heavenly south and enlarges in the direction of the movement of the needles of the clock, in sense east-west, to 360 degrees.

The latitude is named height, which is measured on the vertical circle that passes for the position of the star, extended among 0 degrees, in the horizon, and 90 degrees, in the zenith that coincides with the north pole, if the star this above the horizon or among 0 degrees and -90 degrees, in the nadir that coincides with the south pole, when star this by underneath.

The heavenly sphere, in the framework topocentric, has exactly as center the position of the observer on the terrestrial surface. The projection of the axis of the world on the plan of the horizon constitutes the line meridian whose extremes are the North and South cardinal, the perpendicular to this line has in their extremes the cardinal points: East, approximate place at the outset of the Sun, and western, approximate place of their concealment. On the terrestrial Equator the heavenly sphere is perfectly perpendicular to globe of the earth.

Graphic 1. Heavenly sphere

The horizontal system of coordinates is useful to know the movement of the stars respect to horizon of the place but has the disadvantage to be localities, that is to say, depends on the geographical position of the observer. Besides, the movement of the Land goes changing the position of the horizon on the heavenly sphere causing the translation of the coordinates of the observer with the time (to See Graphic 2).

Graphic 2. Horizontal coordinates

- Equatorials if refer to the Equator. This system coordinate can be:

a) Horary equatorial if is a matter of continuing the movement of the sky with stars.

In the horary equatorial system the length is named horary angle, which is measured on the heavenly equatorial plan from the local meridian that corresponds to 0 degrees, and against the movement of the needles of the clock. The latitude is named declination and is measured from the Equator along the meridian that passes for the star that it extends among 0 degrees, in the Equator, and 90 degrees, in the North Pole, or -90 degrees, in the South Pole.

Since the local meridian are fixed, with respect to observer, the set of the heavenly vault will pass for him in the period of a day.

In this system of coordinates the declination is the same one for all the observers and although the horary angle is different the conversion is easy since differs in the angle that there are among the points where the observers are.

The horary coordinates are the most adequate to study and to describe the diurnal movement of the stars in an lapse short, with that object it uses telescopes mounted on parallel axes to polar axis and to plan of the equator, when telescopes rotate with the angular speed of diurnal movement of the Land. The star maintains fixed when the telescope it orients with specific declination and it does rotate with angular speed of diurnal movement of the Land (to See Graphic 3).

Graphic 3. Coordinates horary equatorials

B) Equatorial absolute if the objective is to set the positions of the stars in the heavenly vault.

In the equatorial absolute system the length is named ascension straight, measure among the point Aries, 0 degrees, and the meridian that passes for the star, in the contrary direction to the movement of the needles of the clock. The length is named declination and is measured the same as in the equatorial horary system. The origin of the length, that is to say, point Aries, carries out a complete turn to day with respect to observer.

The coordinates of a star, that is to say, length and latitude, are the same for all the observers, save a small effect

Acquaintance as parallaxes, therefore, is independent completely of the position of the observer (to See Graphic 4).

The coordinate equatorials are useful for the associated study of diurnal phenomena movement of the sky.

Graphic 4. Coordinates equatorials absolute

C) Ecliptics if the plan of reference is the Ecliptic.

In the coordinates ecliptics the length and latitude are named heavenly to distinguish them of the geographical coordinates that are referred to the Land.

The length is the angle formed among the point Aries, 0 degrees, and the ecliptic meridian that passes for the star, in opposite direction of the movement of the pointers of the clock, that is to say in sense western-east.

The latitude is measured from the ecliptic plan, where its value is 0 degrees. The latitude varies in direction to ecliptic north, to 90 degrees. Or the latitude varies toward the ecliptic south, to -90 degrees. The heavenly latitude of the Sun is always 0 degrees and its length enlarges from zero, in Aries, to 360 degrees.

The plan of the ecliptic tends to remain fixed with respect to average position of the stars, although, is found disturbed by the attraction of the Moon and the planets on the Land, that cause their continuous variation with a very slow progressive movement, named secular. The secular movement it superimpose small periodic oscillations; by this reason, in the astronomical observations of precision are defined in a moment specific with respect to ecliptic middle, being found the Land and the Sun over or under that plan middle (to See Graphic 5).

Graphic 5. Coordinates ecliptics

The heavenly latitude of the Sun is always Zero degrees, its length enlarges constantly from Zero degrees (in Aries) to 360 degrees.

These coordinates are independent completely of the observer and are used for the associated study of annual movements of the Land.

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4.4 Land

The position of the observer or of the star is established by means of systems of reference, in relative polar coordinates to globe of the earth, and it defined with respect to their surface, through two angles; one refers to the length and the other to the latitude, coordinates that as opposed to them referred to the heavenly sphere do not receive another denomination. The geographical coordinates are:

- Geodesic coordinates depends on the form and dimensions of the Land. They are defined from the normal line in each point, where is supposed situated an observer, respect named ellipsoid of reference, geometric body of mathematical formulation of revolution of two axes, being the smaller one the axis of turn that passes for its poles, whose surface approaches the real form of the physical surface of the Land. Nevertheless, Land is more approximate to geode, surface defined by the condition to be normal in each point to the direction of the gravitation and that due to the difficulty of its mathematical description is replaced for ellipsoid very seemed to geode, the difference among the radios of one and another is to the most greatest thing of 100 meters.

By each point of the ellipsoid passes a meridian and a parallel, being the meridian of origin Greenwich, and the parallel of origin the Equator.

Any point on the ellipsoid remains determined by the coordinates of length, measured by the arc of the angle formed by the plans of the meridians of Greenwich and of the observer, and the latitude, measured by the arc of the existing angle among the plans of the Equator and the parallel where is found the observer.

The geodesic coordinates of a specific place cannot be measured directly but are calculated mathematically from measuring, in a triangle of a network, the angles and the distance of at least of a side, named base, layout on the topographical surface of the Land, and not of the ellipsoid, for which is precise to reduce, said measure, by means of adequate corrections of height to the distance that would have directly on the ellipsoid. The triangulations, named geodesic, are drawn in networks from a chosen station of observation as departure and known as fundamental point, whose coordinates possess the property to coincide with the astronomical geographical coordinates, with this is fixed the position of the ellipsoid with respect to geode. From the fundamental point a network with other points is established or secondary stations, whose geodesic coordinates, can be calculated geometrically on the ellipsoid (to See Graphic 6).

Graphic 6. Geodesic coordinates

The geodesic coordinates permits the making of very exact maps that in astronomy of position are not required except in some very precise investigations of the Moon, eclipses, and artificial satellites.

- Astronomical system that are completely independent of the form and dimensions of the Land, and are determined by means of the vertical astronomical line that indicates the direction of gravitation in the place of observation.

This direction presents irregularities of a point to another of the terrestrial surface and, in general, does not cut the axis of rotation of the Land that passes for the poles, due, mainly, to the irregular distribution of the masses in the interior of the Land.

Besides, in a same point suffers continuously small oscillations due especially to variations of gravity attraction of the Sun and the Moon. This causes that the astronomical geographical coordinates, referred to the vertical mobile, also, oscillate with the time.

Due to the irregularity of the vertical Equator the astronomical parallels are irregular curves and do not coincide with the geographical Equator of rotation neither with the parallels with respect to this. The astronomical poles, neither, coincide with the geographical poles.

The astronomical latitude of an observer is defined like the complement of the sharp angle among the vertical one and the axis of rotation of the Land.

The astronomical length of an observer is defined like the angle among the plan of the meridian that passes for the point of the observer and the plan meridian of Greenwich (to See Graphic 7).

Graphic 7. Astronomical coordinates

- Geocentric coordinates are referred to center of the Land, represented by the ellipsoid, which permits to reduce the observations about the positions of the stars performed since the terrestrial surface to its center, with what a valid only system of reference is adopted   for all the observers situated in different places, so that its observations turn out to be comparable. These coordinates are used in the astronomical tables and ephemeris.

The geocentric coordinates of a point of the ellipsoid are the length that is the same length of the geodesic coordinates and the latitude is defined for the angle that forms the radio vector, or distance among the center and the point of the observer, and the plan of the Equator (to See Graphic 8).

Graphic 8. Geocentric coordinates

The geocentric coordinates of a point A of the ellipsoid terrestrial are: geocentric length that is equal to the geodesic of A and the geocentric latitude equal to angle that the radio forms with the plan of the equator of the ellipsoid.

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4.5 Transformations among heavenly and terrestrial coordinates

Procedures exists that permit the conversion among the coordinates that use the terrestrial system of reference and the coordinates that utilize the heavenly system of reference. These procedures serve in both senses and, regularly, cover the geocentric, topographical frameworks and heavenly framework. The topographical framework is the "observed", referred to terrestrial system of reference and that rote with the Land. The geocentric framework is used like intermediate system for the conversion. The heavenly framework is one of the systems whose framework is considered fixed in the space.

Subsequently is presented the procedure of transformation topographical coordinates to barycentre coordinates.

Step 1: In the procedure of topographical transformation it rotates the latitude since the horizon to equator and the length of the local meridian to first meridian.

It is required to know the latitude, length, and height of the place of observation. For a greater accuracy the effects of the tides on the deflation of the vertical component and on the height should be included.

Step 2: Translation of the origin from the point of geocentric observation.

It requires to know the geodesic coordinates of length, latitude, and height for nearby stars. For distant stars, just as stars, the translation of origin treats as a small corresponding rotation with respect to paralelactic change in direction.

Step 3: Rotation of the terrestrial framework for the polar movement; for example, from the conventional pole to true heavenly pole.

The current values of the coordinates of the pole appear in different publications, one of them is "The Astronomical Almanac".

Step 4: Rotation of the terrestrial framework around the true pole from the meridian of Greenwich to heavenly framework where the first meridian passes through the first equinox.

Step 5: Rotation of the heavenly framework for nutation from the true pole and the true equinox to middle pole and to middle equinox of the date.

The values of nutation, in length and obliquity, can be calculated utilizing harmonic series based on one of the theories of nutation.

Step 6: Rotation of the heavenly framework for precession from the middle pole and the middle equinox of the date to the equator and standard equinox of J2000.0.

The steps 5 and 6 can be combined in singular angle-matrix rotation whose daily values are published in "The Astronomical Almanac".

Step 7: Translation of the origin from the geocentric system to barycentre of the solar system.

The geocentric coordinates with regard to the barycentre can be obtained in "The Astronomical Almanac" that gives position and speed.

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4.6 Movements of the Land

The Land is a planet of the solar system in relative movement regarding the Sun. The Sun revolves around the center of masses of the Galaxy that this formed by a gigantic swirl of near 200 thousand million stars, to a distance of near 28000 years light, delaying approximately 234 million years in performing a complete revolution to the speed of 217 km /s. Besides, with respect to the most nearby star the Sun moves toward a point, Apex, of the constellation of Hercules to near 20 km/S.

The Land revolves around the Sun along an orbit elliptic, with the Sun situated in one of the focus. The greater axis of the ellipse, 299,2 million kilometers, line is named of the apsis, being its extremes the perihelion, 147,1 million kilometers, or more nearby point to the Sun, and the aphelion, 152,1 million kilometers, more distant point of the Sun. The eccentricity of the ellipse, that is to say, the relation among the distance among the center of the ellipse to focus and the semi axis greater, is approximately equal to 0,017 (to See Graphic 9).

Graphic 9. Elliptic path of the Land

The plan that contains the orbit of the Land is named ecliptic which this inclined in 23,5 degrees with respect to the plan of the terrestrial Equator, which originates the stations of the year due to the different inclination with which impact the solar rays on the different terrestrial latitude. The lineal speed average is of some 29,8 kilometers, being the speed areolar constant according to the law of the areas of Kepler (to See Graphic 10).

Graphic 10 . Orbit inclined of the Land

The points of the terrestrial surface, since where the observations of the stars are done, move with respect to the stars, that seem to describe a arc in direction east to west of the place, reaching the highest point, named culmination, on the horizon when stars cross the meridian of the observer. The Sun, the Moon, and the planets possess also this movement with respect to observer, which is named diurnal movement and is the apparent movement of the firmament with stars just as appears an observer in the Land. This apparent movement is different in different places.

In the North Pole and in the South Pole the stars describe parallel circles with respect to horizon and are always visible the same stars. In the Equator its paths are perpendiculars to plan of the horizon, being visible all the stars. In the intermediate latitude among the Equator and the poles the sky with stars seems to rotate around the high heavenly pole, describing circles inclined with respect to horizon.

The orto of a star is the moment of its crossing with the horizon by the east being done visible, and sunset is the moment that crosses for the west being hidden.

The observation of the diurnal movement of the stars is the consequence of the movement of rotation of the Land around its center of masses and of the instant axis of rotation which does not coincide exactly with the lesser axis of the ellipsoid, although the discrepancy is very small.

The rotation of the Land tends to be uniform but presents three types of variations in the speed of rotation that are:

- Irregular, that is to say, aleatory fluctuations, as consequence the duration of the day can vary even in 0,001 seconds.

- Secular that consists of a constant decrease of the speed of rotation of the Land, enlarging the duration of the middle day in 0,00164 seconds for century.

- Periodic in correspondence with the stations of the year varying in near 60 milliseconds along the year.

The orientation of the axis of rotation of the Land is animated of a swinging movement. Consequently, also oscillate the plans of the equator and of the ecliptic with respect to the position middle of the stars. The swinging is similar to tromp axis that dances describing a movement conic. Two superposition movements exist that are:

- Precession that consists of the displacement of the terrestrial axis in a cone in around to axis of the ecliptic. The movement is retrograde, delaying near 25920 years in carrying out a complete turn. The precession goes changing the position of the heavenly north pole with respect to the stars (to See Graphic 11).

Graphic 11. Precession

The polar star of our days, belonging to it Bear Smaller, moves away continuously of the pole, that inside 12960 years will be found at more than 45 degrees of the same one. In that epoch the star Vega of Lira, will pass to be the polar star, to near 4 degrees of the North Pole.

- Nutation that is the movement oscillatory of the pole of the equator regarding the circle less than the precession causes around the pole of the ecliptic. This movement is along an ellipse that travels through in 18,6 years in sense retrograde (to See Graphic 12).

Graphic 12. Nutation

The movement of the equinox due to the precession increases, approximately in constant way, the heavenly lengths of all the stars at nearly 50" per year and affects harshly the latitude. The movement of nutation has amplitude nearby to 9” that is the sum of the components in length and obliquity. Also, exists, a precession of the equinox nearby to 12" for century on account of the small rotation of the plan of the ecliptic.

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4.7 Effects of the position and movement of the stars and the observer

4.7.1 Parallaxes

Parallaxes describe the difference in the apparent direction of a star seen from two different locating. For example, the sun and the planets are observed from the surface of the Land and many almanacs publish its geocentric position.

The direction in which a star is seen depends on its position and of the position of the observer. The change in the direction of a heavenly body caused by the change of the position of the observer is known like parallaxes change. The quantity of change in the direction pertaining to the current line of change, that is to say, the line that crosses the line of vision, in the position of the observer, is known as the parallaxes of the star. For bodies inside the solar system the line of change is the radio equatorial of the Land. For the stars the line of change is the astronomical unit of distance (AU) or the middle radio of the orbit of the Land around the Sun. The parallaxes of a planet in the solar system are named horizontal or diurnal parallaxes. The parallaxes of a star are named parallaxes annual to cause that the parallaxes change occurs in the period of a year.

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4.7.2 Aberration

Due to that the light possesses a finite speed; the direction in which a star is seen for an observer in movement does not correspond to the straight line among the observer and the star. The existing discrepancy can be attributed in part to the movement of the star and in part to the rotational and orbital movements of the observer. The part of this displacement that is independent of the movement of the observer is named correction for light-time; the remainder of the displacement that is independent of the movement and position of the star is named stellar aberration. The sum of the two parts is referred like planetary aberration because is applicable, mainly, to the planets of the solar system. In the case of the stars the correction light-time is ignored. For the majority of the purposes of the astronomy the aberration is calculated in function to the speed of observer and to the speed of light.

The stellar aberration cover the effects of the diurnal rotation of the Land, of its orbital movement around the barycentre of the solar system and the movement of the center of masses in the space that are linked to the terrestrial observer. The consequence is that the stellar aberration is considered like the sum of the secular, annual, and diurnal aberrations, being for the two first the most maximum nearby effect to 1.3" and 20", respectively. If the stars are considered and the center of masses of the animated solar system of movement rectilinear uniform the corrections for light-time and the secular component are indistinguishable and is equal to the movement of the star multiplied by the factor light-time. Only in very precise calculations for the stellar aberration the formulae are used of the Special Relativity.

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4.7.3 Deflation of light

For very exact calculations is necessary included the action of the gravity field of the Sun on the light or waves of radio, that curve their paths and increases their time of crossing affecting the direction in which the observations are performed.

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4.7.4 Refraction of light

The refraction of light, rays laser, or radio waves in the terrestrial atmosphere also affects the direction of the observations although a great deal more than the deflation. The intensity of the refraction depends on the altitude of the star regarding the horizon of the observer and of the prevailing atmospheric conditions, due to which cannot be included in the ephemeris. Many analytic theories and tables of refraction supposes that, in the atmosphere, the surfaces concentric possess the same index of refraction and that to set it is sufficient to know the pressure, temperature and relative humidity in the point of observation.

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4.8 Position of the planets

The orbits of the planets are established with respect to a heavenly system of ecliptics heliocentric coordinates, where the orbit real of the planet is projected on the heavenly sphere of radio vector unit (to see Graphic 13).

  Graphic 13. Real orbit projected on the heavenly sphere

The position of a planet, in its elliptic orbit, remains determined by means of to set in the heavenly sphere:

- The position of the plan of the ellipse with respect to plan of the ecliptic is determined by the length of the ecliptic and the inclination of the orbit that equals to angle formed by these two plans. If the movement of the planet is direct the inclination is lower to 90 degrees, and if is retrograde, is between 90 and 180 degrees.

- The orientation of the ellipse in that plan that is defined by the angle argument of latitude of the perihelion, among the line of apsis and the line that passes for the points of cut among the plan of the orbit and the ecliptic.

- The form and dimensions of the ellipse that result of the value of the major semi axis of the ellipse and of its eccentricity.

- In the time, the position of a planet on the ellipse is calculated, initially, from the laws of Kepler.

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4.8.1 Orbital parameters

The orbital parameters are seven that determine size, figure, and orientation of the orbit of the planet in the space and its position in a specific instant known as the epoch. These parameters are:

- Length of the node ascending, that is to say, point in which an orbit inclined crosses the ecliptic in north direction.

- Inclination.

- Argument of latitude of the perihelion.

- Major semi axis of the ellipse.

- Eccentricity of the ellipse.

- Moment of the step of the planet by the perihelion.

- Period of revolution.

Due to that the major semi axis of the ellipse and the period of revolution are related by the third law of Kepler the parameters are reduced to six.

To determine these parameters are required to observe, at least, three different positions of the planet, that provide three ascensions straight and three declines. Although, the observations it prefers more.

Acquaintances the parameters of the orbit of the planet can be determined the coordinates equatorials rectangular (x, y, z) in the heliocentric system. This coordinates must be converted to geocentric astronomical coordinates.

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4.8.2 Daily Movement

The movement of daily planet middle, in its orbit, can be determined using the equation:

n = 2Pi/P = k (1+m/a3/2) 1/2

Where:

n is the movement in radians for day

π is 3,1416

P is the half solar period in days

k is the constant Gauss of gravitation

m is the mass of the planet

a is the major semi axis of the ellipse

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4.8.3 Movement in systems of two bodies

On a short lapse the movement of a planet around the Sun or of a satellite around a planet can be supposed as if the two bodies to exist alone in the space and being moved each one around the other. In any instant the movement of the planet with the equations of the dynamics of Newton can be determined completely, named problem of two bodies, from initial conditions acquaintances.

Nevertheless, this is the simplest case than corresponds to Kepleriana ellipse and to a planetary system simplified Sun and to a respected only planet forming a remote system and its center of masses in rest or being moved to a uniform speed in the space. The center of masses is tried like the origin of a not rotary system of coordinates, used to define a framework inertial which is obtained the equation for the movement of the planet with respect to Sun. This is the following equation:

r2 = - G (M + m) r1/r 3

Where:

r2 is the acceleration of the planet with respect to the Sun

r1 is the position of the planet with respect to the Sun

r is the distance among the planet and the Sun

G is the gravitation constant

M is the mass of the Sun

m is the mass of the planet

If the vector r1 has component x, y, z respect system of coordinates the previous equation equals to three equations of the form:

x2 = - G (M + m)x1/r3

When the unit of mass is taken equal to the mass of the Sun and the unit of time to a day the equation returns:

r2 = - k 2 (1 +m) r1/r3

Where:

k is the Gaussian constant of gravitation

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4.8.4 Extension at more than two bodies

The calculation of the orbits of the planets is complicated extraordinarily when the planetary disruptions due to the presence of the other planets are considered. The rigorous integration of the equations of the movement for the Sun and two planets more, problem of the three bodies, was generalized by Sundman, by means of convergent series of powers, to n bodies. But, the integration generates various millions of terms in the developments in series to calculate the ephemeris of the planets some months after an initial observation. For its solution is required to utilize computers of great capacity.

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4.8.5 Additional Disruptions

Other disruptions due to the planets that should be included in the calculations, when it wants to obtain very exact results, are:

- Its not symmetrical sphericity.

- The radial variation of its density.

- Its distortion on account of the solid tides.

In case of artificial satellites it needs, additionally, the following effects:

- Atmospheric resistance and solar wind.

- Pressure of the solar radiation.

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4.8.6 Procedure shortened

Due to that the majority of the mass of the planetary system is found concentrated on the Sun and, as consequence, the attraction among the planets are a lot smaller to which exists among the Sun and they, a procedure used to simplify the calculation of the orbits is to carry out in two phases. In the first one, the problem of the two bodies is resolved suppressing the presence of the other planets and considering the orbit done not disturb, or Kepleriana, that would continue the planet from an instant given, named oscillatory orbit of disturbed orbit and its six parameters, named osculator elements. In the second phase, the correction is done of the oscillatory orbit to find the real orbit by means of the consideration of the disruptions that are small and its osculator elements vary slowly with the time.

For the calculation of the disruptions the approach of the numerical integration and of the general theories are utilized.

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4.8.7 Relativistic correction

At present, in the calculations of the movement of the planets and of the Moon relativistic terms are being included, not thus for the others natural satellites. In these cases are used the parametric equations post-Newton (PPN). Such terms have to see with the following effects:

- When planet positions are converted from the barycentre to the geocentric the time is converted according to the metric of the Relativity.

- The optic observations are corrected of the deflation of light.

- The observations by means of radar are corrected of the retard time wrapped.

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4.8.8 Approach used in the calculation of the effects of the disruptions

Two methodological approach exist in the calculation of the effects of the disruptions in the orbits of the planets, one is numerical integration of the movement of the stars, based on the adjustment of the orbits to the observations, and the other is the general analytic or numerical theories, that express the movement of the stars in function of the time.

For the planets and the moon is obtained a greater accuracy in the results using the numerical integration and for the satellites, whose movement is quick, as those of Galileo satellites of Jupiter is better to utilize the general theories.

The process of correction to achieve the best adjustment to the data observed is named differential process of correction.  

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4.8.8.1 Numerical Integration

Numerical Integration is the most focusing used for the calculation of the orbits of the stars in the solar system, particularly the Moon, and the planets.

The numerical integration is bases on to set the initial conditions for the numerical integration by means of the most adequate adjustment to the data observed, followed by the numerical integration applied on that correction. This it is a process reiterative until the numerical integration represents the observations with the degree of accuracy required.

Many numerical methods of integration exist. The method of Cowell' includes the correction PPN.

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4.8.8.2 General Theories

The methods that first were used for the calculation of the ephemeris went of numerical integration. Since Chapront and other astronomers, in the Bureau of Lengths, were that undertook the general development of new theories on the planets and the moon that appeared among 1970-1992 adjusted at present to numerical integration DE200/LE200. Before to 1950 some theories were, also, formulated on the planets and the Moon using the model of two bodies in terms of small quantities and in accordance with the powers of the disturbed masses. Theories of Newcomb (1898), Hill (1898), Leverrier (1858, 1859, 1861) and Brown (1919) were used together with tables to facilitate the estimation of the ephemeris. These theories were based on a dynamic system of reference or in an equinox of the date and they included the constant of precession and nutation. The theory on the Moon, on account of the accuracy with which is observed and to the complexity of their movement, require of empirical terms of correction for manage to adjusting it to the observations.

The general theories are imposed in front of the numerical integration for the animated natural satellites of quick movement, such as the satellites of Jupiter and Mars, where the numerical methods of integration promptly lose accuracy. Ivanov (1988) devised a theory for Phobos and Deimos satellite of Mars. Lieske (1977, 1980), Vu (1977, 1983), and Thuillot (1983), Pascu (1992) have worked theories on the satellite Galileanos of Jupiter.

Another field likewise to favor of the general theories is that of the artificial satellites.   

The general theories usually utilize series of Fourier or of Chebyshev to represent the movement of the planets that are decomposer in periodicals movements that oscillate around a middle value, and secular, that grow constantly with the step of the centuries. Laplace showed that major semi axis of the ellipses, that the planets travel, are subject to periodic disruptions and that are despicable the secular, fact that assures the stability of the planetary system. The other five osculator elements are subject to both types of disruptions.

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4.8.9 Observations

The data based on dependable observations of the planets and satellites, in our solar system, is mended to year of 1830, covering the 165 last years. The majority of the observations correspond to the observation of the orbital step. Only in the most recent years observations have been obtained using other techniques. These are:

- Radio-Radar.

- Spatial ships envoys to Mercury, Venus and Mars.

- Laser used in the Moon.

The last observations provide very precise positions and the measurement of the distance among the Land, the Moon, Mars, Venus, and Jupiter with an error even in a hundred meters.

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4.9 Differential Corrections

The process to correct a numerical integration or a general theory to give a better adjustment to the observations is named differential process of correction. In that process an equation of condition can be defined by each observation. This equation provides the relations among the position reckoned in the calculation and it observed of a star. The equations of condition combine in normal equations that the better initial conditions are resolved to reach.

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4.10 Conclusions

- For the fixation of the position of the stars exist systems of reference that depend on the election of a framework and the form to specify the coordinates with respect to that framework. Among the systems of reference most used are the barycentre system measured with respect to center of masses of the solar system, the geocentric system referred in relation to center of the Land, the heliocentric system relative to center of the Sun and the heavenly system referred with respect to the heavenly sphere and considered as topocentric system by to be measured with relation to the surface of the Land, the majority of the times.

- In astronomy the units of measure are referred to the circumference. The radian is used that is the arc of circumference of equal length to the radio. The degree that is the 360th splits of the circumference subdivided in 60 minutes and the minute in 60 seconds of arc. The hour that is the 24th splits of the circumference, subdivided in 60 minutes and the minute in 60 seconds of arc.

- The heavenly sphere is an ideal body, to resemblance of the globe of the earth, where are supposed placed the stars, usually with center in the terrestrial observer. It serves to set the positions of the stars and to draw its movements representing them for points on designed circles on the surface of the sphere, defined with respect to a one determined plan. The coordinates are specified by means of two angles that refer to the latitude and to the length. The systems of coordinates used are four that depend on the plan chooses as reference.

1. Horizontal when refer to horizon that is the normal plan to the direction of the gravitation.

2. Equatorials if refer to plan that passes for the equatorial heavenly circle and of the local meridian for the equatorial horary system.

3. Equatorial absolute if the plan pass for the point Aries.

4. Ecliptic when refer to plan on which the apparent path of the Sun in the course of the year is produced.

- In the terrestrial framework the position of the observer or of the star is established by means of systems of coordinates that through two angles, one refers to the length and the other to the latitude, determines a point relative to globe of the earth represented by the ellipsoid whose surface approaches that of the physical surface of the Land. The systems of coordinates used are geodesic, astronomical, and geocentric systems. The geodesic system depends on the form and dimensions of the Land and is defined from the normal line in each point, where is supposed situated an observer, in the named ellipsoid. The astronomical system is completely independent of the form and dimensions of the Land, determined by means of the vertical astronomical line that indicates the direction of gravitation in the place of observation. The geocentric system is referred to center of the Land, represented by the ellipsoid, with what a valid only system of reference is adopted for all the observers situated in different places, so that its measurements turn out to be comparable, is the used in the ephemeris.

- The systems of coordinates of the different frameworks are convertible ones in other. Regularly the conversion covers the heavenly, geocentric, and topographical frameworks. The topographical system is the "observed", referred to terrestrial system of reference   and this rote with the Land. The geocentric system is used like intermediate system for the conversion. The heavenly system is one of the systems whose framework is considered fixed in the space.

- The Land revolves around the Sun along an orbit elliptic inclined in 23,5 degrees with respect to plan of the terrestrial Equator, with the Sun situated in one of the focus. The points of the terrestrial surface, from where the observations of the stars are done, move with respect to the stars, as a result of the movement of rotation of the Land. The stars seem to describe arc in direction east to west of the place. This apparent movement is named diurnal movement. In the North Pole and in the South Pole the stars describe parallel circles respect horizon and are always visible the same stars. In the Equator its paths are perpendiculars with respect to plan of the horizon, being visible all the stars. In the intermediate latitude among the Equator and the poles the sky with stars seems to rotate around the high heavenly pole, describing circles inclined respect horizon.

- The rotation of the Land tends to be uniform but presents three types of variations in its speed of rotation. Irregular that is aleatory fluctuations. Secular that consists of a constant decrease of the speed of rotation of the Land. Periodic according the stations.

- The orientation of the axis of rotation of the Land is animated of a movement of swinging and also oscillates the plans of the equator and of the ecliptic with respect to the average position of the stars. Two superimpose movements exist. One is movement the precession that consists of the displacement of the terrestrial axis in a cone in around to the axis of the ecliptic. Second is movement of nutation that consist of the movement oscillatory of the pole of the equator regarding the minor circle than the precession causes around of the pole of the ecliptic.

- The movement of the equinox due to the precession increases the heavenly lengths of all the stars at nearly 50" per year and affects harshly the latitude. The movement of nutation has amplitude nearby to 9” that is the sum of the components in length and obliquity. Also, the movement exists of precession of the equinox nearby to 12" for century on account of the small rotation of the plan of the ecliptic.

- Astronomical phenomena various exist that affect the direction in which the observations are performed and that should be corrected to obtain the true position of the stars. These phenomenas are: parallaxes that are the difference in the apparent direction of a star seen from two different locating. Aberration due to that the light possesses a finite speed, the direction in which a star is seen for an observer in movement does not correspond to the straight line among the observer and the star. Deflexion due to the action of the gravitation field of the Sun on the light or waves of radio, that curve its path and incremented its time of crossing. The refraction of light, the rays laser, or radio waves, in the terrestrial atmosphere.

- The orbits of the planets are established with respect to a heavenly system of ecliptic heliocentric coordinates, where the real orbit of the planet is projected on the heavenly sphere of radio vector unit. The position of a planet, in its elliptic orbit, remains determined by means of to set in the heavenly sphere: The position of the plan of the ellipse with respect to the of the ecliptic plane. The orientation of the ellipse according plan. The form and dimension of the ellipse.

- They are seven orbital parameters that specify the size, figure, and orientation of the orbit of the planet in the space and its position in a specific instant known as the epoch. These parameters are: 1 Length of the node ascending. 2 Inclination. 3 Argument of latitude of the perihelion. 4 Semi axis greater of the ellipse. 5 Eccentricity of the ellipse. 6 Moment of the step of the planet by the perihelion. 7 Period of revolution.

- In any instant the movement of a planet with the equations of Newton of the dynamics can be determined completely, named problem of two bodies. This is the simplest case than corresponds to the Keplerian ellipse and to a planetary system simplified to Sun and to a respected only planet as forming a remote system and its center of masses in rest or being moved to a uniform speed in the space.

- The calculation of the orbits of the planets is complicated extraordinarily when the planetary disruptions due to the presence of the other planets are considered. The rigorous integration of the equations of the movement for the Sun and two planets more, problem of the three bodies, was generalized for Sundman, by means of series convergent of powers, to n bodies.

- Other disruptions due to the planets that should be included in the calculations, when it wants to obtain very exact results, are, not sphericity symmetrical, density radial variation and distortion on account of the solid tides.

- Due to that the main force actuate is that of the Sun a procedure used to simplify the calculation of the orbits is to carry out in two phases. In the first one, the problem of the two bodies is resolved suppressing the presence of the other planets and considering the orbit done not disturb, or Keplerian orbit. In the second phase, the correction is done of that orbit by means of the inclusion of the disruptions that are small.

- At present, in the calculations of the movement of the planets and of the Moon are being included relativistic terms, not thus for the others satellite natural. For planets and Moon are used the named parameterized post-Newton equations.

- Two methodological approach exist in the calculation of the effects of the disruptions in the orbits of the planets, one is that of numerical integration of the movement of the stars and the other that of the general theories.

- The numerical integration is bases on the most adequate adjustment to the data observed by means of a process reiterative until reaching the representation of the observations with the degree of accuracy required.

- General, analytic, or numerical theories, that express the movement of the planets as function of the time.

- The observations of the planets and satellites covers the last 165 years. The majority of the observations correspond to the observation of the orbital step. Only in the most recent years observations have been obtained using other techniques as those of radio-radar, rays laser used in the Moon and spatial ships envoys to Mercury, Venus, and Mars.

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5. MODEL PRESENT

Nowadays the estimation of the ephemeris of the solar system is carries out by means of procedures developed by prestigious institutions of astronomy. One of the procedures that generate the ephemeris of the planets and the Moon was adopted like international standard in 1990. This procedure was done in the United States. The ephemeris standard is named DE200/LE200.

The ephemeris are obtained for a framework chosen applying the equations of movement in a space corrected with the General Relativity metric known as parameterized post-Newton. The equations are adjusted to the positions observed, using a general theory about the nutation.

In DE200/LE200 the framework of reference is based on the catalogue of stars FK5. The equations of movement are taken of the gravitational model presented by Newhall in 1983. The system of astronomical constant is the named IAU 1976. The theory of nutation is the IAU 1980.

The gravitational model under the numerical focusing of integration applies to each one of the planets utilizing a iterative method .

The observations before using them in the calculations of the ephemeris are submitted to a process of correction that is carried out under certain theoretical considerations defined according to the class to which the observations belong. The classes are: optical, radar, sonds, and laser.

The corrections that are prominent from the point of view of my theory about the presence of the effect of the speed of gravity in the observations are the corrections that are performed to the observations taken optimally. These are corrections of phase, day, and tendency. The correction of phase, that is bases on geometric considerations, can collect the effect of the speed of gravity that I maintain can exists in the positions pertaining to it register original. This effect theoretically is not considered for to adjust estimated positions to real positions. The effect of the speed of gravity I believe that is included by means of the empirical correction that are used in formulae.  

In DE200/LE200 the differences among the positions reckoned and positions observed after the correction are like maximum of a second arc. Utilizing the original formulae of Kepler the difference can reach to 600 second arc.

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5.1 Fundamental ephemeris

The fundamental ephemeris are the basic estimations of the positions and speeds of planets and other bodies of the solar system.

They are fundamental ephemeris because is the base to obtain:

- The orbital elements of the planets.

- The apparent ephemeris, that is to say, those that are referred to system of coordinates defined by the true equator of the Land and the equinox of the date.

- The representative ephemeris that are those for any date and time.

The fundamental ephemeris DE200/LE200 was built in the "Jet Propulsion Laboratory" in 1980. It is the result of:

1. To reorient the framework of reference of the ephemeris based on B1950, known as DE118/LE62, to framework based on J2000 .

The origin of the system of reference DE118 is approximately the FK4.

DE118 was rotated on its own dynamic equinox of 1950 to produce DE119.

DE119 was expressed in the epoch J2000 and rotated on its own equinox of J2000 to produce DE200.

2. To obtain the astronomical constant by means of the best adjustment to the data observed, using the technique of most minimum squares.

Some of the data correspond to observations of traffic obtained by the U.S. Observatory. Those observations appear in the framework FK4.

3. To integrate numerically the dynamic equations of the movement of the bodies of the solar system.

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5.2 Framework of reference

DE200/LE200 utilizes the FK5 that is a framework kinetic, that is to say almost-inertial, based on the stars. Its origin is linked to an equinox defined by the solar system. In practice the origin does not refer to a simple only point, therefore this referred to a meridian of ascension straight 0, that does not pass exactly through one of the given equinoxes by the ephemeris of the solar system and that not this on an only plan.

The origin of FK5 is defined like a catalogue of equinoxes in contrast with a specific equinox as origin of one of the ephemeris of the solar system, because of it knows like a dynamic equinox.

In the case of the ephemeris DE200/LE200 its origin in FK5 is very nearby to the frameworks of reference referred to sources of radio.

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5.3 Gravitational Model

The equations of the movement utilized in D200/LE200 include all the prominent forces that act in the solar system. A prominent force is the one that produces an effect observable and measure.

The model mathematician understands the following effects:

- That of the form of the Land and the Moon that is included in the long-term calculations, in order to achieve a greater accuracy. The mutual interaction among the forms of the Land and the Moon is ignored.

- The action of the terrestrial tides on the Moon. The tides bend the line Land-Moon producing a geocentric acceleration of the Moon.

- The librations of the Moon, that is to say, its movement oscillatory.

- The gravitational interactions among the nine planets, the Sun, the Moon, and the five asteroids: Ceres, Pallas, Dress, Iris, and Bamberga that have effects pronounced on the Land-Mars. These effects went discovered in the trips of the ships Mariner 9 and Viking.

The gravitational forces on the planets, Sun and natural satellites mentioned are model considering them like points of mass in the isotropic, parameterized post-Newton (PPN) metric for n-bodies (Will, 1974). This metric PPN includes the not linear superposition of the gravitation of the Sun and the planets and the curvature of the space produced by the mass of these.

The plan of reference is the half terrestrial equator of B1950.0. The axis x coincides approximately with the equinox 1950 of the catalogue FK4.

The equation of the acceleration of the point of mass for a planet

Subi is presented in the Equation 1.

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Equation 1.

´

ri = Σj#iµ j (sj - si) / [sj - si ]3 {1 - 2 (β + α) / c2 Σk#i µ k / [sk - si ]

- (2β - 1)/ c2 S k#j µ k [sk - sj ] + α([vi ]/c2) + (1 + α)([vj ]/c2)

- 2(1 + α) / c2 v i v j - 3 / 2c 2 {(s i - s j) v / [s j - s i ]2}

+ (sj - si ) rj / 2c2}α + 1 / c2 Σj#i µj / [sj - si ]3 α(si - sj )

+ [ (2 +2α)vi - (1 + 2α)vj ]α (vi - vj) + (3 + 4α) / 2c2

+ Σ j#i µj r j / [ s j - si ] + Σ5 m=1 µm (s m - s i) / s3im

Where:

si is the position barycentre of the star i in the solar system

vi is its speed

ri is its acceleration

Σ µj of the star j is the constant one of gravitation multiplied by the mass

ß it is the parameter PPN that measures the not linear superposition of the gravitation

α it is the parameter PPN that measures the curvature of the space

In the General Relativity

  ß=α=1

c is the speed of light

The variables with m refers to the asteroids.

The position of the asteroids not this integrated and the polynomials represent the heliocentric Keplerian ellipses.

The barycentre of the solar system is the formulated by Estabrook, in 1971, as:

Σ µ i {1 + [v i] 2 / 2c2 - 1 / 2c2 Σj#i µj / [s j - s i] } s i = 0

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5.4 Evaluation of the model of force

The model of force is resolved by means of numerical integration using the method of Adams. In each iteration, the integration covers:

1. Integral calculation of the position and speed of nine planets, the Moon, and the angles of librations.

2. Keplerian calculation of the position and the speed of asteroids.

3.      Relativistic correction of the mass for the planets, the Moon and the asteroids using the positions and speeds, calculated in the step 1.

Also it is fact for the mass of the Sun, but on the position and speed obtained in the iteration prior.

4. Calculation of the position and present speed of Sun regarding the barycentre of the solar system.

5. Calculation of the acceleration of the Sun.

6. Calculation of the acceleration of the nine planets and the Moon using the

Equation 1.

7. Calculation of the ephemeris of the Moon with regarding the Land.

8. Calculation of the acceleration of the angles of librations.

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5.5 Parameters

The numerical process of integration requires of the values of an set of parameters. Some they refer to the positions and initial speeds of planets and Moon that result of the adjustment, using the technique of most minimum squares, to the data observed. Other parameters, such as the masses, are external and although, some of them, as the mass of the system Land-Moon, can be obtained of the data, rarely are changed save when a statistically significant advantage can be obtained. A parameter obtained of the measurements performed with laser is that of the secular acceleration of Moon.

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5.6 Observations

Standish, 1990, it describes the data used in DE200/LE200. These are:

- Data observed optimally and used in the Jet Propulsion Laboratory (JPL), that originate of 39579 done registrations of traffic between 1911 and 1977 by the U.S. Naval Observatory (USNO) and 4790 plates taken, between 1973 and 1979, of Saturn and its satellites, by the University of Virginia, Leander McCormick Observatory. Also 386 observations are included, originating from the USNO about Neptune, taken among 1846-1974, and Pluto, taken among 1914-1974, that are supplied like corrections for length and latitude due to that for these planets does not count on an orbit complete which will know during the century XXII.

- Measurements carried out, between 1964 and 1977, by means of radar of the roundtrip time of the electromagnetic sign since a terrestrial station to Mercury and Venus. The time was measured using an atomic clock. The calculation includes the retard attributed to effect of the Relativity, according to the formula given by Shapiro, in 1964. It covers 362 observations of Mercury and 945 of Venus.

- Observations carried out, between 1973 and 1980, spatial from ships of Jupiter and Mars about distance, mass, and field of gravitation. It covers two observations of Jupiter and 1406 of Mars.

- Measurements performed, between 1969 and 1980, through laser of the Moon, from the McDonald Observatory, using any of the retro reflectors left by the ships Apollo 11, 14 and 15 and the Lunadhod 2. It covers 2954 observations.

The adjustment of most minimum squares esteems 175 parameters from the 50424 observations.

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5.7 Corrections

Depending on the technical one used for to obtain the observations are performed the corrections for to remove from the instrumental errors, to adapt them to the astronomical theories or to normalize them. The corrections that mainly are carried out are the following:

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5.7.1 Radar

The observations obtained by means of radar are base on the roundtrip time of the electromagnetic sign among the Land and Mercury or Venus. This time this affected by three types of retards due to the effects of:

- Relativity reckoned by Shapiro in 1964.

- Solar crown that is caused for the density of the electrons ionized. It was reckoned for Muhleman and Anderson in 1981.

- Troposphere of the Land analyzed by Chao in 1970.

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5.7.2 Sond

They are observations taken by spatial ships some in orbit of Jupiter and Mars and other on the surface of Mars. With posterity were transmitted through electromagnetic sign to the Land. These observations are affected by:

- The uncertainty in the decision of the orbit of the sond with relation to center of mass of the planet.

- The retards consider for the case of the observations taken by means of radar. Especially the uncertainty about the density of the ionization of the electrons of the solar crown for the signs by Mariner 9 send from Mars on account of that this planet was found in conjunction with the Sun.

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5.7.3 Laser

The observations obtained by means of laser of the Moon are very exact and its correction during adjust of most minimum squares owes to instrumental errors that accompany to each observation.

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5.7.4 Optics

The observations of traffic were obtained by means of telescopes and are of different nature that have to be expressed of such way that turn out to be comparable for which are transformed to system FK4 using the formulae of Schwan. The observations are published for the USNO and have to be presented in the catalogues of Washington in the concurrent epoch.

Prior to its use or publication the observations are submit to a process of correction of day, tendency, and phase.

The correction of phase is of fundamental importance for my theory on the effect of the speed of gravity in the observations due to that:

-  It adjusts the observations geometrically to the orbits that continue the planets.

- It utilizes phase correction formulae that are strictly empirical.

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5.7.4.1 Day

For each catalogue of Washington the observations obtained, among 1975-1977, during the diurnal hours, about the Sun, Mercury and Venus are corrected in function to the declination of the star and at the moment of the day.

The corrections are obtained resolving the following equations and removing their effect of said observations:

Ùa = A1 + A2 * senos

Ù>s = D1 + D2 * senos

Where:

s  is the decline of the star

A1 , A2 , D1, D2 are empirical quantities

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5.7.4.2 Tendency

The middle movement of the internal planets remains strongly determined by the adjustment of most minimum squares and its deviations with relation to the observations appears like the relation among the secular tendency and the residues. The analysis of the behavior of these residues in the time has permitted fully to show that they can be explained for the action combined of the lineal tendency of the scale of time of Brouwer, that for the reduction of the previous observations to 1959 it was adopted like standard, and the error of the precession constant of Newcomb. That is to say, such differences, when are important, are proper in part to incorrect values of precession and to an incorrect movement of equinox in the system of reference FK4. The USNO corrects these deviations by means of the following procedure:

- The changes in the secular tendency are model resolving the equations:

Ùa = (Ù>k + Ùn senoa * tans) * T50

Ù>s = (Ùn * cosa) * T50

Where T 50 is the previous time to 1950

These corrections it subtracts of the values observed of all the observations of traffic of the planets and the Sun.

- If it is assumed that the changes in the secular tendency are due only to errors of precession and change in the equinox then the equations are used:

Ùk = -E + Ùp * cose - Ù>l >

Ùn = Ù>p * senoe

Where:

E is the movement of the equinox

Ù> p is the correction to the lunisolar precession

Ù> l is the correction to the planetary precession

e is the value of the obliquity of the Land

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5.7.4.3 Phase

Before the publication of the observations the USNO carries out the correction of the effect of phase. This correction has its base on theoretical effects expected with relation to the orbital geometric situation.

Due to that for the USNO not this clear the origin of such effects it utilizes empirical formulae of adjustment chosen by "strictly empirical considerations". Nevertheless it thinks that they are able to originate of "effects of irradiation", that is to say, to the difference in solar radiation among planets and satellites by its distance inside the solar system, some of they appear dark. About this conjecture not any verification exists.

My theory by to introduce the effect of the speed of gravity as postulate of the astronomy of position considers that the telescopic observation of the position of a planet presents an retard in front of the position that the theory foresees. For example, when the gravitation interaction among the Sun and Mercury reaches the most maximum value, that is to say, in the position of perihelion, the theories of the planetary movement that do not include the effect of the speed of gravity will present a lag relating to the position of real perihelion that is obtained in the traffic register of Mercury.

This lag should be of delay, that is to say, the real position will result straggler with relation to it foretold. The ignorance of this phenomenon obliges that it have to introduce an empirical formula of correction of phase.

The empirical system of correction of phase that utilizes the USNO covers the following steps:

1. For the measurements of the center of light, for the planets of Mercury and Venus, the formula used is:

|Ùa> | |seno Q |

| | = s/r | | | [C0 + C1I +C2I2+ C3I 3]

| Ùs> | |coseno Q> |

 

Where:

I is the aforesaid angle of phase in units of 90 degrees (I = i/90)

Q is the angle of the position of the half of the edge visionary

i  is the angle of phase among the Sun and the Land, subtended in the star observed

C0, C1, C 2, C 3 are the resolved coefficients by means of the system of most minimum squares

The polynomial cubic expression is that of Lindegren, 1977.

2. For the other measurements of the illuminated planets Mercury and Venus, the original correction is used of the USNO and, additionally, the formula:

| Ùa> | |sine Q> |

| | = | | [L0 + L1I +L2I <2+ L3I <3]

| Ù>s | |cosine Q |

 

Where:

L0, L1, L 2, L3 are in arc seconds units.

3. For the four remaining lighting planets and one of the dark planets the original correction is used of the USNO and, additionally, the formula:

 

| Ùa> | |seno Q |

| | = | | Bk seno2i

| Ùs> | |coseno Q |

 

Where k = 4, 5,....., 8 for Mars, Land,.... , Neptune. This is empirical formula and can be compared with that of Chollet, 1984, that it was derived from physical considerations done by him.

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5.8 Landslides in the positions of the planets

The differences among the orbits of the stars calculated and the dynamic behavior of the real physical system can be owed to the following causes among others:

- Defects of the theory that, while, is not important the current correction added by the Relativity, in change if is very important the correction that necessarily should be done under the supposition that the gravitation spreads with a specific finite speed, since in the Newton´s theory the supposition unsustainable adopted is the instant action to distance of the gravitation and in the post Newton is ignored this problem.

So much, in the model of force of the numerical integration as in the general theories on the planets and satellites the speed of gravity is ignored.

- Unknown movements of the system of reference.

- Instability in the dynamic system.

- Errors in the parameters.

- Errors in the algorithms used in the calculations.

- Cumulative errors of truncate and redounded.

- Imperfect convergence of the algorithms.

- Changes in the coordinates.

- Reliability of the programs of the computer systems utilized.

- Errors in the instruments of registration of the observations.

The problem to determine which of these causes explain the differences found is of a great deal of difficulty and its analysis requires of a multidisciplinary effort.

The experimental error introduced in the observations manages to reduce by means of the repetition of the observations with the better techniques than the development permits.

In the case of the deficiencies in the theory have come devising general theories for the planets, the artificial and natural satellites that reduce the error in the forecasts that grow in direct proportion to the speed with which the stars orbit in the solar system, coming to be extreme in the case of the satellite Galileans of Jupiter. But in all the theories are omitted to consider the effect of the speed of propagation of the gravitation.

A special difficulty represent the parameters of the dynamic equations since appear some independent, that is to say, the parameters that previously were seen taken externally, and other whose numerical values depend on the observations and, consequently, are affected by the theoretical deficiencies and the experimental errors.

To determine in the numerical methods of integration the constant of integration, as could be established, is necessary to study during many years, in the past, to star to be able to predict its movement and to go reducing for successive approximations the discrepancies among the positions calculated and the positions observed.

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5.9 The precision reached

The precision in astronomy of position presents two extreme alternatives: the keplerian that throws the most maximum error in the estimation of the orbits of the planets and that of DE200/LE200 that minimizes them.

5.9.1 In keplerian astronomy of position

With the elements of the keplerian classical theory it was reached the more low precision in the astronomy of position.

Nevertheless, it supports important applications as are: programs of observation of the stars, to aim telescopes and prediction of certain phenomena that permit the good planning and design of the spatial missions of ships.

In the tables A and B the orbital elements are presented and the most maximum error on the period 1800-2050. If the extrapolation is done for extensive one more period the error can be substantially greater, which is characteristic of its low able of prediction.

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Table A. Orbital elements of the planets a, e, I according to the theory of classical Kepler

Planet

a

e

I

Mercury

 . 38709893

 . 00000066

 . 20563069

 . 00002527

  7.00487

-23.51

Venus

 . 72333199

 . 00000092

 . 00677323

-. 00004938

  3.39471

  -2.86

Land-moon

baryicentre

  1.00000011

  -. 00000005

 . 01671022

-. 00003804

  . 00005

-46.94

Mars

  1.52366231

  -. 00007221

 . 09341233

 . 00011902

  1.85064

-25.47

Jupiter

  5.20336301

 . 00060737

 . 04839266

-. 00012880

  1.30530

  -4.15

Saturn

  9.53707032

  -. 00301530

 . 05415060

-. 00036762

  2.48446

  6.11

Urano

19.19126393

 . 00152025

 . 04716771

-. 00019150

  . 76986

  -2.94

Neptune

30.06896348

  -. 00125196

 . 00858587

 . 00002514

  1.70817

  -3.64

Pluto

39.48168677

  -. 00076912

 . 24880766

 . 00006465

17.14175

  11.07

The elements are given in the epoch J2000 (JED 2451545.0) with regard to the ecliptic middle and equinox J2000. The angles are in degrees and its centennial proportions are in second arc for century

a is major semi axis of the ellipse

e is eccentricity

I is inclination

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Table B. Orbital elements the planets W, w, L according to the keplerian classical theory

Planet

W

w

L

Mercury

48.33167

-446.30

77.45645

573.57

252.25084

261628.29+415 rev

Venus

76.68069

-996.89

131.53298

-108.80

181.97973

712136.06+162 rev

Land-moon

baricentro

-11.26064

-18228.25

102.94719

1198.28

100.46435

1293740.63+99 rev

Mars

49.57854

-1020.19

336.04084

1560.78

355.45332

217103.78+53 rev

Jupiter

100.55615

1217.17

14.75385

839.93

34.40438

557078.35+8 rev

Saturn

113.71504

-1591.05

92.43194

-1948.89

49.94432

513052.95+3 rev

Urano

74.22988

1681.40

170.96424

1312.56

313.23218

246547.79+1 rev

Neptune

131.72169

-151.25

44.97135

-844.43

304.88003

786449.21

Pluto

110.30347

-37.33

224.06676

-132.25

238.92881

522747.90

The elements are given in the epoch J2000 (JED 2451545.0) with regard to the ecliptic middle and equinox of J2000. The angles are in degrees and its centennial proportions are in second arc for century

W is length of ascension

w is length of the perihelion

L is average length

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Table C. Most maximum errors from the formulae of classical Kepler

Planet

Ascensión straight

Decline

Distance

 

Arc

"

1000

Km

Arc

"

1000

Km

Arc

"

1000

Km

Mercury

  20

   6

  5

   1

  5

    1

Venus

  20

  10

  5

   2

  20

   10

Land

  20

  15

  5

   4

  20

   15

Mars

  25

  25

  30

  30

  40

   40

Jupiter

300

1000

100

  350

200

  600

Saturn

600

4000

200

1400

600

  4000

Urano

  60

  800

  25

  400

125

  2000

Neptune

  40

  800

  20

  400

100

  2000

Pluto

  40

1100

  10

  250

  70

  2000

The covered lapse is 1800-2050. The system of reference is heliocentric and the system of coordinates is the equatorial absolute system.

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5.9.2 In astronomy of position based on DE200

The most minimum error at present is reached, in astronomy of position, with DE200/LE200 that, also, covers the period 1800-2050, that is to say, 250 years, and is adjusted to an important number of observations achieved optimally, by means of radar, laser, and spatial ships. The error is smaller than 1, often a great deal smaller, second arc.

But, this high degree of precision for the planets in part is reached including the empirical corrections of phase.

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5.10 Conclusions

- There are several classes of fundamental ephemeris: apparent and representative. The fundamental ephemeris is the basic estimations of the positions and speeds of the planets and other bodies of the solar system that serve for the estimation of the other ephemeris.

- DE200/LE200 is the procedure adopted in the world like standard for the generation of the fundamental ephemeris. DE200/LE200 utilizes like framework the FK5 that is almost-inertial and is referred to a dynamic equinox. Its origin is very nearby to the frameworks of reference referred to sources of radio.

- DE200/LE200, for the estimation of the movement of the planets,

Sun and natural satellites, utilizes a system of equations that includes all the prominent forces that act in the solar system. A prominent force is the force that produces an effect that can be observed or to be measured. These forces are model considering the stars as points of mass in the isotropic space, with metric Einsten for n-bodies. This metric one includes the not linear superposition of the gravitation of the Sun and the planets and the curvature of the space produced by the mass of these.

- The solution of the previous model of force is carried out by means of numerical integration.

- The numerical process of integration requires of the values of an assembly of parameters. Some they refer to the positions and initial speeds of the planets and the Moon that result of the adjustment to the data observed, using the technique of most minimum squares. Other parameters are assigned externally as are the values of the masses of the planets.

- The adjustment of most minimum squares esteems 175 parameters from 50424 observations that cover the lapse of 1846-1980. These observations were registered 44755 with telescope, 1307 with radar, 1408 with spatial sonds and 2954 with laser.

- The observations are submitted to a process of correction that is carried out by means of technical dependents of as that were obtained. The correction of the observations is carries out to remove from the instrumental errors, to adapt them to the astronomical theories or to normalize them.

- For my theory that maintains the existence of the effect of the speed of gravity in the observations interests a class of correction. This is the correction of phase due to that adjusts the observations geometrically to the orbits that continue the planets utilizing formulae of correction that are strictly empirical.

- The position of the stars obtained of the observations does not coincide with the position reckoned with the formulae of the heavenly mechanics. This phenomenon is of landslide and can originate of different causes. My theory attributes to effect introduced by delay of the gravitation like one of those causes, which not this included in the present models of planetary movement.

- In astronomy of position the most maximum errors are produced with the equations of Kepler. The most minimum errors are achieved with DE200/LE200 although covers the correction of phase that lacks of a theory that explain it.

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6 PROPOSAL TO MEASURE THE SPEED OF GRAVITY

According to my theory the ephemeris of the planets present the error of not including the effect of the speed of gravity. This error causes mainly the advancement in the time of the effect of the force of gravitation of the Sun in the orbit of the planets due to the theoretical deficiency that does not know the speed with which the gravitation interaction occurs. Said effect really occurs a time later, that is to say, the speed of gravity produces a delay in the planetary positions based on the behavior of the gravitation interaction. The advancement is the consequence to suppose the instant action of the gravitation and, by consequence, to ignore its speed in the equations of movement.

The gravitation interaction changes continuously in inverse relation of the distance among the Sun, and the planets. The gravitation interaction is, known as force of gravitation. The intensity of the force of gravitation remains defined according to the position that the planets occupy in every single moment inside the travelled through of their orbits. Such maximum intensity occurs in the position of perihelion that is to say, of most maximum approach of a planet to the Sun. The gravitation interaction decays its intensity from this position of perihelion until reaching its most minimum value when the planet occupies the position of aphelion, that is to say, of most maximum distance regarding the Sun. The intensity of the force of gravitation grows among the aphelion and the perihelion. These changes that occur permanently in the gravitation interaction it communicates with the speed of gravity.

The theories of Newton, of the Relativity and post Newton on the orbits of the planets do not consider the effect of the speed of propagation of the gravitation which equals than supposing it infinite. The models of movement of the planets and satellites, derived from these theories, advance in the time the position that should reach the star in its orbit in function by gravitation force actuate on star in every single moment. This advancement constitutes a landslide of the star that will be detected for to observe the step of the star and to compare it with the position that should have according to the theory.

The landslide that presents the stars on account of the gravitation propagation will be inversely proportional to the magnitude of the speed of the gravitation. If this speed is immensely large the difference among the position calculated based on ignoring it will tend to coincide with the position observed to step of the star. If the speed of gravity is equal to speed of light the difference is large. The exercise to reckon the landslide of the done planets under the supposed previous thus shows it.

The landslide for any star that continue a elliptic orbit defines a function that takes decreasing values among aphelion and perihelion positions and growing among this and aphelion. The difference among the most minimum and most maximum values of said function will be greater according to the greater eccentricity that present the ellipse.

The landslide also determines another function that is it defined among planets. In this case the maximum landslide is for Mercury and decreases in the order of the planets in the solar system. The minimum landslide is for Pluto.

The functions of landslide can be obtained by means of the method of most minimum squares. For the position of perihelion have found a function that generates the values of the landslide of the planets.

This function constitutes an important tool to reckon the speed of the gravitation from the positions observed corrected in tendency and day. The correction that for this purpose does not fit to cause is that of phase since can collect exactly the proper error of the effect of gravitation.

In astronomy of position the most maximum errors that are committed in the estimation of the orbits of the planets originate of the keplerians equations. If these errors are compared with the originated in the effect of propagation of the gravitation, assigning it the speed of light is tested that this advanced of Einstein is false. The gravitation possesses a greater speed.

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6.1 DE200-LE200 is partial

DE200-LE200 does not include the effect of the speed of gravity in the gravitation interaction interplanetary. This interaction should occur with a specific finite speed that should to be able to detect due to the large existing distances among the planets also among these and the Sun.

The most minimum distance interplanetary is the existing distance among the Sun and the position of perihelion of Mercury near of 46 million kilometers, that the light delays in travelling through 3.88 minutes. In that time Mercury advances 25.9 seconds of arc. Supposing that the speed of gravity is equal than speed of light the perihelion of Mercury would be presented run in those 25.9 arc seconds in the moment in which the most maximum value of its gravity interaction occurred with the Sun.

The constant of integration through the empirical formulae of correction of phase in my opinion are able that they compensate the effect of the communication of the gravitation that it does not included in the gravity model pertaining to DE200-LE200. This deficiency is general of all the models that are used at present.

The purpose of the astronomy of position is to set the direction of the heavenly bodies and not its distance that is stranger, for many applications of this discipline. When the position of the stars is considered projected on the conventionally heavenly sphere of radio unit, the distance does not include in the equations of position.

But the time spent by the gravitation in being communicated among the stars will produce in their positions calculated differences that should appear when are compared with positions observed. Due to that the model of gravitation is partial, these differences have to be empirical adjusted by means, I believe, of the constant of integration of correction of phase. Before me nobody fallen in account of this fundamental error.

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6.2 The landslide

The landslide I define it like the difference in the position calculated of a planet considering the instant effect of gravitation and the same position reckoned from the inclusion of the effect of gravitation occurring with a specific speed.

Under the supposition that the effect of gravitation of the Sun on a planet is maximum in the perihelion and most minimum in the aphelion I reckoned the landslides utilizing the following procedure:

1. According to sidereal revolution, that is to say, the time that the planets spent in one complete orbit around the Sun, I calculated the time average spent by the planets in travelling through a second of arc.

2. For aphelion and perihelion positions I estimate the time that the gravitation delays in being spread among the Sun and each planet supposing, as it does the majority of the physical contemporaries, that the gravitation has the same speed of light.

3. For each planet I estimate its advance in seconds of arc, that should be presented in aphelion and perihelion positions, resolving the rule of three that relates the time spent by the planet in travelling through a second of arc with the time that the gravitation of the Sun spends in being communicated to planet.

The statement of said rule of three is: If the planet spends certain time in travelling through a second of arc, ¿How seconds of arc will travel the planet in the time that delays the gravitation of the sun in reaching it?

4. The advance that I estimate for each planet relates it to the position that the planet would have in the case that the gravitation spread instantly. This relation is only to express said advance as relative landslide with relation to that position.

Besides, for the planets I calculate the landslide among aphelion and perihelion positions, what permits to predict the change that will be produced in the position from a planet with relation to the positions observed in such instants.

In the Table 1, I presented for the planets of the solar system the landslides in second arc that are proper by not to include the effect of the speed of gravity , in the calculation of the orbital position of the stars. This speed is supposed equal than the speed of light.

For the case of the Land due to that heavenly latitude of the Sun is always 0 degrees and its length enlarges from zero, in Aries, to 360 degrees, the landslides for the aphelion and the perihelion correspond exactly to landslides of length.

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Table 1. Landslide of the planets due to the speed of gravity

(Second of arc)

Planet

Ahelio

Perihelion

Difference

Mercury

38,80

25,90

  13,24

Venus

24,20

  23,91

  0,28

Land

20,82

  20,15

  0,68

Mars

18,14

  15,04

  3,10

Jupiter

9,43

  8,56

  0,87

Saturn

7,11

  6,36

  0,75

Urano

4,90

  4,46

  0,44

Neptune

3,78

  3,72

  0,065

Pluto

4,07

  2,45

  1,62

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6.3 Characteristics of the landslide

The maximum landslide of the planets is for Mercury, that is the most nearby planet of the Sun and most minimum for Pluto that is the most distant planet of the solar system. The landslide of the planets decreases among Mercury and Pluto.

If the evolution of the landslide is observed for any of the planets among the instants of the aphelion and the perihelion a periodic movement is established, equal to the half of the time of the sidereal revolution. The landslide is maximum in the aphelion and most minimum in the perihelion. The greater difference of the landslide among the aphelion and the perihelion presents it the orbit of Mercury with 13.24 seconds of arc.

The landslide of the planets, for analysis, breaks down in the factors of distance and sidereal revolution and it omitted the speed with which spreads the gravitation.

This factors are very important for to obtain from the observations of the positions of the planets the function of correction of the landslide that is attributable to the propagation of the gravitation. The factors that result are:

- Factor in direct function to the distance among the Sun and the planets. This it can be expressed taking like unit the distance among Sun-Mercury. The result is shown in the Table 2.

- Factor in inverse function to the time that the planets spend in travelling through a second of arc. This it can be expressed taking like unit the time spent by Mercury. The result is shown in the Table 3.

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Table 2. Factor distance

(Unit of distance: Sun-Mercury)

Planet

Ahelio

Perihelion

Mercury

   1

  1

Venus

   1,55743

  2,30622

Land

   2,17832

  3,15665

Mars

   3,56961

  4,43326

Jupiter

  11,6882

  15,8942

Saturn

  21,57648

  28,91824

Urano

  43,04583

  58,68433

Neptune

  64,9652

  95,66728

Pluto

  105,72472

  95,31974

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Table 3. Factor in inverse function to time that spends a planet in travelling through a second of arc

(Unit: time spent by Mercury)

Planet

Time in travelling through an Arc"

Mercury

  1

Venus

 , 4004

Land

 , 2463

Mars

 , 1310

Jupiter

 , 0208

Saturn

 , 0085

Urano

 , 0029

Neptune

 , 0015

Pluto

 , 0010

The two previous factors can unite through multiply and to express them in a function that has like coefficient the speed of gravity. This function serves to correct the landslide that presents the planets. The values that take the function of correction of the landslide in the aphelion and in the perihelion are shown in the Table 4 and in the Graphic 14.

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Table 4. Values of the function of correction of the landslide the planets (Pattern: Landslide Mercury)

Planet

Ahelio

Perihelion

Mercury

  1

  1

Venus

 , 623594

 , 92341

Land

 , 53652

 , 777482

Mars

, 467618

 , 580757

Jupiter

, 243114

 , 330599

Saturn

 , 1834

 , 245805

Urano

 , 124832

 , 170184

Neptune

 , 097447

 , 1435

Pluto

 , 105724

 , 095319

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Graphic 14. Behavior of the landslide

 

6.4 Function of correction of the landslide

For each position of the planets, during the travelled through of its orbit, a function of generation of the value of the displacement of the position can be obtained, when is include the effect of the speed of gravitation, with relation to the position calculated without that effect.

For the position of perihelion I estimate a function of correction of the planetary landslide utilizing the method of most minimum squares. This is the following function:

ΔC = (-0,0093231077 * P4 + 0,2097699233 * P3 - 1,521220407 * P2 + 2,890163388 * P + 6,199866622) / G

Where:

ΔC is the landslide in seconds of arc

P is the number of the planet in the solar system: Mercury 1,

  Venus 2, Land 3, Mars 4, Jupiter 5,. . , Pluto 9

G is the speed of gravity

This function has an r square greater that, 99. Nevertheless it is possible to obtain functions with an r even better.

In the Table 5 is compared the planetary landslides that I calculated under the supposed one that the speed of gravity is of 300 thousand kilometers by second with planetary landslides that I reckoned with the previous function.

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Table 5. Comparison of the landslide of the planets according to the position of perihelion

(Second of arc)

Planet

Landslide

Function

Difference

Mercury

25,90

25,90

0,00

Venus

23,91

  24,75

  -0,84

Land

20,15

  20,29

  -0,14

Mars

15,04

  14,87

  0,17

Jupiter

8,56

10,05

  1,49

Saturn

6,36

6,68

-0,32

Urano

4,46

  4,86

  -0,40

Neptune

3,72

  3,93

  -0,21

Pluto

2,45

  2,49

  -0,04

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6.5 Comparison of the errors of Kepler and that of gravitation

The most maximum errors that are committed in the astronomy of position applied to solar system, as was established previously, originate of the calculation of the orbits of the planets from the equations of movement of Kepler. These errors are compared, in the Table 6, with the most maximum error that I have reckoned would cause the effect of propagation of the gravitation, under the supposed one that possesses a speed equal than the speed of light. The most maximum error occurs for the estimation of the position of the aphelion of the planets.

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Table 6. Most maximum errors from the keplerian classical formulae compared with the most maximum error attributable to effect of gravitation

Planet

Most maximum errors using the equations of Kepler

Most maximum error attributable to the gravitation

 

Ascensión straight

Arc "

Decline

Arc "

Arc "

Mercury

  20

   5

38,80

Venus

20

5

24,20

Land

20

5

20,82

Mars

25

30

18,14

Jupiter

300

100

9,43

Saturn

600

200

7,11

Urano

60

25

4,90

Neptune

40

20

3,78

Pluto

40

10

4,07

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6.6 Analysis of the results

The landslide is directly proportional to the distance and inversely to the sidereal revolution.

The landslide will tend zero when the speed of gravity tends to infinite.

The landslide that results to consider the gravitation being spread with a speed equal than speed of light for the planets: Mercury, Venus and the Land turns out to be significantly greater that the errors in ascension straight and declination that I reckoned with the equations of Kepler that are the most maximum errors that are committed in astronomy of position. This it shows unmistakably that the speed of gravity surpasses speed of light.

In the case that to arise an explanatory theory of the constant that correct the error of phase of the optic observations even would remain for explaining the error of the ephemeris DE200/LE200 that arrives to one second arc. Then it should be expected that the speed of gravity surpassed the 7 millions of kilometers by second. Thus speed of gravity greater than 23.3c.

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6.7 Formula for to calculate the speed of gravity

To ascertain the speed of gravity can be used the following formula:

G = d / (Δc * r)

Where:

G is the speed of gravity

d is the distance, in kilometers , among a planet and the Sun, in a moment specific, for example, in the aphelion or in the perihelion