THE GRAVITY
Version 2.0
ALFONSO
LEON GUILLEN GOMEZ
All reserved rights
SANTAFE OF
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 19941995. 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
2. Proposed for to measure the speed of gravity according tides,1993.
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
TABLE OF CONTENT
1.1 Criticism of
the theory of the Relativity
1.2 Quantum Theory
of the gravitation
1.3 Speeds greater
that speed of light
2.3 Mechanical of
Newton and Euclidean space
3.1 Traditional
system of fixation of the time
3.2 The expressions
of the time
3.3 Differences and conversions
4.5 Transformations
among heavenly and terrestrial coordinates
4.7 Effects of the
position and movement of the stars and the observer
4.8.3 Movement in
systems of two bodies
4.8.4 Extension at
more than two bodies
4.8.8 Approach used
in the calculation of the effects of the disruptions
5.4 Evaluation of
the model of force
5.8 Landslides in the positions of the planets
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
6 PROPOSAL TO
MEASURE THE SPEED OF GRAVITY
Table 1. Landslide
of the planets due to the speed of gravity
6.3
Characteristics of the landslide
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
6.7 Formula for to
calculate the speed of gravity
Table 1. Landslides
of the planets
"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 bigbang as
well as to predict its future that can be bigcrunch.
Nevertheless, we are far from understanding
fully the gravitation. The most recent questioning about its origin, speed
and nature quantumwave 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
fiveyear 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.
Press here for
return to table of content
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, as a gravitonwave 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
waveparticle or corpusclewave (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, 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.
Press here for
return to table of content
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, 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, 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, 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, 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 Special Relativity considers the space built from rigid bodies, and in General Relativity from mollusc bodies but 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 nonrigid 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 particlewave or wavecorpuscle.
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 (TGUSupergravity) 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 Earth, 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 Earth.
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, the existence in the gravity field of
"excitements ". In this manner the structure wavegraviton 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
accelerationsdecelerations 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.
Although, in Modern Relativity, relativistic mass is considered a mistake since the mass of the particles is constant, that is, during the time that a particle exists its mass is the same, it has not been eliminated like the recognized physicists Philip Gibbs ( 1997), Jim Carr (1998) and Don Koks (2012) manifest at Physics FAQ because relativistic mass continues to be useful. Undoubtedly, inertia increases with speed, tested on particle accelerators. Einstein in "Physics, adventure of thought" wrote: "A body at rest has mass but no kinetic energy, that is, energy of movement. A moving body has mass and kinetic energy. It resists change to movement more strongly than the body at rest. Everything happens, then, as if the kinetic energy of a body increases its resistance. " How? We do not know yet. However, our current models and ability to measure are consistent with the thesis of many physicists eliminating the relativistic mass. Einstein, in this work, also considered gravity as a nongeometric phenomenon but of energy, unifying matter and field only differentiated quantitatively, when he wrote: "Matter is the place where the concentration of energy is very large and the field is where the energy concentration is small", but he warned is a matter of future resolve. Also, it is question of future to establish the masses of the photon and graviton whose limit imposed for the mass of the photon is <.18 × 10 ^{53} kg and for the mass of the graviton is <1.6 × 10 ^{69} kg. But according to current standard values the mass of the photon and gluons is zero while the graviton is a theoretical particle. However, for the author, whose vision is in the future, having mass the photon its speed in the vacuum is 300 thousand km / s, therefore, the speed of the graviton with mass much smaller than photon its speed must be greater (thesis formulated in 19691970).
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, 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. 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 Nobel 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, the
bosones W+, W and Z_{0} 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 fissionfusion by
excellence conversions occurs among massenergy.
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 (spacelike 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, 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, Einstein would have discovered the double
character wavequanta 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 Nobel 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, 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, as
material.
(4) Very near the absolute zero of Kelvin
exists the state condensed of BoseEinstein. 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, 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
BoseEinstein 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 PoundRebka 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 BoseEinstein 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 EinsteinBose. 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 Earth. 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 BigBang 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 BigBang?. And which was the material content of spacetime at moment BigBang?. I respond the speed of material was closed to infinite speed and material was supergravity according with BigBang 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 19691970 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 19691970.
(10) A positive potential gravity reduces the speed of photons opposite to particles. This action of gravity on light violates conservation of the momentumenergy, according Paul Marmet.
Press here for
return to table of content
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, 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 bigbang, 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, 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, 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, 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 02 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 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 posteinstenian 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.
Press here for
return to table of content
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, that possesses
mass and exists in the spacetime. The matter, in physics, is really the
substance that equal to field has a structure granularwave, 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 W_{0}, 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
Nobel. In 1983 Carlos Rubbia and Simon Van der Meer, that went experimental
discoverers, also gained the Nobel. 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 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
MichelsonMorley, that is, 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, 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, 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 almostspherical 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, 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 EinsteinBose, 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.
Press here for
return to table of content
Among 19911993 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 Earth 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 Earth, 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 Earth. In sicigias, moments of conjunction and
opposition, such forces operate on the same straight line and the resultant
is maximum force on the Earth. 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 Earth 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 Earth 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.
Press here for
return to table of content
 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 almoststatic 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, 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 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
quantawave 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, 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, 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, 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, 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 MichelsonMorley 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 Earth.
 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 Earth. In sicigias, moments of conjunction and
opposition, such forces operate on the same straight line and the resultant
is maximum force on the Earth. 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 Earth 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.
Press here for
return to table of content
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 physicalmathematics 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, 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 Earth 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
postNewton 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.
Press here for
return to table of content
The description cinematic, that is, 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, 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 threedimensional 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 actionreaction.
 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 Â± 0,0031) . 10^{11} m^{3} 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.
Press here for
return to table of content
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 twodimensional
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 10^{23} 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 Earth. Although
the curvature of the path of the object is appreciated, with every clarity,
certain are that it turns out to be very small.
Press here for
return to table of content
The formulae of the dynamics of
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 NewtonÂ´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 Earth.
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.
Press here for
return to table of content
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 almostinertials.
One of such finite regions is that of the
EarthMoon 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 Earth 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.
Press here for
return to table of content
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
FaradayMaxwell 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 4dimensions 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. Â¿How, this occurs?
Einstein did not explain. Einstein doubted about spacetime nature between geometric
pure and energetic medium. Â¿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.
Press here for
return to table of content
 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
NewtonÂ´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 Earth.
 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 Earth 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.
Press here for
return to table of content
The time is considered absolute. Along many
years were measured using astronomical techniques that refer the movement of
the Earth 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 Earth 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.
Press here for
return to table of content
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,
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 Earth.
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}.
Press here for
return to table of content
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 Earth 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 Earth 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, 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 Earth 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, 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 Earth. A true solar day is on the average, three minutes fiftysix 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 Earth 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
Earth 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.
Press here for
return to table of content
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, 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.
Press here for
return to table of content
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,
365,256361 days solar medias.
The time elapsed among two consecutive steps of
the Sun by the equinox of spring, point Aries; that is, 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, 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.
Press here for
return to table of content
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.
Press here for
return to table of content
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, 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.
Press here for
return to table of content
 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 Earth. 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
 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, a Julian century and B1900.0
corresponds exactly to the date 1900 January .5. The new version is indicated
with the suffix J.
Press here for
return to table of content
For the purposes of the astronomy of position
is necessary to understand the three following aspects:
 The Earth 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 Earth 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 Earth, 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 Earth 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 Earth 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 Earth is
specified in geocentric coordinates referred to ellipsoid, that rotes with the
Earth, 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,
threedimensional. 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 Earth 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.
Press here for
return to table of content
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 Earth.
 Geocentric referred or measured with relation to
center of the Earth.
 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.
Press here for
return to table of content
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 twentyfourth 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.
Press here for
return to table of content
For an observer situated on the surface of the
Earth, 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 Earth 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 Earth, 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 eastwest.
 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 Earth.
 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 0
degrees, corresponds to heavenly south and enlarges in the direction of the
movement of the needles of the clock, in sense eastwest, 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, depends on the geographical
position of the observer. Besides, the movement of the Earth 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 Earth. The star maintains fixed when the telescope it
orients with specific declination and it does rotate with angular speed of
diurnal movement of the Earth (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, point Aries, carries out a complete turn to day with respect to observer.
The coordinates
of a star, that is, 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 Earth.
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
in sense westerneast.
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 Earth, 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 Earth 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
Earth.
Press here for
return to table of content
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 Earth. 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 Earth. Nevertheless, Earth 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 Earth, 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 Earth, 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 Earth that passes for the poles, due, mainly, to the
irregular distribution of the masses in the interior of the Earth.
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 Earth.
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 Earth, 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.
Press here for
return to table of content
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 Earth. 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
anglematrix 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.
Press here for
return to table of content
The Earth 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 Earth 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,
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 Earth
The plan that contains the orbit of the Earth 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 Earth
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 Earth. 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 Earth 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 Earth tends to be uniform
but presents three types of variations in the speed of rotation that are:
 Irregular, that is, 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 Earth, 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
Earth 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.
Press here for
return to table of content
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 Earth 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, 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 Earth. For the stars the line of change is
the astronomical unit of distance (AU) or the middle radio of the orbit of the
Earth 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.
Press here for
return to table of content
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
lighttime; 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
lighttime 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 Earth, 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 lighttime and the secular component are indistinguishable
and is equal to the movement of the star multiplied by the factor lighttime.
Only in very precise calculations for the stellar aberration the formulae are
used of the Special Relativity.
Press here for
return to table of content
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.
Press here for return
to table of content
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.
Press here for
return to table of content
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.
Press here for
return to table of content
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,
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.
Press here for
return to table of content
The movement of daily planet middle, in its
orbit, can be determined using the equation:
n
= 2Pi/P =
k (1+m/a^{3/2}) ^{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
Press here for
return to table of content
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/r^{3}
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/r^{3}
Where:
k is the Gaussian constant of
gravitation
Press here for
return to table of content
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.
Press here for
return to table of content
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.
Press here for
return to table of content
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.
Press here for
return to table of content
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 postNewton (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.
Press here for
return to table of content
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.
Press here for
return to table of content
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.
Press here for
return to table of content
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
19701992 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.
Press here for
return to table of content
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:

RadioRadar.

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 Earth, the Moon, Mars, Venus, and Jupiter with an error even
in a hundred meters.
Press here for
return to table of content
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.
Press here for
return to table of content
 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 Earth, 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 Earth, 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 Earth.
The systems of coordinates used are geodesic, astronomical, and geocentric systems. The
geodesic system depends on the form and dimensions of the Earth 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 Earth, 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 Earth,
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 Earth. 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
Earth 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 Earth. 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 Earth 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 Earth. Periodic according the stations.
 The
orientation of the axis of rotation of the Earth 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 postNewton 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 radioradar, rays laser
used in the Moon and spatial ships envoys to Mercury, Venus, and Mars.
Press here for
return to table of content
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 postNewton. 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.
Press here for
return to table of content
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, those
that are referred to system of coordinates defined by the true equator of the
Earth 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.
Press here for
return to table of content
DE200/LE200 utilizes the FK5 that is a
framework kinetic, that is almostinertial, 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.
Press here for
return to table of content
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 Earth and the Moon that is included in the longterm calculations, in order to
achieve a greater accuracy. The mutual
interaction among the forms of the Earth and the Moon is ignored.
 The action of the terrestrial tides on the Moon. The tides bend the line EarthMoon
producing a geocentric acceleration of
the Moon.
 The librations of the Moon, that is,
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 EarthMars. 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 postNewton (PPN) metric for
nbodies (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.
Press here for
return to table of content
r_{i} = Σ_{j#i}µ _{j} (s_{j} 
s_{i}) / [s_{j}  s_{i} ]^{3}
{1  2 (β + α) / c^{2} Σ_{k#i} µ _{k} / [s_{k}  s_{i} ]
 (2β  1)/ c^{2} S _{k#j} µ _{k} [s_{k } s_{j} ] + α([v_{i} ]/c^{2}) + (1 + α)([v_{j} ]/c^{2})
 2(1 + α) / c^{2} v _{i}
v _{j}  3 / 2c ^{2} {(s _{i}  s _{j}) v / [s _{j}  s _{i} ]^{2}}
+ (s_{j}  s_{i }) r_{j} / 2c^{2}}α + 1 / c^{2} Σ_{j}_{#}_{i}
µ_{j} / [s_{j}  s_{i }]^{3}
α(s_{i}  s_{j}
)
+ [ (2 +2α)v_{i}  (1 + 2α)v_{j} ]α (v_{i }  v_{j}) + (3 + 4α) / 2c^{2}
+ Σ _{j#i} µ_{j }r _{j } / [ s _{j}  s_{i} ] + Σ^{5 }_{m=1} µ_{m} (s _{m}  s _{i}) / s^{3}_{im}
Where:
s_{i} is the position barycentre of the star i in the solar system
v_{i} is its speed
r_{i} is its acceleration
Σ µ_{j} 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} / 2c^{2}  1 / 2c^{2} Σ_{j#i} µ_{j} / [s _{j}  s _{i}]
} s _{i} = 0
Press here for
return to table of content
_{ }_{}
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 Earth.
8. Calculation of the
acceleration of the angles of librations.
Press here for
return to table of content
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 EarthMoon, 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.
Press here for
return to table of content
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 18461974, and Pluto, taken among 19141974, 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.
Press here for
return to table of content
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:
Press here for
return to table of content
The observations obtained by
means of radar are base on the roundtrip time of the electromagnetic sign among
the Earth 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 Earth analyzed by Chao in 1970.
Press here for
return to table of content
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 Earth.
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.
Press here for
return to table of content
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.
Press here for
return to table of content
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.
Press here for
return to table of content
5.7.4.1 Day
For each catalogue of Washington
the observations obtained, among 19751977, 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:
Ã™a = A1 + A2 * senos
Ã™>s = D1 + D2 * senos
Where:
s
is
the decline of the star
A1 , A2
, D1, D2
are
empirical quantities
Press here for
return to table of content
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,
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:
Ã™a = (Ã™>k + Ã™n senoa * tans) * T50
Ã™>s = (Ã™n * 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:
Ã™k = E + Ã™p * cose  Ã™>l >
Ã™n = Ã™>p * senoe
Where:
E is the movement of the equinox
Ã™>
p
is the correction to the lunisolar precession
Ã™>
l
is the correction to the planetary precession
e
is the value of the obliquity of the Earth
Press here for
return to table of content
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
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, 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, 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:
Ã™a>  seno Q 
  = s/r    [C0 + C1I +C2I2+ C3I 3]
 Ã™s>  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 Earth, 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:
 Ã™a>  sine Q> 

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

Ã™>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:
 Ã™a>  seno Q 
  =   Bk seno2i
 Ã™s>  coseno Q 
Where k = 4, 5,....., 8 for
Mars, Earth, .... , Neptune. This is empirical formula and can be compared with
that of Chollet, 1984, that it was derived from
physical considerations done by him.
Press here for
return to table of content
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 NewtonÂ´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, 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.
Press here for
return to table of content
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.
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
18002050. 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.
Press here for
return to table of content
Planet 
a 
e 
I 
Mercury 
. 38709893 . 00000066 
. 20563069 . 00002527 
7.00487 23.51 
Venus 
. 72333199 . 00000092 
. 00677323 . 00004938 
3.39471 2.86 
Earthmoon 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
Press here for
return to table of content
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 
Earthmoon 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
Press here for
return to table of content
Planet 
AscensiÃ³n 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 
Earth 
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 18002050. The system of reference is
heliocentric and the system of coordinates is the equatorial absolute system.
Press here for
return to table of content
The most minimum error at present is reached, in astronomy of position,
with DE200/LE200 that, also, covers the period 18002050, that is, 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.
Press here for
return to table of content
 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 almostinertial 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 nbodies. 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 18461980. 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.
Press here for
return to table of content
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, 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, 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, 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.
Press here for
return to table of content
DE200LE200 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 DE200LE200. 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.
Press here for
return to table of content
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, 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, Â¿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 Earth 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.
Press here for
return to table of content
(Second of arc)
Planet 
Ahelio 
Perihelion 
Difference 
Mercury 
38,80 
25,90 
13,24 
Venus 
24,20 
23,91 
0,28 
Earth 
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 
Press here for
return to table of content
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 SunMercury. 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.
Press here for
return to table of content
(Unit of distance: SunMercury)
Planet 
Ahelio 
Perihelion 
Mercury 
1 
1 
Venus 
1,55743 
2,30622 
Earth 
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 
Press here for
return to table of content
(Unit: time spent by Mercury)
Planet 
Time in travelling through an Arc" 
Mercury 
1 
Venus 
, 4004 
Earth 
, 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.
Press here for
return to table of content
Planet 
Ahelio 
Perihelion 
Mercury 
1 
1 
Venus 
, 623594 
, 92341 
Earth 
, 53652 
, 777482 
Mars 
, 467618 
, 580757 
Jupiter 
, 243114 
, 330599 
Saturn 
, 1834 
, 245805 
Urano 
, 124832 
, 170184 
Neptune 
, 097447 
, 1435 
Pluto 
, 105724 
, 095319 
Press here for
return to table of content
Graphic 14. Behavior 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 * P^{4 }+ 0,2097699233 * P^{3 } 1,521220407 * P^{2 }_{ }+ 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, Earth 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.
Press here for
return to table of content
(Second of arc)
Planet 
Landslide 
Function 
Difference 
Mercury 
25,90 
25,90 
0,00 
Venus 
23,91 
24,75 
0,84 
Earth 
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 
Press here for
return to table of content
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.
Press here for
return to table of content
Planet 
Most maximum errors using the equations of Kepler 
Most maximum error attributable to the gravitation 


AscensiÃ³n straight Arc " 
Decline Arc " 
Arc " 
Mercury 
20 
5 
38,80 
Venus 
20 
5 
24,20 
Earth 
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 
Press here for
return to table of content
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 Earth
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.
Press here for
return to table of content
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
Δc is the
landslide, in seconds of arc, observed for the planet, with relation to the position calculated with DE200/LE200
without including the correction of phase.
r
is the time that the planet delays in
travelling through a second of arc. This time it can obtain from the sidereal revolution
of the planet
More exact measurements of the speed of gravity can be obtained with variant of this formula, for example, taking r from the instant speed since to deducing it of the sidereal revolution the resultant time is the average spends by the planet in travelling through a second of arc that does not coincide with the variations of speed that the planet suffers in its translation in a ellip