Because it's not an n-body problem. The precession is due to the fact that the orbit of a test particle in the Schwarzschild geometry, that describes the spacetime geometry around the Sun, isn't closed (whereas it would be closed in the Newtonian limit).

The precession, in the Newtonian limit can only be due to, either,

effects of the finite size of the Sun and/or the presence of planets such as Venus, Earth and Jupiter.

The precession due to the curving of spacetime by the Sun just needs the Sun, since the curvature produced by the other planets is negligible in comparison.

Thank you for your answer.

But I am looking for an n-body solution that can accurately simulate the orbits of the primary Solar System bodies simultaneously. From this solution, I should be able to extract the total precession of Mercury’s orbit (approximately 575 arc seconds per century).

The problem of N-bodies from the standpoint of the Theory of Relativity cannot be solved. The Theory of Relativity considers the interaction of one moving body with another. At the same time, mass, time and space change in accordance with the movement of this body.

If we consider the interaction of N-bodies, then it is necessary to change the mass, time and space for each body simultaneously in N-1 ways, for example, the body must have N-1 masses at the same time !!!

The Theory of Relativity is defective and false! It must be thrown away and forgotten.

The additional rotation of Mercury's perihelion is due to the oblateness of the Sun [1] - [2].

1. Smulsky J.J. New Components of the Mercury's Perihelion Precession // Natural Science. - 2011, Vol. 3, No.4, 268-274. doi:10.4236/ns.2011.34034. http://www.scirp.org/journal/ns, ISSN Print: 2150-4091, ISSN Online: 2150-4105.

2. Smulsky J.J. Dark Matter and Gravitational Waves // Natural Science, 2021, 13, 76-87. doi:10.4236/ns.2021.133007.

As far as I know there is no General Relativity based n-body simulation that can calculate perihelic precession of Mercury but in following article the problem is solved in flat space time.

Periodic relativity: the theory of gravity in flat space time

https://arxiv.org/abs/0707.4539v11

Thank you to those who responded to this question by commenting here and direct messages to me on researchgate.net

I appreciate receiving guidance to read Orbital Ephemerides of the Sun, Moon, and Planets by E. Myles Standish and James G. Williams.

This paper states:

“8.3 Equations of Motion

Equations of motion describe the forces upon the planets, Sun and Moon which affect their motions and the torques upon the Moon which affect its orientation. It is believed that the equations described here are correct and complete to the level of accuracy of the observational data. I.e., given the accuracy of the observations, there is nothing to suggest that other forces or different forces are present in the solar system. The uncertainties existing in the planets’ and Moon’s motions are certainly explainable, considering the uncertainties in the observations and in the fitted initial conditions and dynamical constants.

The major elements of this section were developed at JPL over the past few decades. Just the formulae are given here; also included are references to their descriptions, previously published by those responsible for their development.

The equations of motion used for the creation of DE405/LE405 included contributions from: (a) point- mass interactions among the Moon, planets, and Sun; (b) general relativity (isotropic, parametrized post- Newtonian); (c) Newtonian perturbations of selected asteroids; (d) action upon the figure of the Earth from the Moon and Sun; (e) action upon the figure of the Moon from the Earth and Sun; (f) physical libration of the Moon, modeled as a solid body with tidal and rotational distortion, including both elastic and dissipational effects, (g) the effect upon the Moon’s motion caused by tides raised upon the Earth by the Moon and Sun, and (h) the perturbations of 300 asteroids upon the motions of Mars, the Earth, and the Moon.”

Based on this information, NASA JPL has created an n-body simulation that provides an accurate model of the solar system. This model is not based on Generally Relativity, however, it includes influences predicted by the parametrized post-Newtonian approximation.

https://ssd.jpl.nasa.gov/planets/eph_export.html provides more information about the JPL PLANETARY AND LUNAR EPHEMERIDES

However, based on all the searching I have done and the comments received above, it appears that an n-body simulation cannot be created based on General Relativity!

This indicates something is wrong with General Relativity!

Dear Morris G. Anderson,

I completely agree with your words: “This indicates something is wrong with General Relativity!” Moreover, as I have already written, the whole Theory of Relativity is defective and false. It is built on hypotheses, this is its main drawback. The entire modern fundamental science is built on the model of the Theory of Relativity. Therefore, the micro- and macro–world created by her is an imaginary one, and the real world is completely different.

“The method of cognition of the surrounding world with the help of hypotheses has taken root in modern science. To explain any phenomenon, a hypothesis about its mechanism is put forward. On its basis, a ramified explanation of this phenomenon is built, i.e. its theory is developed. With the appearance of new data, this explanation contradicts them. To get rid of the contradiction, an additional hypothesis is introduced. In the future, new contradictions appear which are then eliminated by new hypotheses. And so the process has been going on for 100 years…

Now fundamental science is faced with the task not of creating a new surrounding world, but of analyzing the constructed ideas about the micro- and macrocosm. It is necessary in these constructions to reveal unreasonable hypotheses and remove the chains of imaginary constructions associated with them from science. By consistently doing this work, we will receive real knowledge about the world around us...

I encourage novice researchers to engage in this work, and not get carried away with the creation of grandiose structures from hypotheses, which will disappoint them with their meaninglessness by the end of their lives” [1].

1. Smulsky J.J. Dark Matter and Gravitational Waves // Natural Science, 2021, 13, 76-87. doi:10.4236/ns.2021.133007.

There is no need for an n-body answer, because there is nothing close enough to Mercury to affect its orbit except the Sun, and the bending of space-time by the Sun. This problem was solved by Einstein's Theory of General Relativity more than a century ago, and there has never been any observation that suggests that we need to complicate a simple answer that works absolutely perfectly. So although I don't want to criticize anyone, those individuals who noted above that they think there is a need for a better answer are just wasting their time and that of anyone who reads their papers.

Dear Courtney Seligman,

It was not Einstein who solved the problem of the perihelion of Mercury, but Paul Gerber in 1898. But his solution is not correct [1]. The light speed of gravity can give only 1/200 of the additional rotation of the perihelion.

The correct additional rotation of the perihelion of Mercury gives the oblateness of the Sun.

1. Smulsky J.J. Dark Matter and Gravitational Waves // Natural Science, 2021, 13, 76-87. doi:10.4236/ns.2021.133007.

The way planetary dynamicists deal with the orbits of planets at the cm level is to use a so called "parameterized post-newtonian" (PPN) approximation of general relativity. JPL/NASA codes providing the planet orbits over centuries are available online.

See for example

Article Relativistic aspects of the JPL planetary ephemeris

For general n-body codes in the weak field limit, see for example:

Article General Relativistic N-body simulations in the weak field limit

Thank you. I will study these papers.

Morris G. Anderson :

The Real Story Behind Mercury’s perihelion advance:

[Long after Newton’s law of universal gravitation was generally accepted as the basis of the planetary motion in the solar system, the French astronomer Le Verrier in 1859 announced (based on many years of careful observations and calculations) that the perihelion of the planet Mercury evidently undergoes precession, at a slightly faster rate than can presumably be accounted for by Newtonian mechanics, given the known distribution of the planets and the other objects in the solar system. Since Newton’s laws allows only a unitary and centrally directed force, an explanation for Le Verrier’s finding was arbitrarily attributed to a perturbation caused by the secondary effect of the gravitational forces from other planets; but did not explain why the precession rate varied with different planets, especially the high precession rate of Mercury. The perihelion precession of Mercury is 5,600 arcseconds (1.5556°) per century relative to the Earth. Newtonian mechanics, presumably taking into account all the effects from the other planets, predicts (without strong basis, since it is a very complex many-body problem)a precession of 5,557 arcseconds (1.5436°) per century, but the rest 43 arcseconds (a mere0.076%!) remained un-explained.

In 1898 a German school teacher named Paul Gerber [13] wrote a paper in which he proposed a velocity-dependent propagation of gravity that predicted non-Newtonian 43 arcseconds advance of orbital perihelia per revolution given by the expression k(pi)M/(Lc^2); where c is the posited speed of propagation of gravity, M is the sun's mass, L is the semi-latus-rectum of the orbit, and k is a constant depending on the precise form of the assumed potential. Although there are controversies about this formulation, Gerber showed successfully that a value of the constant k = 6 gave the correct additional 43 arcseconds of Mercury’s perihelion advance.

Albert Einstein in his 1915 - 1916 publications [14,15] claimed to have given a precise account of the discrepancy of precession of Mercury, and deduced Garber’s above relation based on his newly proposed theory of general relativity (GR). The understanding that Einstein’s GR based on impeccable mathematics and a totally different and novel perspective of space and time gave an exact account of the expression given by Garber for the non-Newtonian precession of Mercury; became an instant cause of celebration by Einstein himself. This purported achievement by Einstein is considered [16] a poetic marvel in modern physics and the strongest “proof” of GR! Einstein retroactively admitted (after questions were raised) that Gerber obtained the correct expression for Mercury’s perihelion advance before him. But Einstein dismissed any possibility that someone could explain the additional 43 arcseconds precession of Mercury or that Gerber’s expression for it could be obtained, without using his theory of general relativity.

According to Einstein [17], “Mr. Gehrcke wants to make us believe that the Perihelion shift of mercury can be explained without the theory of relativity. So there are two possibilities. Either you invent special interplanetary masses. [...] Or you rely on a work by Gerber, who already gave the right formula for the Perihelion shift of mercury before me. The experts (?) are not only in agreement that Gerber’s derivation is wrong through and through, but the formula cannot be obtained as a consequence of the main assumption made by Gerber. Mr. Gerber’s work is therefore completely useless, an unsuccessful and erroneous theoretical attempt. I maintain that the theory of general relativity has provided the first real explanation of the perihelion motion of Mercury. I have not mentioned the work by Gerber originally, because I did not know it when I wrote my work on the perihelion motion of Mercury; even if I had been aware of it, I would not have had any reason to mention it".

Einstein’s claim of Mercury’s perihelion advance was contested by so-called “100 authors against Einstein” led by Philipp Lenard, Gehrcke, Silverstein, Reuterdahl et all, who opposed Einstein’s theories accusing him of many things, such as incorrect formulation, plagiarism etc.,and questioned his priority. Ironically, W.W. Engelhardt in his recent publication [18] uses similar reasoning like Einstein and raised the controversial issue that Gerber’s expression cannot be derived from Einstein’s GR. Engelhardt claimed that instead of GR Einstein used a modified Newtonian theory to derive Gerber’s expression and not from his theory of general relativity; hence contest the justification of the claim by Einstein of the proof of his theory of relativity. Engelhardt using purported Einstein’s modified Newtonian mechanics derived an expression for the Gerber’s equation, which is one-third of Gerber’s formula.]

This is a copy of a section, extracted from an article, For the references please see the following article:

Article Quō Vādis Theoretical Physics and Cosmology? From Newton's M...

Dear Abdul Malek,

It is all truth! Einstein knew about Paul Gerber's article [1] and studied it well. Based on this article, in his 1915 article [2] he imitated his derivation of Paul Gerber's result on the rotation of Mercury's perihelion 43 arcsec/century. But Einstein's derivation is a complete fiction. Everyone can be convinced of this if he studies the articles of Paul Gerber and Einstein!

However, the solution by Paul Gerber of the problem on the influence of the finite velocity of gravity on the rotation of the perihelion of Mercury is incorrect. This is a difficult problem. It was solved (pp. 204 – 211 in [3]) and it turned out that the light velocity of gravity gives the rotation of Mercury's perihelion 0.23 arcsec/century, and not 43 arcsec/century, i.e. 187 times less.

In astronomy, there are different coordinate systems. When counted from the moving equator of the Earth, the rotation of the perihelion of Mercury, according to observations, occurs at a speed of 5603 arcsec/century, when counted from the moving orbit of the Earth it is 573 arcsec/century, when counted from a fixed space it is 583 arcsec/century [4].

As a result of the interaction of the Solar System bodies, according to Newton's law of gravity, the perihelion of Mercury rotates at a speed of 530 arcsec/century relative to a fixed space [4] - [5]. Therefore, the excess rotation of Mercury's perihelion is 53 arcsec/century, or it is not 43 arcsec/century.

When solving the problem of the interaction of the bodies of the solar system, the bodies are considered as material points. The action of a strictly spherical body is equivalent to the action of a material point. But the Sun is not spherical, but an oblate body. Taking into account the shape of the Sun gives 53 arcsec/century missing before the observations [4], [6].

Therefore, the finite velocity of gravity is not needed to calculate gravitational interactions. The General Theory of relativity, like the Special Theory of relativity, must be thrown out and forgotten. All modern fundamental science is built on them.

And this science is defective and false. Why it is defective and false? Because it created an unrealistic picture of the micro- and macro-world, it does not pave the way for the further development of society and does not prevent negative trends in it. Society does not need such science. Society is aware of this. It treats its discoveries as circus tricks, and in search of a solution to the problems it faces, it directs its eyes to journalists and politicians [7], [8].

This excerpt from the book [7] was voiced by the outstanding thinker Borislav Vankov from Sofia in Russian https://youtu.be/60oQqIPIa3Q, in English https://youtu.be/ypMHq1LN6EU, in German https://youtu.be/R1lQh1a15NMand Bulgarian https://youtu.be/k215_StxuFAlanguages.

References

1. Gerber, P. (1898) Die raumliche und zeitliche Aubreitung der Gravitation. Z. Math. Phis., Vol. 43.- P. 93-104. http://bourabai.narod.ru/papers/gerber/gerber.htm.

2. Einstein A. Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie. Preussische Akademie der Wissenschaften, Sitzungsberichte, 1915 (part 2), 831 - 839. I had read this article in: Einstein А. Explanation of motion of a perihelion of a Mercury in a general theory of a relativity / A. Einstein. The Collection of Scientific Works: In 4 vol.- Moscow.: Science Publishing House.- 1965.- Vol. 1.- P. 439-447.

3. Smulsky, J.J. (2004). The Theory of Interaction. Ekaterinburg: Cultural Information Bank. 302 p. http://www.ikz.ru/~smulski/TVEnA5_2.pdf.

4. Smulsky, J.J. (2011) New Components of the Mercury's Perihelion Precession. Natural Science. Vol. 3, No.4, 268-274. doi:10.4236/ns.2011.34034. http://www.ikz.ru/~smulski/Papers/NCmMePNSc.pdf.

5. Smulsky, J.J. and Smulsky, Ya.J. (2012) Dynamic Problems of the Planets and Asteroids, and Their Discussion. International Journal of Astronomy and Astrophysics, Vol. 2, No. 3, pp. 129-155. doi:10.4236/ijaa.2012.23018.

6. Smulsky J.J., (2018). Future Space Problems and Their Solutions. Nova Science Publishers, New York, 269 p. ISBN: 978-1-53613-739-2. http://www.ikz.ru/~smulski/Papers/InfFSPSRu.pdf.

7. Smulsky, J.J. (2019) The Upcoming tasks of Fundamental Science. M.: Sputnik+ Publishing House, 134 p. ISBN 978-5-9973-5228-8. (In Russian). http://www.ikz.ru/~smulski/Papers/InfPrZaFN.pdf.

8. Smulsky, J.J. (2021) Dark Matter and Gravitational Waves. Natural Science, 13, 76-87. doi:10.4236/ns.2021.133007. https://www.scirp.org/journal/paperinformation.aspx?paperid=107880.

Morris G. Anderson > "This model is not based on Generally Relativity, however, it includes influences predicted by the parametrized post-Newtonian approximation".

The PPN approximation can only be a scholastic effort, without much practical value; because Newton's theory of one-sided and "universal gravitational attraction" for the solar system in particular and extra-terrestrial astro-dynamics in general is false! Please see:

"KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Legacies in Theoretical Physics, Cosmology and in Ruling Ideas" :

Article KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Le...

And the new RG question: "What is Physics and what is Metaphysics?" :

https://www.researchgate.net/post/What_is_Physics_and_what_is_Metaphysics

It must also be emphasized that in space exploration technology and astro-dynamics; the engineers use Leibniz's 'vis viva' equation and onboard or remote navigation systems, which has nothing to do with Newton's and Einstein's theories; while the "physicists" sing the glory of Newton's and Einstein's theories, in scholarly publications and press releases!

https://en.wikipedia.org/wiki/Vis-viva_equation

Yes, there are numerical simulations based on General Relativity that can calculate the perihelion precession of Mercury. The precession of Mercury's orbit is one of the earliest and most famous predictions of Einstein's theory of General Relativity.

General Relativity predicts that the orbit of a planet will precess due to the curved spacetime caused by the mass of the Sun. This effect is known as the "gravitational advance of the perihelion." In the case of Mercury, General Relativity predicts a perihelion precession of about 43 arcseconds per century, which is in good agreement with observations.

N-body simulations are numerical simulations that model the motion of multiple bodies under the influence of their mutual gravitational interactions. These simulations can be used to calculate the gravitational advance of the perihelion for various planetary orbits, including that of Mercury.

There are several publicly available n-body simulations that are based on General Relativity and can calculate the perihelion precession of Mercury, such as REBOUND and the Mercury integrator in the SWIFT package.

These simulations use numerical techniques to solve the equations of motion for the planets and account for the effects of General Relativity on their orbits.

Thank you for your answer!

Has anyone published a paper illustrating that these codes can calculate the precession of Mercury with a n-body simulation of the solar system? I would like to see how the results compare with the 575.3100 ± 0.0015''/century value published by Ryan S. Park et al 2017 AJ 153 121

Morris G. Anderson

It's for example calculated at p. 38 (Table)

https://www.researchgate.net/publication/369561533_Relativistic_Gravitational_Force

Dear Prof. Sverker Edvardsson,

I looked at your preprint “Relativistic Gravitational Force”. It immerses the reader in the imaginary world of the Theory of Relativity. There is no need to use it. The electromagnetic interaction of two charges is determined by the force, which depends on the distance and velocity [1]. The gravitational interaction is determined by Newton's law of universal gravitation, only for the correct calculation of the motion of the perihelion of Mercury it is necessary to take into account the oblateness of the Sun [1] - [2]. The theory of relativity must be thrown out and forgotten!

1. Smulsky J.J. Dark Matter and Gravitational Waves // Natural Science, 2021, 13, 76-87. doi:10.4236/ns.2021.133007. https://www.scirp.org/journal/paperinformation.aspx?paperid=107880.

2. Smulsky J.J. New Components of the Mercury's Perihelion Precession // Natural Science. - 2011, Vol. 3, No.4, 268-274. doi:10.4236/ns.2011.34034. http://www.ikz.ru/~smulski/Papers/NCmMePNSc.pdf.

Dear Joseph Smulsky : I agree with you that GR has no basis in objective reality because “spacetime” is an abstract geometrical construct, please see:

"The Mystery of the Lorentz Transform: A Reconstruction and Its Implications for Einstein's Theories of Relativity and cosmology"

INSPIRE: https://inspirehep.net/literature/2158754

Even Newton’s one-sided theory of universal gravitational attraction is defective. The root of the cosmic Fairy Tales of “Big Bang” created finite and expanding universe, dark/black cosmic entities etc. lies in the unrealistic theories of Einstein and Newton; which arises from no or poor understanding of the nature of gravitation and matter in eternal motion.

The following new (empirical) gravitational potential (for two-body system) based on all three of Kepler’s Laws, Vis Viva of Leibniz and Hegel’s idea of the “Absolute free motion of matter particles”; hopefully will give a correct representation of gravitation and will eliminate the need for Big Bang, dark/black etc., mystical entities to explain the dynamics and the phenomenology of the cosmos.

Ep = m(a/r^3 – GM/r -Cr^2);

Where Ep is the gravitational potential, G is the Newtonian gravitational constant, r is the distance , M and m are the masses of the sun and a planet respectively; and the constants a, and C are to be determined from empirical and observational evidence.

Please see:

"KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Legacies in Theoretical Physics, Cosmology and in Ruling Ideas":

Article KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Le...

Dear Prof. Sverker Edvardsson,

Thank you for posting the link to your paper "Relativistic Gravitational Force." The section "3.8 Relativistic precession rates of the planets" helps me better understand the process.

I am also happy to see your success in calculating the total precession of Mercury by your method.

If I understand correctly, your RGF method and the Post Newtonian Approximation rely on calculating orbits based on mass-to-mass interaction instead of the curvature of space described by General Relativity.

I'm still looking for an example of calculating Mercury's total precession based on the curvature of space described by General Relativity.

Thanks for your help.

Morris G. Anderson

> If I understand correctly, your RGF method and the Post Newtonian Approximation rely on calculating orbits based on mass-to-mass interaction instead of the curvature of space described by General Relativity.

Yes both use the so-called N-body computational method, i.e., viewing it as acting forces between particles or bodies. RGF is a new relativistic method derived from within special relativity that works well in most relativistic celestial mechanics problems (Section 3.7 is the most important one). The Post Newtonian Approximation is derived from within general relativity and is a good approximation for weak fields and velocities much less than c (the speed of light) and applied in flat space.

> I'm still looking for an example of calculating Mercury's total precession based on the curvature of space described by General Relativity.

The Mercury two-body precession is derived in almost any GR book, but always using (gross?) approximations. The N-body precession of Mercury is something that would be extremely difficult in the nonlinear GR theory and perhaps this cannot even be done.

However, for the two-body precession you can have a look in chapter 5 of:

https://hal.science/hal-01571766v2/document

It is an exact treatment using GR. I think this part is of interest from a physicist's perspective. Large parts of this document, however, is from a "mathematics" perspective and probably not trustworthy.

Dear Abdul Malek,

I am glad to your words: “that GR has no basis in objective reality because “spacetime” is an abstract geometrical construct”.

Quite right, the Theory of Relativity is not a science, it is a product of human imagination. It is an Einsteinian heresy in science! And the sooner we throw it away, the more reliable science will become. Such a science will solve all the problems facing Mankind [1].

However, I do not agree with your words about the fallacy of Newton's law of gravitation. Throughout the 18th and 19th centuries there were repeated proposals to supplement it with terms proportional to 1/r^3, as you suggest. Exponential additives, acceleration additives, and additives that take into account the finite velocity of gravity propagation were also proposed. The need for supplements was required because the results of the theory of the motion of the Moon did not match the observations. As soon as this theory improved, everyone understood that additives were not needed. Now I have solved the problem of the motion of the Moon in 100 million years: all the results coincide with the observations [2]. By this I confirm that supplements are not needed.

In the 20th century, an additive was put forward that takes into account the finite speed of gravity propagation to explain the excess rotation of Mercury's perihelion. I have shown that this additive cannot explain this problem [3]. I found that only the oblateness of the Sun can explain this problem [4]. I solved the problem of interaction according to Newton's law of gravity of the bodies of the Solar system with the oblate Sun for 6000 years. The parameters of the orbits of all planets coincided with the observations [5]-[6]. So no supplements are needed.

Why offered supplements?

1. Due to inaccurate solution of the interaction problem.

2. Because of its wrong solution.

3. Due to incorrect interpretation of the observed phenomena.

The Big Bang, Black Holes, and other modern inventions are misinterpretations of observed phenomena.

1. Smulsky, J.J. (2019) The Upcoming tasks of Fundamental Science. M.: Sputnik+ Publishing House, 134 p. ISBN 978-5-9973-5228-8. (In Russian). http://www.ikz.ru/~smulski/Papers/InfPrZaFN.pdf.

2. Smulsky J.J. (2022). The Evolution of the Moon’s Orbit Over 100 Million Years and Prospects for the Research in the Moon. In: Lunar Science - Habitat and Humans. Edited by Yann-Henri Chemin. London, United Kingdom: IntechOpen, 2022, 18-39, DOI: 10.5772/intechopen.102392. http://mts.intechopen.com/articles/show/title/the-evolution-of-the-moon-s-orbit-over-100-million-years-and-prospects-for-the-research-in-the-moon.

3. Smulsky, J.J. (2004). The Theory of Interaction. Ekaterinburg: Cultural Information Bank. http://www.ikz.ru/~smulski/TVEnA5_2.pdf

4. Smulsky J.J. Dark Matter and Gravitational Waves // Natural Science, 2021, 13, 76-87. doi:10.4236/ns.2021.133007. https://www.scirp.org/journal/paperinformation.aspx?paperid=107880.

5. Smulsky J.J. New Components of the Mercury's Perihelion Precession // Natural Science. - 2011, Vol. 3, No.4, 268-274. doi:10.4236/ns.2011.34034. http://www.ikz.ru/~smulski/Papers/NCmMePNSc.pdf.

6. Smulsky, J.J. (2018) Future Space Problems and Their Solutions. Nova Science Publishers, New York, 269 p. ISBN: 978-1-53613-739-2. http://www.ikz.ru/~smulski/Papers/InfFSPS.pdf.

Sincerely yours Prof. Joseph J. Smulsky

Institute of Earth's Cryosphere, Tyum SC of SB RAS, Federal Research Center

Malygina Str. 86,

625026, Tyumen, Russia.

Tel. +7-3452-68-87-14,

http://www.ikz.ru/~smulski/smul1/;

http://wgalactica.ru/smul1/.

GR applied to mercury perihelion precession. The answer is Newtonian sufficeth if interpreted including galactic torque.

Preprint Diffusion Gravity (5): Perihelion Precessions as Indicators ...