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There have been more recent calculations of the motion of the planet Mercury by Russian scientists. These calculations use the same multi-body calculations used in the past,
There have been more recent calculations of the motion of the planet Mercury by Russian scientists. These calculations use the same multi-body calculations used in the past,
but also using a six step to calculate the precession of the perihelion of Mercury:
but also using a eight step to calculate the precession of the perihelion of Mercury:


1) differential equations of motion and their solution method. <ref>Melnikov,V.P., Smulsky,J.J., Krotov O.I., Smulsky,L.J. Orbits of The Earth And The Sun And Possible Their Influences On of The Earth Cryosphere (Statement of a Problem And The First Results) // Cryosphere of the Earth. - 2000. - Vol. IV, No. 3, Pp. 3-13. (In Russian).</ref><ref>Melnikov V. P., Smulsky J.J. The Astronomical Factors Of Influence On The Earth's Cryosphere And The Problem Of Their Research // Earth Cryosphere, 2004 Vol. VIII, No. 1. Pp. 3-14. (In Russian).</ref><ref>Smulsky J.J., Optimization of Passive Orbit with the Use of Gravity Maneuver // Cosmic Research, 2008, Vol. 46, No. 5, pp. 456–464. Original Russian Text ©, 2008, published in Kosmicheskie Issledovaniya, 2008, Vol. 46, No. 5, pp. 484–492.</ref><ref>Mel’nikov V.P., Smul’skii I.I., Smul’skii Ya.I., 2008. Compound modeling of Earth rotation and possible implications for interaction of continents // Russian Geology and Geophysics, 49, 851–858.</ref><ref>Grebenikov E.A., Smulsky J.J. Evolution of the Mars Orbit on Time Span in Hundred Millions Years / Reports on Applied Mathematics. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2007. 63 p.(In Russian ).</ref><ref>Melnikov V.P., Smulsky J.J.Astronomical theory of ice ages: New approximations. Solutions and challenges. - Novosibirsk: Academic Publishing House "GEO", 2009. - 84 p. The book in two languages. On the back side in Russian: Mel'nikov V.P., Smul'skiy I.I. Astronomicheskaya teoriya lednikovykh periodov: Novye priblizheniya. Reshennye i nereshennye problemy. - Novosibirsk: Akademicheskoe izdatel'stvo "Geo", 2009. - 98 stranitz.</ref><ref>Smulsky J.J. (book) Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).</ref><ref>Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House. – 2008 - Pp. 433-434</ref>
1) differential equations of motion and their solution method. <ref>Melnikov,V.P., Smulsky,J.J., Krotov O.I., Smulsky,L.J. Orbits of The Earth And The Sun And Possible Their Influences On of The Earth Cryosphere (Statement of a Problem And The First Results) // Cryosphere of the Earth. - 2000. - Vol. IV, No. 3, Pp. 3-13. (In Russian).</ref><ref>Melnikov V. P., Smulsky J.J. The Astronomical Factors Of Influence On The Earth's Cryosphere And The Problem Of Their Research // Earth Cryosphere, 2004 Vol. VIII, No. 1. Pp. 3-14. (In Russian).</ref><ref>Smulsky J.J., Optimization of Passive Orbit with the Use of Gravity Maneuver // Cosmic Research, 2008, Vol. 46, No. 5, pp. 456–464. Original Russian Text ©, 2008, published in Kosmicheskie Issledovaniya, 2008, Vol. 46, No. 5, pp. 484–492.</ref><ref>Mel’nikov V.P., Smul’skii I.I., Smul’skii Ya.I., 2008. Compound modeling of Earth rotation and possible implications for interaction of continents // Russian Geology and Geophysics, 49, 851–858.</ref><ref>Grebenikov E.A., Smulsky J.J. Evolution of the Mars Orbit on Time Span in Hundred Millions Years / Reports on Applied Mathematics. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2007. 63 p.(In Russian ).</ref><ref>Melnikov V.P., Smulsky J.J.Astronomical theory of ice ages: New approximations. Solutions and challenges. - Novosibirsk: Academic Publishing House "GEO", 2009. - 84 p. The book in two languages. On the back side in Russian: Mel'nikov V.P., Smul'skiy I.I. Astronomicheskaya teoriya lednikovykh periodov: Novye priblizheniya. Reshennye i nereshennye problemy. - Novosibirsk: Akademicheskoe izdatel'stvo "Geo", 2009. - 98 stranitz.</ref><ref>Smulsky J.J. (book) Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).</ref><ref>Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House. – 2008 - Pp. 433-434</ref>
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4) developed a compound model of body rotation (i.e. rotation of spherical masses).<ref>Mel’nikov V.P., Smul’skii I.I., Smul’skii Ya.I., 2008. Compound modeling of Earth rotation and possible implications for interaction of continents // Russian Geology and Geophysics, 49, 851–858.
4) velocity of perihelion rotation relative to motionless space. .<ref>Grebenikov E.A., Smulsky J.J., ibid</ref><ref>Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion, ibid</ref>

⚫
</ref><ref>Melnikov V.P., Smulsky J.J.Astronomical theory of ice ages: New approximations. Solutions and challenges. - Novosibirsk: Academic Publishing House "GEO", 2009. - 84 p. The book in two languages. On the back side in Russian: Mel'nikov V.P., Smul'skiy I.I. Astronomicheskaya teoriya lednikovykh periodov: Novye priblizheniya. Reshennye i nereshennye problemy. - Novosibirsk: Akademicheskoe izdatel'stvo "Geo", 2009. - 98 stranitz
5) exact solution of axisymmetrical problem of n-bodies. <ref>Smulsky,J.J. Axisymmetrical problem of gravitational interaction of N-bodies //Mathematical modelling. - 2003, Vol. 15, No 5, Pp. 27-36</ref>

6) developed a compound model of body rotation (i.e. rotation of spherical masses).<ref>Mel’nikov V.P., Smul’skii I.I., Smul’skii Ya.I., 2008. Compound modeling of Earth rotation and possible implications for interaction of continents // Russian Geology and Geophysics, 49, 851–858.
⚫
</ref><ref>Melnikov V.P., Smulsky J.J.Astronomical theory of ice ages: New approximations. Solutions and challenges. - Novosibirsk: Academic Publishing House "GEO", 2009. - 844p. The book in two languages. On the back side in Russian: Mel'nikov V.P., Smul'skiy I.I. Astronomicheskaya teoriya lednikovykh periodov: Novye priblizheniya. Reshennye i nereshennye problemy. - Novosibirsk: Akademicheskoe izdatel'stvo "Geo", 2009. - 98 stranitz
</ref><ref>Smulsky J.J. Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).
</ref><ref>Smulsky J.J. Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).
</ref><ref>Smulsky J.J. Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House. – 2008 - Pp. 433-434. (In Russian).</ref>
</ref><ref>Smulsky J.J. Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House. – 2008 - Pp. 433-434. (In Russian).</ref>


5) calculated the action of compound model of rotating mass body on a satellite.<ref>Smulsky J.J. Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).
7) calculated the action of compound model of rotating mass body on a satellite.<ref>Smulsky J.J. Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).
</ref>
</ref>


6) calculated the action of the Solar System on Mercury's orbit.<ref>Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House.</ref>
8) calculated the action of the Solar System on Mercury's orbit.<ref>Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House.</ref>


{| class="wikitable" border="1" style="margin-left:auto; margin-right:auto;"
{| class="wikitable" border="1" style="margin-left:auto; margin-right:auto;"
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| || By results of interaction under the Newton law of gravity. Velocity of rotation of a perihelion relative to motionless space
| || By results of interaction under the Newton law of gravity. Velocity of rotation of a perihelion relative to motionless space
|-
|-
| 530 – (table 1 above) || Planets and the Sun interact as material points
| 530 – <ref>Smulsky J.J., Compound model..., ibid</ref>(table 1 above) || Planets and the Sun interact as material points
|-
|-
| 582<ref>Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House.</ref>|| Planets interact as material points, and the oblateness and rotation of the Sun is taken into account as compound model
| 582<ref>Smulsky J.J., Compound model...ibid</ref>|| Planets interact as material points, and the oblateness and rotation of the Sun is taken into account as compound model
|-
|-
| || Conclusions
| || Conclusions
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|}
|}
'=======================================================================<br />
'=======================================================================<br />
Therefore, the observed velocity of perihelion rotation relative to motionless space is solely determined interaction under [[Newton's law of universal gravitation]].

<br />
<br />


Revision as of 21:46, 31 December 2010

Welcome to the user page for editor David Charles Weber
Main interests:

Relativity theory

Vulcanism caused by meteor impacts.


=============================================================================


Below is my scratchpad for editing.

- this is a work in progress, so please do not discuss this
================================================================================
D c weber (talk) 13:09, 23 December 2010 (UTC)
===============================================================================

Recent calculation of the Perihelion precession of Mercury

There have been more recent calculations of the motion of the planet Mercury by Russian scientists. These calculations use the same multi-body calculations used in the past, but also using a eight step to calculate the precession of the perihelion of Mercury:

1) differential equations of motion and their solution method. [1][2][3][4][5][6][7][8]

2) developed a computer program (Galactica).[9]

3) derived formulae for geometric transformations.[10]

4) velocity of perihelion rotation relative to motionless space. .[11][12]

5) exact solution of axisymmetrical problem of n-bodies. [13]

6) developed a compound model of body rotation (i.e. rotation of spherical masses).[14][15][16][17]

7) calculated the action of compound model of rotating mass body on a satellite.[18]

8) calculated the action of the Solar System on Mercury's orbit.[19]

Table 2 - Sources of the precession of perihelion for Mercury using the Sun's rotation
Amount (arcsec/Julian century) Explaination
Based on Observational Data
-5028.82 [20] Velocity of movement of vernal equinox point relative to motionless space
5603.0 [21] Velocity of perihelion rotation relative to the mobile vernal equinox point with including velocities changes of ecliptic and of Mercury orbit
582.53 [22] Velocity of perihelion rotation relative to motionless space
By results of interaction under the Newton law of gravity. Velocity of rotation of a perihelion relative to motionless space
530 – [23](table 1 above) Planets and the Sun interact as material points
582[24] Planets interact as material points, and the oblateness and rotation of the Sun is taken into account as compound model
Conclusions
0.53 [25] Discrepancy with just Newtonian Mechanics (calculated difference between Newton theory and actual precession)
42.98 ±0.04 [26][27] General relativity
42.45 Discrepancy with General Relativity (calculated difference between GR theory and actual precession)

'=======================================================================
Therefore, the observed velocity of perihelion rotation relative to motionless space is solely determined interaction under Newton's law of universal gravitation.



notes==============================

  1. ^ Melnikov,V.P., Smulsky,J.J., Krotov O.I., Smulsky,L.J. Orbits of The Earth And The Sun And Possible Their Influences On of The Earth Cryosphere (Statement of a Problem And The First Results) // Cryosphere of the Earth. - 2000. - Vol. IV, No. 3, Pp. 3-13. (In Russian).
  2. ^ Melnikov V. P., Smulsky J.J. The Astronomical Factors Of Influence On The Earth's Cryosphere And The Problem Of Their Research // Earth Cryosphere, 2004 Vol. VIII, No. 1. Pp. 3-14. (In Russian).
  3. ^ Smulsky J.J., Optimization of Passive Orbit with the Use of Gravity Maneuver // Cosmic Research, 2008, Vol. 46, No. 5, pp. 456–464. Original Russian Text ©, 2008, published in Kosmicheskie Issledovaniya, 2008, Vol. 46, No. 5, pp. 484–492.
  4. ^ Mel’nikov V.P., Smul’skii I.I., Smul’skii Ya.I., 2008. Compound modeling of Earth rotation and possible implications for interaction of continents // Russian Geology and Geophysics, 49, 851–858.
  5. ^ Grebenikov E.A., Smulsky J.J. Evolution of the Mars Orbit on Time Span in Hundred Millions Years / Reports on Applied Mathematics. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2007. 63 p.(In Russian ).
  6. ^ Melnikov V.P., Smulsky J.J.Astronomical theory of ice ages: New approximations. Solutions and challenges. - Novosibirsk: Academic Publishing House "GEO", 2009. - 84 p. The book in two languages. On the back side in Russian: Mel'nikov V.P., Smul'skiy I.I. Astronomicheskaya teoriya lednikovykh periodov: Novye priblizheniya. Reshennye i nereshennye problemy. - Novosibirsk: Akademicheskoe izdatel'stvo "Geo", 2009. - 98 stranitz.
  7. ^ Smulsky J.J. (book) Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).
  8. ^ Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House. – 2008 - Pp. 433-434
  9. ^ see all 8 references of "1) differential equations"
  10. ^ Grebenikov E.A., Smulsky J.J. Evolution of the Mars Orbit on Time Span in Hundred Millions Years / Reports on Applied Mathematics. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2007. 63 p.(In Russian).
  11. ^ Grebenikov E.A., Smulsky J.J., ibid
  12. ^ Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion, ibid
  13. ^ Smulsky,J.J. Axisymmetrical problem of gravitational interaction of N-bodies //Mathematical modelling. - 2003, Vol. 15, No 5, Pp. 27-36
  14. ^ Mel’nikov V.P., Smul’skii I.I., Smul’skii Ya.I., 2008. Compound modeling of Earth rotation and possible implications for interaction of continents // Russian Geology and Geophysics, 49, 851–858.
  15. ^ Melnikov V.P., Smulsky J.J.Astronomical theory of ice ages: New approximations. Solutions and challenges. - Novosibirsk: Academic Publishing House "GEO", 2009. - 844p. The book in two languages. On the back side in Russian: Mel'nikov V.P., Smul'skiy I.I. Astronomicheskaya teoriya lednikovykh periodov: Novye priblizheniya. Reshennye i nereshennye problemy. - Novosibirsk: Akademicheskoe izdatel'stvo "Geo", 2009. - 98 stranitz
  16. ^ Smulsky J.J. Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).
  17. ^ Smulsky J.J. Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House. – 2008 - Pp. 433-434. (In Russian).
  18. ^ Smulsky J.J. Numerical modeling of evolution of the satellite of a rotating body / In Col. The Theoretical and Applied tasks of the Nonlinear Analysis. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2008. Pp. 100-117. (In Russian).
  19. ^ Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion / The Fundamental and Applied Problems of the Mechanics: Proceeding of the VI All-Russian scientific Conference, devoted 130-th anniversary of Tomsk state university and 40-th anniversary NII of Applied Mathematics and the Mechanics of Tomsk State University. Tomsk, September 30 - October 2, 2008 - Tomsk: University Publishing House.
  20. ^ J.L. Simon, P. Bretagnon, J. Chapront, et. al., “Numerical Expression for Precession Formulae and Mean Elements for the Moon and the Planets”, Astron. Astrophys, vol. 282, pp. 663-683 (1994).
  21. ^ J.L. Simon, P. Bretagnon, J. Chapront, et. al., “Numerical Expression for Precession Formulae and Mean Elements for the Moon and the Planets”, Astron. Astrophys, vol. 282, pp. 663-683 (1994).
  22. ^ J.L. Simon, P. Bretagnon, J. Chapront, et. al., “Numerical Expression for Precession Formulae and Mean Elements for the Moon and the Planets”, Astron. Astrophys, vol. 282, pp. 663-683 (1994).
  23. ^ Smulsky J.J., Compound model..., ibid
  24. ^ Smulsky J.J., Compound model...ibid
  25. ^ Smulsky J.J., Compound model of rotation of the Sun and displacement of Mercury perihelion , cited above
  26. ^ L. Iorio "On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging" (2004)
  27. ^ Myles Standish, Jet Propulsion Laboratory (1998)
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