Astronomy Letters

, Volume 31, Issue 5, pp 340–349 | Cite as

Relativistic effects and solar oblateness from radar observations of planets and spacecraft

  • E. V. Pitjeva


We used more than 250 000 high-precision American and Russian radar observations of the inner planets and spacecraft obtained in the period 1961–2003 to test the relativistic parameters and to estimate the solar oblateness. Our analysis of the observations was based on the EPM ephemerides of the Institute of Applied Astronomy, Russian Academy of Sciences, constructed by the simultaneous numerical integration of the equations of motion for the nine major planets, the Sun, and the Moon in the post-Newtonian approximation. The gravitational noise introduced by asteroids into the orbits of the inner planets was reduced significantly by including 301 large asteroids and the perturbations from the massive ring of small asteroids in the simultaneous integration of the equations of motion. Since the post-Newtonian parameters and the solar oblateness produce various secular and periodic effects in the orbital elements of all planets, these were estimated from the simultaneous solution: the post-Newtonian parameters are β = 1.0000 ± 0.0001 and γ = 0.9999 ± 0.0002, the gravitational quadrupole moment of the Sun is J2 = (1.9 ± 0.3) × 10−7, and the variation of the gravitational constant is Ġ/G = (−2 ± 5) × 10−14 yr−1. The results obtained show a remarkable correspondence of the planetary motions and the propagation of light to General Relativity and narrow significantly the range of possible values for alternative theories of gravitation.

Key words

celestial mechanics cosmology Sun 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. I. Afanasieva, M. D. Kislik, Yu. F. Kolyuka, and V. F. Tikhonov, Astron. Zh. 67, 1326 (1990) [Sov. Astron. 34, 670 (1990)].ADSGoogle Scholar
  2. 2.
    J. D. Anderson, J. K. Campbell, R. F. Jurgens, et al., 6th Marcel Grossman Meeting on General Relativity, Ed. by H. Sato and T. Nakamura (World Sci., 1992), p. 353.Google Scholar
  3. 3.
    J. D. Anderson, P. B. Esposito, W. Martin, et al., Astrophys. J. 200, 221 (1975).CrossRefADSGoogle Scholar
  4. 4.
    J. D. Anderson, M. S. Keesey, E. L. Lau, et al., Acta Astronautica 5, 43 (1978).Google Scholar
  5. 5.
    J. D. Anderson, E. L. Lau, S. Turyshev, et al., Bull. Am. Astron. Soc. 34, 660 (2002).ADSGoogle Scholar
  6. 6.
    B. Bertotti, L. Iess, and P. Tortora, Nature 425, 374 (2003).CrossRefADSGoogle Scholar
  7. 7.
    T. M. Brown, J. Christensen-Dalsgaad, W. A. Dziembowski, et al., Astrophys. J. 343, 526 (1989).CrossRefADSGoogle Scholar
  8. 8.
    V. A. Brumberg, Relativistic Celestial Mechanics (Nauka, Moscow, 1972).Google Scholar
  9. 9.
    V. A. Brumberg and E. Groten, Astron. Astrophys. 367, 1070 (2001).CrossRefADSGoogle Scholar
  10. 10.
    V. M. Canuto, S.-H. Hsieh, and J. R. Owen, Mon. Not. R. Astron. Soc. 188, 829 (1979).ADSGoogle Scholar
  11. 11.
    T. Damour and J. H. Taylor, Astrophys. J. 366, 501 (1991).CrossRefADSGoogle Scholar
  12. 12.
    T. L. Duvall, W. A. Dziembowski, P. Goode, et al., Nature 310, 22 (1984).ADSGoogle Scholar
  13. 13.
    T. M. Eubanks, D. N. Matsakis, J. O. Martin, et al., American Physical Society APS/AAPT Joint Meeting (1997).Google Scholar
  14. 14.
    M. Froeschle, F. Mignard, and F. Arenou, Hipparcos—Venice 97, ESA-402 (Venice, 1997), p. 49.Google Scholar
  15. 15.
    S. Godier and J. P. Rozelot, Astron. Astrophys. 355, 365 (2000).ADSGoogle Scholar
  16. 16.
    R. W. Hellings, P. J. Adams, J. D. Anderson, et al., Phys. Rev. Lett. 51, 1609 (1983).CrossRefADSGoogle Scholar
  17. 17.
    R. W. Hellings, P. J. Adams, J. D. Anderson, et al., Int. J. Theor. Phys. 28, 1035 (1989).CrossRefGoogle Scholar
  18. 18.
    H. A. Hill, R. J. Bos, and P. R. Goode, Phys. Rev. Lett. 49, 1794 (1982).ADSGoogle Scholar
  19. 19.
    G. A. Krasinsky, Commun. of IAA RAS 148, 1 (2002).Google Scholar
  20. 20.
    G. A. Krasinsky, E. V. Pitjeva, M. V. Vasilyev, and E. I. Yagudina, Commun. of IAA RAS 139, 1 (2001).Google Scholar
  21. 21.
    G. A. Krasinsky, E. V. Pitjeva, M. V. Vasilyev, and E. I. Yagudina, Icarus 158, 98 (2002).CrossRefADSGoogle Scholar
  22. 22.
    D. E. Lebach, B. E. Corey, I. I. Shapiro, et al., Phys. Rev. Lett. 75, 1439 (1995).CrossRefADSGoogle Scholar
  23. 23.
    X. X. Newhall, E. M. Standish, Jr., and J. G. Williams, Astron. Astrophys. 125, 150 (1983).ADSGoogle Scholar
  24. 24.
    L. Paterno, S. Sofia, and M. P. Di Mauro, Astron. Astrophys. 314, 940 (1996).ADSGoogle Scholar
  25. 25.
    F. P. Pijpers, Mon. Not. R. Astron. Soc. 297, L76 (1998).CrossRefADSGoogle Scholar
  26. 26.
    S. Pireaux and J.-P. Rozelot, Astrophys. Space Sci. 284, 1159 (2003).CrossRefADSGoogle Scholar
  27. 27.
    E. V. Pitjeva, Byull. Inst. T. A., Ross. Akad. Nauk 15, 538 (1986).ADSGoogle Scholar
  28. 28.
    E. V. Pitjeva, Celest. Mech. 55, 333 (1993).ADSGoogle Scholar
  29. 29.
    E. V. Pitjeva, Third International Workshop on Position Astronomy and Celestial Mechanics, Ed. by G. A. Lopez, E. I. Yagudina, U. M. Martinez, and B. A. Condero (Observ. Astron. Univ. Valencia, 1996), p. 583.Google Scholar
  30. 30.
    E. V. Pitjeva, Tr. Inst. P. A., Ross. Akad. Nauk 4, 22 (1999).Google Scholar
  31. 31.
    E. V. Pitjeva, Tr. Inst. P. A., Ross. Akad. Nauk 5, 58 (2000).Google Scholar
  32. 32.
    E. V. Pitjeva, Celest. Mech. 80, 249 (2001).CrossRefADSGoogle Scholar
  33. 33.
    E. V. Pitjeva, Tr. Inst. P. A., Ross. Akad. Nauk 10, 112 (2004).Google Scholar
  34. 34.
    E. V. Pitjeva, Transit of Venus: New Views of the Solar System and Galaxy, IAU Coll. 196, Ed. by D. W. Kurtz (Cambridge University Press, 2005).Google Scholar
  35. 35.
    R. D. Reasenberg and I. I. Shapiro, On the Measurement of Cosmological Variations of the Gravitational Constant, Ed. by L. Halpern (Florida Univ. Press, USA, 1978), p. 71.Google Scholar
  36. 36.
    R. D. Reasenberg, I. I. Shapiro, P. E. MacNeil, et al., Astrophys. J. 234, L219 (1979).CrossRefADSGoogle Scholar
  37. 37.
    D. S. Robertson, W. E. Carter, and W. H. Dillinger, Nature 349, 768 (1991).CrossRefADSGoogle Scholar
  38. 38.
    I. I. Shapiro, G. H. Pettengill, M. E. Ash, et al., Phys. Rev. Lett. 28, 1594 (1972).CrossRefADSGoogle Scholar
  39. 39.
    I. I. Shapiro, G. H. Pettengill, M. E. Ash, et al., Phys. Rev. Lett. 20, 1265 (1968).ADSGoogle Scholar
  40. 40.
    E. M. Standish, Bull. Am. Astron. Soc. 32, 870 (2000).ADSGoogle Scholar
  41. 41.
    E. M. Standish, Astron. Astrophys. 233, 252 (1990).ADSGoogle Scholar
  42. 42.
    E. M. Standish, Astron. Astrophys. 336, 381 (1998).ADSGoogle Scholar
  43. 43.
    E. M. Standish and A. Fienga, Astron. Astrophys. 384, 322 (2002).CrossRefADSGoogle Scholar
  44. 44.
    J. G. Williams, D. H. Boggs, J. O. Dickey, and W. M. Folkner, Ninth Marcel Grossman Meeting, Ed. by V. G. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Sci., 2002), p. 1797.Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2005

Authors and Affiliations

  • E. V. Pitjeva
    • 1
  1. 1.Institute of Applied AstronomyRussian Academy of SciencesSt. PetersburgRussia

Personalised recommendations