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On the geodetic rotation of the major planets, the Moon and the Sun

On the geodetic rotation of the major planets, the Moon and the Sun. G.I. Eroshkin and V.V. Pashkevich. Central (Pulkovo) Astronomical Observatory of the Russian Academy of Science St.Petersburg Space Research Centre of the Polish Academy of Sciences Warszawa 2009. A im:.

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On the geodetic rotation of the major planets, the Moon and the Sun

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  1. On the geodetic rotation of the major planets, the Moon and the Sun G.I. Eroshkin and V.V. Pashkevich Central (Pulkovo) Astronomical Observatory of the Russian Academy of Science St.Petersburg Space Research Centre of the Polish Academy of Sciences Warszawa 2009

  2. Aim: The problem of the geodetic (relativistic) rotation of the major planets the Moon and the Sun (Eroshkin G.I., Pashkevich V.V., 2007) is studied by using the DE404/LE404 ephemeris, with respect to the proper coordinate systems of the bodies (Seidelmann P.K. et al., 2005).For each body the files of the Euler angles of the geodetic rotation are determined over the time span from AD1000 to AD3000 with one day spacing. The most essential terms of the geodetic rotation are found by means of the least squares method and spectral analysis methods. The mean longitudes of the planets and the Moon adjusted to the DE404/LE404 ephemeris were taken from (Brumberg and Bretagnon, 2000).The mean longitudes ofPluto adjusted to the DE404/LE404 ephemeris was taken from previous investigation (Eroshkin G.I., Pashkevich V.V., 2007).

  3. The angular velocity vector of the geodetic rotation for any body of Solar system: Here the indices i and j refer tomajor planets, the Moon and the Sun;G – gravitational constant; – mass of the j-th body;c – velocity of light in vacuum; – barycentric positions and velocities of these points;sign × standsfor the vector product .

  4. Fig.1. Reference system used to define orientation of the planet.

  5. Table 1.Recommended values for the direction of the north pole of rotation and the prime meridian of the Sun and planets (2000) (Seidelmann et al., 2005) d- interval in days from J2000; T - interval in Julian centuries (of 36525 days) from J2000.

  6. Table 2. Recommended values for the direction of the north pole of rotation and the prime meridian of the Moon (2000)(Seidelmann et al., 2005)

  7. Fig.2. Triangle used to definethe direction of theangular velocity vector of geodetic rotationfor any body of the Solar system.

  8. Reduction formulae

  9. The Earth σψ σθ σφ

  10. The EarthDetail σψ σθ σφ

  11. The Moon σψ σθ σφ

  12. Mercury σψ σθ σφ

  13. Pluto σψ σθ σφ

  14. Table 3. The main secular and periodic terms of the geodetic rotation in longitude of the planetary equator

  15. Venus σψ σθ σφ

  16. Mars σψ σθ σφ

  17. Jupiter σψ σθ σφ

  18. Saturn σψ σθ σφ

  19. Uranus σψ σθ σφ

  20. Neptune σψ σθ σφ

  21. The Sun σψ σθ σφ

  22. Table4. The secular terms of geodetic rotation for σψ,σθandσφ

  23. Table5. The periodic terms of geodetic rotation for σψ,σθandσφ

  24. Table5. The periodic terms of geodetic rotation for σψ,σθandσφ (c o n t i n u e d)

  25. Table5. The periodic terms of geodetic rotation for σψ,σθandσφ (c o n t i n u e d) λ9 =0.2480488137 + 25.2270056856T λj(j=1,...9) – mean longitudes of the planets; λ10 –mean geocentric longitude of the Moon; T–means the Dynamical Barycentric Time (TDB) measured in thousand Julian years (tjy) (of 365250 days) from J2000.

  26. CONCLUSION • For the Sun, giant planets and Pluto the geodetic rotation is insignificant. • For the terrestrial planets and the Moon the geodetic rotation is significantand has to be taken into account for the construction of the high-precision theories of the rotational motion of these bodies. • Geodetic rotation has to be taken into account if the influence of the dynamical figure of a body on its orbital-rotational motion is studied in the post-Newtonian approximation. • The lunar laser ranging data processing has to use the relativistic theory of the rotation of the Moon, as well as that of the Earth.

  27. REFERENCES • V.A..Brumberg, P.Bretagnon Kinematical Relativistic Corrections for Earth’s Rotation Parameters // in Proc. of IAU Colloquium 180, eds. K.Johnston, D. McCarthy, B. Luzum and G. Kaplan, U.S. Naval Observatory, 2000, pp. 293–302. • Seidelmann P.K., Archinal B.A., A'Hearn M.F., Cruikshank D.P., Hil-ton J.L., Keller H.U., Oberst J., Simon J.L., Stooke P., Tholen D.J., and Thomas P.C. (2005): Report of the IAU/IAG Working Group on Carto-graphic Coordinates and Rotational Elements: 2003, Celestial Mechanics and Dynamical Astronomy, 91, pp. 203-215. • Eroshkin G.I., Pashkevich V.V. (2007): Geodetic rotation of the Solar system bodies, Artificial Satellites, Vol. 42, No. 1, pp. 59–70.

  28. A C K N O W L E D G M E N T S The investigation was carried out at the Central (Pulkovo) Astronomical Observatory of the Russian Academy of Science and the Space Research Centre of the Polish Academy of Science, under a financial support of the Cooperation between the Polish and Russian Academies of Sciences, Theme No 38.

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