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
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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.
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On the geodetic rotation of the major planets, the Moon and the
Sun G.I. Eroshkin and V.V. Pashkevich
Central (Pulkovo) Astronomical Observatoryof the Russian Academy of Science
St.PetersburgSpace Research Centre of the Polish Academy of Sciences
Warszawa
2009
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 of Pluto adjusted to the DE404/LE404 ephemeris was taken from previous investigation (Eroshkin G.I., Pashkevich V.V., 2007).
Aim:
Here the indices i and j refer to major 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 × stands for the vector product .
jm
The angular velocity vector of the geodetic rotation for any body of Solar system:
32
1 32 .
2j
i i j i jj i
i j
GmR R R R
c R R
, , ,i i j jR R R R
Fig.1. Reference system used to define orientation of the planet.
Table 1. Recommended values for the direction of the north pole of rotation and the prime meridian of the Sun and planets (2000)
The Sun α0=286°.13 δ0=63°.87 W=84°.10+14°.1844000d d - interval in days from J2000;
T - interval in Julian centuries (of 36525 days) from J2000.
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)
The Moon
α0=269°.9949 +0°.0031T -3°.8787 sin E1 -0°.1204 sin E2 +0°.0700 sin E3 -0°.0172 sin E4 +0°.0072 sin E6 -0°.0052 sin E10 +0°.0043 sin E13δ0= 66°.5392 +0°.0130T +1°.5419 cos E1 +0°.0239 cos E2 -0°.0278 cos E3 +0°.0068 cos E4 -0°.0029 cos E6 +0°.0009 cos E7 +0°.0008 cos E10 -0°.0009 cos E13W=38°.3213 +13°.17635815d -1°.4 x 10-12d2 +3°.5610 sin E1 +0°.1208 sin E2 -0°.0642 sin E3 +0°.0158 sin E4 +0°.0252 sin E5 -0°.0066 sin E6 -0°.0047 sin E7 -0°.0046 sin E8 +0°.0028 sin E9 +0°.0052 sin E10 +0°.0040 sin E11 +0°.0019 sin E12 -0°.0044 sin E13
5.19846640063 77713.7714481804 T .D 4 6.20347594486 3340.6124266998T .
5 0.59954632934 529.6909650946T
6 0.87401658845 213.2990954380T
7 5.48129370354 74.7815985673T
8 5.31188611871 38.1330356378T
λ9 = 0.2480488137 + 25.2270056856T
10 3 180 ,D
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.
CONCLUSION
• For the Sun, giant planets and Pluto the geodetic rotation is insignificant.
• For the terrestrial planets and the Moon the geodetic rotation is significant and 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.
R E F E R E N C E S
1. 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.
2. 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.
3. Eroshkin G.I., Pashkevich V.V. (2007): Geodetic rotation of the Solar system bodies, Artificial Satellites, Vol. 42, No. 1, pp. 59–70.
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.