Construction of the Numerical and Semi-Analytical Solutions of the Rigid Earth Rotation at a Long Time Intervals

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This research is the continuation of our studies of the rigid Earth rotation at a long time intervals (Pashkevich V.V. and Eroshkin G.I., 2005). The main purpose of this investigation is the construction of the new high-precision Rigid Earth Rotation Series 2012 (RERS2012), dynamically adequate to the JPL DE406/LE406 ephemeris (Standish E. M., 1998). The dynamics of the rotational motion of the rigid Earth is studied numerically by using Rodrigues-Hamilton parameters over 2000 and 6000 years. The numerical solution of the rigid Earth rotation is implemented with the quadruple precision of the calculations. The orbital motions of the disturbing celestial bodies are defined by the DE406/LE406 ephemeris. The initial conditions of the numerical integration are taken from SMART97 (Bretagnon P. et al., 1998) and S9000 (Pashkevich V.V. and Eroshkin G.I. 2005). The results of the numerical solutions of the problem are compared with the semi-analytical solutions of the rigid Earth rotation (SMART97 and S9000, respectively) with respect to the fixed ecliptic of epoch J2000. The investigation of these discrepancies is carried out by the least squares and spectral analysis methods for the relativistic (Kinematical) case, in which the geodetic perturbations (the most essential relativistic perturbations) in the Earth rotation are taken into account. As a result, the Rigid Earth Rotation Series (RERS2012) is constructed, which is dynamically adequate to the DE406/LE406 ephemeris over 2000 and 6000 years. The discrepancies between the new numerical solutions and the semi-analytical solutions of MRS2012 do not surpass 12 μas over 2000 year time interval and 2 mas over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of RERS2012 series with the DE406/LE406 ephemeris.

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  • Eroshkin G.I. (2000): High-Precision method of the Numerical Solution of the Celestial Mechanic problems based on Chebyshev Polynomial Interpolation In: Book of abstracts Astrometry Geodynamics and Celestial Mechanics at the turn of XXIth century (eds. A.M.Finkelstein et al.) The Conference of the St.Petersburg in the IPA RAS 19-23 June 2000} pp. 229-230 (in Russian).

  • Bretagnon P. Francou G. Rocher P. Simon J.L. (1998) SMART97: a new solution for the rotation of the rigid Earth Astron. Astrophys. Vol. 329pp. 329-338.

  • Eroshkin G.I. Pashkevich V.V. and Brzeziński A. (2002): Extension of the high-precision numerical theory of the rigid Earth rotation to the case of a long time interval Artificial Satellites 37 4 pp. 169-183.

  • Pashkevich V. V. Eroshkin G. I. (2005) Application of the spectral analysis for the mathematical modelling of the rigid Earth rotation Artificial Satellites Vol. 40 No. 4 pp. 251-259.

  • Standish E. M. (1998) JPL Planetary and Lunar Ephemerides DE405/LE405 JPL Interoffice Memorandum 312.F-98-048.

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