Construction of the solutions of the rigid Earth rotation problem at a long time interval

The main purpose of this research is the construction of the new high–precision rigid Earth rotation series, dynamically adequate to the JPL DE406/LE406 ephemeris. 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 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 initial conditions of the numerical integration are taken from the corresponding semi-analytical solutions of the rigid Earth rotation. The investigation of the discrepancies between high–precision numerical solutions and semi-analytical solutions of the rigid Earth rotation problem is carried out by the least squares and spectral analysis methods. The problem was solved taking into account most significant of the relativistic perturbation in the rotational motion of the Earth — geodetic perturbations. 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.