Application of the Spectral Analysis for Modeling the Rotations of the Moon

The main purposes of this research are the development of the optimal spectral analysis schemes for the investigation of the rotational motion of the Moon and then the comparison between the result of the optimal spectral analysis of the rotational motions of the Earth and the Moon. Dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9 year time interval. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) represented by Cassini relations and the semi-analytical solutions of the lunar physical libration problem (Eckhardt, 1981), (Moons, 1982), (Moons, 1984), (Pešek, 1982). The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the optimal spectral analysis methods for the Newtonian case. All the periodic terms representing the behavior of the residuals are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2010) is constructed, which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2010. The discrepancies between the new numerical solution and MRS2010 do not surpass 20 mas over 418.9 year time interval. The result of the comparison demonstrates that MRS2010 series represent more accurately the Moon rotation than SMR series.