Construction of the semi-analytical and numerical solutions to the problem of rotational motion of the moon

Abstract

New high-precision, semianalytical and numerical solutions to the problem of the rotational motion of the Moon are obtained, for use in the long 418.9-year time frame. The dynamics of the rotational motion of the Moon is studied numerically using the Rodrigues-Hamilton parameters, relative to the fixed ecliptic for the epoch J2000. The results of the numerical solution to the problem under study are compared with a compiled semianalytical theory of Moon rotation (SMR). The initial conditions for the numerical integration have been taken from the SMR. The comparative discrepancies derived from the comparison between the numerical solutions and the SMR do not exceed 1.5″ on the time-scale of 418.9 yr. The investigation of the comparative discrepancies between the numerical and semianalytical solutions is performed using the least squares and spectral analysis methods in the Newtonian case. All the periodic terms describing the behavior of the comparative discrepancies are interpreted as the corrections to the semianalytical SMR theory. As a result, the series are constructed to describe the rotation of the Moon (MRS2010) in the time interval under study. The numerical solution for the Moon’s rotation has been obtained anew, with new initial conditions calculated using MRS2010. The discrepancies between the new numerical solution and MRS2010 do not exceed 20 arc milliseconds on the time-scale of 418.9 years. The results of the comparison suggest that that the MRS2010 series describe the rotation of the Moon more correctly than the SMR series.