Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals

Abstract

Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals The main purposes of this research are the construction of the new high-precision Moon Rotation Series (MRS2011), dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris, over long time intervals. The comparison of the new highprecision Moon Rotation solutions of MRS2011 with the solution of MRS2010 (Pashkevich and Eroshkin, 2010), which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval, is performed. The dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9, 2000 and 6000 years. The numerical solution of the Moon rotation is implemented with the quadruple precision of the calculations. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) (Pashkevich and Eroshkin, 2010) with respect to the fixed ecliptic of epoch J2000. The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the least squares and spectral analysis methods for the Newtonian case. All the secular, periodic and Poisson terms, representing the behavior of the residuals, are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2011) is constructed, which is dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris over 418.9, 2000 and 6000 years. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2011. The discrepancies between the new numerical solution and the semi-analytical solution of MRS2011 do not surpass 20 mas over 418.9 year time interval, 64 mas over 2000 year time interval and 8 arc seconds over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of MRS2011 series with the DE/LE ephemeris.

New High-Precision Values of the Geodetic Rotation of the Major Planets, Pluto, the Moon and the Sun

“…As a result from (8) and (9), following expressions are obtained: (10) Expressions for the perturbing terms of the physical librations of the Moon for the fixed ecliptic of epoch J2000 are defined by the following (Pashkevich and Eroshkin, 2011): (11) where W , U and V are the perturbing terms of the physical librations of the Moon in the longitude, in the inclination and in the node longitude, respectively; \ is the longitude of the descending node of epoch J2000 of the lunar equator; I is a constant angle of the inclination of the lunar equator to the fixed ecliptic J2000 ( I ~ 1 o 32'); T is the inclination of the lunar equator to the fixed ecliptic J2000; M is the proper rotation angle of the Moon between the descending node of epoch J2000 and the principal axis of the minimum moment of inertia; L e is the mean longitude of the Moon and : is the mean longitude of the ascending node of its orbit.…”

MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation

“…The discrepancies of the comparison between the numerical solutions and semi-analytical series MRS2011B for Newtonian (dynamical) case in the previous investigation (Pashkevich and Eroshkin 2011) are depicted in Figure 1. The discrepancies of the comparison between the numerical solutions and semi-analytical series MRS2014 for Newtonian (dynamical) case in the previous investigation (Pashkevich 2015) are depicted in Figure 3.…”

“…The problem formularized in the Rodrigues -Hamilton parameters (Pashkevich and Eroshkin 2011), which in this paper are expressed via the perturbing terms of the physical librations of the Moon: cos sin sin sin , 2 2 2 2 sin cos cos cos . 2 2 2 …”