Parameters of numerical and analytical ephemerides of the moon use complex systems analysis methods

Abstract

Copyright © SGEM WORLD SCIENCE (SWS) Society 2020. This work considers the study of libration dynamics of the planets' moons. To analysis such processes, it is necessary to use methods for investigating complex systems, as an influence from neighboring celestial bodies on spin-orbital motion of a moon should be taken into account. This fully applies to the Moon's rotation about its axis. The construction of modern theories of the physical libration of the Moon (PLM) is based on gravimetric, seismic, satellite observations, and lunar laser ranging, which in its turn has allowed to increase the accuracy by several orders of magnitude compared to the PLM theories of the end of the 20th century. At the moment, some of the most accurate ephemerides are DE created at JPL NASA [1]. The DE ephemerides are based on the coefficients of the Chebyshev polynomials produced by integrating motion equations of the Solar system bodies; the physical libration of the Moon as well as the Earth's nutation are taken into account in the integrating process [2]. To produce PLM parameters from DE ephemerides, one should use a complex algorithm of determining necessary data [3]. It must be noted that the study of the orbital - rotational motion of the moon in the section of celestial mechanics is allocated in a separate area. Such a separation is primarily connected with the fact that this problem cannot be solved within the framework of the 2-body problem. It is necessary to take into account the second perturbing body, it follows from this that the first integrals of motion will not be enough to obtain an exact analytical solution to this problem (before the advent of computers, it was necessary to pre-calculate the coordinates of the moon, most important for sailors of those times).