Анализ орбитальных теорий для построения численной теории физической либрации Луны

The problem of comparing the numerical and analytical theories of the orbital motion of the Moon came before us at the stage of constructing a numerical theory of physical libration. In the course of the study, it was important for us to understand how the differences in the accuracy of the description of the center of mass motion will affect the behavior of the libration. Now we present the results of the first stage of the comparison, namely: the description of the time behavior of differences between the two types of orbital theories. We work with the analytical theory by Gutzwiller and Schmidt built in the framework of the main problem, and the modern numerical theory DE431 by JPL NASA, which takes into account a large number of factors that go beyond the main problem and which would be difficult or even impossible to take into account when obtaining an analytical solution. Having made the necessary reductions when we brought both theories to a unified reference frame, we compared both solutions on an interval of 800 years. As a result, we have obtained that the amplitude in longitude for this period does not exceed 80 arcseconds, and in latitude 10 arcseconds. The main sources of discrepancies are perturbations from planets and asteroids, motion of the ecliptic plane, the Earth's figure, tidal effects, and general relativity in numerical ephemerides, which were not included in analytical theory.