Simple calculation of the Moon apsides motion

Abstract

A simple and clear method is proposed to calculate the averaged motion of the apsis line in the Moon orbit. The obtained result is $3^{\circ}1'12''$ for the starry period of the Moon revolution around the Earth or $40^{\circ}22'48''$ per year. The modern observed value of the latter quantity is $40^{\circ}41'$ per year. In "Principia" Newton derived $1^{\circ}31'28''$ for the Moon month and $20^{\circ}12''$ per year. That is approximately two times less than the observable values. Unlike the Newton approach we use a simple and obvious averaging of the Sun disturbing force for the starry period of the Moon revolution around the Earth. The applicability of the obtained formulae to satellites of other planets and to the planets themselves is grounded. Comparing Newton's calculation with our method we reveal the reason, rather convincing, that brings Newton to inadequate result.