Simple calculation of the Moon apsides motion

TL;DR

This paper presents a straightforward method to calculate the Moon's apsides motion, yielding results closer to observations than Newton's classical calculations, and discusses its applicability to other planetary satellites.

Contribution

It introduces a simple averaging approach for the Sun's disturbing force to accurately estimate the Moon's apsides motion, improving upon Newton's classical results.

Findings

Calculated Moon apsides motion: 3°1'12'' per lunar revolution

Annual apsides motion: 40°22'48'' compared to observed 40°41'

Newton's method yields about half the observed value

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.