Simple calculation of the Moon apsides motion.

A simple and clear method to calculate the averaged motion of the apsis line in the Moon orbit is proposed. The obtained result is 3°1′12′′$$ {3}^{{}^{\circ}}{1}^{\prime }1{2}^{\prime \prime } $$ for the starry period of the Moon revolution around the Earth or 40°22′48′′$$ {40}^{{}^{\circ}}2{2}^{\prime }4{8}^{\prime \prime } $$ per year. The modern observed value of the latter quantity is 40°41′$$ {40}^{{}^{\circ}}4{1}^{\prime } $$ per year. In "Principia" Newton derived 1°31′28′′$$ {1}^{{}^{\circ}}3{1}^{\prime }2{8}^{\prime \prime } $$ for the Moon month and 20°12′′$$ {20}^{{}^{\circ}}1{2}^{\prime \prime } $$ per year, that is approximately two times less than the observed values. Contrary to 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 argued. Comparing Newton's calculation with our method, we reveal the reason, rather convincing, that brought Newton to an imprecise result. [ABSTRACT FROM AUTHOR]