On a New Analytic Theory of the Moon's Motion I: Orbital Angular Momentum

Abstract

A new analytic theory of the Moon's motion is deduced from the Lagrangian of the Sun-Earth-Moon system expressed with relative velocities. In its first-order approximation, the first-degree terms of the ratio of distances from Earth to the Moon and to the Sun are taken. The calculated relative variation in the Moon's orbital angular momentum is resolved into components whose integrals yield the inclination of the orbital plane, the ecliptic longitude of the ascending node and the norm of the angular momentum as functions of the angle between the Moon and the ascending node.