Stability of Motion Near Sun-Perturbed Earth-Moon Triangular Libration Points

Abstract

An extension is presented of an analysis by Schechter [1] of sun-perturbed motion near the earth-moon L ₄ point. In the present paper motion is confined to two dimensions. With the help of computerized symbolic manipulation and some new recurrence formulae [6] inspired by Deprit [4], a canonical perturbation treatment is carried to 4th order in the small quantities: lunar eccentricity, distance from L₄/earth-moon distance, moon mass/earth mass, solar mean motion/lunar mean motion; (earth-moon distance/earth-sun distance) is included as a second order small quantity. Ignoring lunar eccentricity, stable one-month periodic orbits, synchronized with the sun, are found, from the 3rd-order Hamiltonian, somewhat larger than in Schechter’s second order treatment, and in very good agreement (3%) with Kolenkiewicz and Carpenter. Unstable three-month periodic orbits are also found in fairly close proximity to the stable one-month orbits, and the limited extent of the region of the stability is estimated in suitable phase coordinates. The inclusion of the 4th-order terms gave a slight deterioration rather than a further improvement in the agreement on the stable orbits. The inclusion of the lunar eccentricity up to 3rd-order yielded stable quasi-periodic orbits slightly larger than the previous stable orbits.

This research was sponsored by the National Aeronautics and Space Administration under Research Grant NsG 133–61.