A Restricted Problem of Four Bodies

Abstract

A restricted four-body problem of the Sun, the Moon, the Earth, and a deep-space probe of high eccentricity, large semi-major axis and large inclination is studied. Emphasis is centered on the variations of the Jacobian constant of the associated restricted three-body problem due to the Sun, higher order geopotential functions and the atmospheric drag. The orbital evolution of the probe under the various forces is also analyzed. The study employs a special perturbations orbit propogation program using an eighth-order Gauss-Jackson integrator. Preliminary numerical results are presented.