Perturbations of a Satellite's Orbit Due to the Earth's Oblateness

Abstract

The free-flight motion of a satellite around a spherical earth is investigated neglecting atmospheric deceleration. This treatment is then extended by recognizing the earth's oblateness, which is represented by an additional quadrupole field. For nearly circular orbits, one finds that perturbations of the usual planar motion may be described analytically. These are characterized by a precession of the orbit plane around the equator, that is, a regression of the nodes, amounting to as much as forty miles per revolution. The large magnitude of these effects indicates that one may exploit a satellite's motion, as measured by conventional radio techniques, to determine the earth's oblateness to a new precision.