Resonance Effects in Satellite Orbits

Abstract

If a satellite were moving in an axially symmetric gravitational field, free from other disturbing forces, two integrals of the equations of motion would be known: the energy per unit mass of the satellite and the third component of the angular momentum per unit mass. For a terrestrial satellite one cannot write such integrals since the field depends on the longitude. If a set of canonical variables, such as Delaunay variables, is chosen, the time can easily be removed from the Hamiltonian and an integral of the new set of equations of motion is obtained. The use of that integral when studying the earth’s gravitational field is investigated for orbits whose mean motion is almost commensurable with the Earth’s angular velocity. Numerical results were derived by using orbital data of a synchronous satellite in a nearly circular orbit and with a small value for the ratio of mean cross-sectional area/ mass.