Long-term evolution of near-geostationary orbits

Abstract

A model for the long-term evolution of free-drifting near-geostationary satellite orbits is presented. A firstorder analytical averaging transformation is applied to the perturbation equations in order to eliminate the short-term (with period of order of one day) variations of the orbital elements. The model includes lunisolar gravitational forces up to the second parallactic term of the moon, zonal and tesseral harmonics of the Earth's potential field up to the fourth degree, as well as the solar radiation force. The algebraic computations have been carried out by an automated Poisson series manipulation. Extremely compact expressions could be established after manually recombining the computer-generated results in terms of a few well-selected parameters. The results obtained are of particular interest for predicting the motion of geostationary spacecraft after their useful lifetime has expired and stationkeeping maneuvers are no longer executed. The validity of the model presented has been evaluated by a comparison with numerical results obtained for the European Space Agency's GEOS-2 satellite, which is at present orbiting about 260 km above geostationary altitude.