On the generation of satellite position (and velocity) by a mixed analytical-numerical procedure

Abstract

The generation of accurate Earth-satellite ephemerides by numerical integration, over a period of perhaps weeks, can consume an inordinate amount of computer time. No satisfactory purely analytical procedure exists, but if short-period components of the standard elliptic elements are removed analytically, the resulting mean elements can be integrated with a step time that is longer than the satellite's orbital period. The definition of the mean elements depends on the particular perturbations included in the orbit generator and regarded as non-resonant. It is best if short-period perturbations are not applied to the orbital elements themselves but to the satellite's position (and velocity if required), expressed in a system of cylindrical polar coordinates, and the paper shows how mean elements can be recovered from position and velocity. A computer program has been written to test the proposed procedure for generating ephemerides, using a truncated potential field. Some results from this program are presented.