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

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.