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 are 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 nonresonant. 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 special system of polar coordinates (cylindrical or spherical), and the paper shows how mean elements were recovered from position and velocity. A computer program was written to test the proposed procedure for generating ephemerides, using a truncated potential field.