A generalization of Kepler orbits for large satellites

Abstract

In a central gravity field mass points and homogeneous spherical bodies are moving on Kepler orbits. For bodies of arbitrary shape, e.g. artificial satellites, Kepler orbits are only an approximation. Thé deviations from the Kepler orbits increase with the body extension a relative to the orbit radius r. The ratio a/r is small for hitherto existing satellites: a/r ⋍ 10^-6. Anyhow, satellites with a/r ⋍ 10^-4 are projected for special missions. Further, satellites are in discussion reaching from close to the earth surface up to altitudes far beyond the synchronous altitude [1]. Such satellites will yield ratios 0 < a/r < 1 during erection.