Comparison between stability limits for satellite motion

Three methods of obtaining stability information on satellite motion are compared by means of numerical and analytical computations. The model of the restricted problem of three bodies is used to describe the motion. Kuiper's (1961) approximate results, Szebehely's (1978) approximate results, and computer solutions obtained by successive iterations show close agreement regarding the maximum values of the orbital radii for stability. The lowest value, i.e., the most conservative estimate, is provided by the simplified form of Szebehely's formula.