Stability of Periodic Orbits in the Restricted Problem

Abstract

Critical orbits, separating stable from unstable periodic orbits, have been computed for the six main families f, g, h, i, l, m and for all values of the mass ratio μ. The results are given by tables and graphs. Domains of stability of the periodic orbits are discussed as a function of μ. The limiting cases µ→0 and µ→1 are studied in detail and the limiting forms of the critical orbits are explained. One particular result is that if the relative mass of one of the bodies is less than 0.0477, all retrograde orbits around that body are stable.