The dynamics of coorbital satellite systems

The dynamical behavior of N coorbital satellites moving with the same average mean motion around a primary has been studied both analytically and by numerical integrations for N from 2 to 9 satellites. Simplified dynamical equations are used to determine the different stationary configurations and their local stability against infinitesimal perturbations. The ring of equally spaced identical satellites is found to be locally unstable for N of six or less, while for N from two to eight there exists another stable compact stationary configuration with separations of 60 deg or less between adjacent satellites. For N of seven or more the equally spaced configuration becomes locally stable, and for N of nine or more it is the only stationary configuration. The motion becomes chaotic for large-amplitude perturbations. The chaotic motion fills a restricted region of phase space whose outer boundary is determined by the maximum velocity curve.