Periodic orbits for small N co-orbital satellite systems

Co-orbital satellite systems exhibit rich dynamical behavior. Using numerical simulations, we systematically explore the full parameter space of the symmetric expansion mode of equal-mass co-orbital satellite systems with N = 2, 3, 4, and 5. These simulations reveal analogs of both tadpole and horseshoe orbits, as well as chaotic zones. These simulations clarify the range of orbital parameters that allow regular co-orbital motions, critical information for evaluating whether these systems are likely to arise and survive in various environments.