Motion of the moonlet in the binary system 243 Ida

The motion of the moonlet Dactyl in the binary system 243 Ida is investigated in this paper. First, periodic orbits in the vicinity of the primary are calculated, including the orbits around the equilibrium points and large-scale orbits. The Floquet multipliers’ topological cases of periodic orbits are calculated to study the orbits’ stabilities. During the continuation of the retrograde near-circular orbits near the equatorial plane, two period-doubling bifurcations and one Neimark–Sacker bifurcation occur one by one, leading to two stable regions and two unstable regions. Bifurcations occur at the boundaries of these regions. Periodic orbits in the stable regions are all stable, but in the unstable regions are all unstable. Moreover, many quasi-periodic orbits exist near the equatorial plane. Long-term integration indicates that a particle in a quasi-periodic orbit runs in a space like a tire. Quasi-periodic orbits in different regions have different styles of motion indicated by the Poincare sections. There is the possibility that moonlet Dactyl is in a quasi-periodic orbit near the stable region I, which is enlightening for the stability of the binary system.