STABILITY OF THE DISTANT SATELLITES OF THE GIANT PLANETS IN THE SOLAR SYSTEM

We conduct a systematic survey of the regions in which distant satellites can orbit stably around the four giant planets in the solar system, using orbital integrations of up to 109 yr. In contrast to previous investigations, we use a grid of initial conditions on a surface of section to explore phase space uniformly inside and outside the planet's Hill sphere (radius r(H); satellites outside the Hill sphere sometimes are also known as quasi-satellites). Our confirmations and extensions of old results and new findings include the following: (1) many prograde and retrograde satellites can survive out to radii similar to 0.5r(H) and similar to 0.7r(H), respectively, while some coplanar retrograde satellites of Jupiter and Neptune can survive out to similar to r(H); (2) stable orbits do not exist within the Hill sphere at high ecliptic inclinations when the semimajor axis is large enough that the solar tide is the dominant non-Keplerian perturbation; (3) there is a gap between similar to r(H) and 2r(H) in which no stable orbits exist; (4) at distances greater than or similar to 2r(H) stable satellite orbits exist around Jupiter, Uranus, and Neptune (but not Saturn). For Uranus and Neptune, in particular, stable orbits are found at distances as large as similar to 10r(H); (5) the differences in the stable zones beyond the Hill sphere arise mainly from differences in the planet/Sun mass ratio and perturbations from other planets; in particular, the absence of stable satellites around Saturn is mainly due to perturbations from Jupiter. It is, therefore, likely that satellites at distances >= 2r(H) could survive for the lifetime of the solar system around Uranus, Neptune, and, perhaps, Jupiter.