Stability of 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 rH; 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: (i) many prograde and retrograde satellites can survive out to radii ∼ 0.5rH and ∼ 0.7rH, respectively, while some coplanar retrograde satellites of Jupiter and Neptune can survive out to ∼ rH; (ii) stable orbits do not exist within the Hill sphere at high ecliptic inclinations when the semi-major axis is large enough that the solar tide is the dominant nonKeplerian perturbation; (iii) there is a gap between ∼ rH and 2rH in which no stable orbits exist; (iv) at distances & 2rH 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 ∼ 10rH; (v) 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 & 2rH could survive for the lifetime of the solar system around Uranus, Neptune, and perhaps Jupiter. Subject headings: celestial mechanics – planets and satellites: formation – planets and satellites: general – minor planets, asteroids