STABILITY OF THE DISTANT SATELLITES OF THE GIANT PLANETS IN THE SOLAR SYSTEM
Yue Shen, Scott Tremaine
2008
Astronomical Journal
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 10^9 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
more »
... results and new findings include the following: (i) many prograde and retrograde satellites can survive out to radii ∼ 0.5r_ H and ∼ 0.7r_ H, respectively, while some coplanar retrograde satellites of Jupiter and Neptune can survive out to ∼ r_ H; (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 non-Keplerian perturbation; (iii) there is a gap between ∼ r_ H and 2r_ H in which no stable orbits exist; (iv) at distances ≳ 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 ∼ 10r_ H; (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 ≳ 2r_ H could survive for the lifetime of the solar system around Uranus, Neptune, and perhaps Jupiter.
doi:10.1088/0004-6256/136/6/2453
fatcat:tyvneeto7fezbf5wy4mmxmfcwa