Gravitational clearing of natural satellite orbits

Abstract

Abstract The distribution of diameters and orbital distances from the parent body of 156 named moons of the planets in the Solar System is not random. All 11 moons with diameters larger than $1\,000\,\mathrm{km}$ are positioned between $400\,000\,\mathrm{km}$ and 4 million km from the parent, whereas the far more numerous small moons are distributed on both sides of this central region and are largely absent from the region in between. This small-satellite ‘exclusion region’ is particularly evident for the gas giants since they have multiple satellites spanning a wide range of distances from the parent. Application of mathematical criteria analogous to those that have been used to help define the ‘gravitational clearing’ of planetary orbits around the Sun suggests that the absence of small satellites in this region around the planets may be a result (atleast in part) of gravitational clearing by the large moons present at these distances from the parent. The most significant exception to the observed diameter-distance distribution—Hyperion, on Saturn—is attributed to its 3:4 orbital resonance with Titan, while other obvious exceptions are the Trojan satellites of Saturn’s moons Tethys and Dione. The smallest satellite diameter that seems necessary for clearing of its ‘sphere of influence’ is around $400\,\mathrm{km}$ .