Gravity simulator

Suppose a moon is in a circular orbit around a planet and that the planet is on a circular orbit around a star. M = Mass of star m = mass of planet R = Distance of planet from star r = Distance of moon from planet T = Period of planet's orbit t = Period of moon's orbit H = Hill radius h = Hill constant The moon's orbit is stable if t < h T where h represents a dimensionless number of order unity. Equivalently, the maximum stable radius for a moon r is given by r < h R (m/M)^(1/3) < h H The "Hill radius" is defined as H = R (m/M)^(1/3) The Hill radius is also the distance to the L1 and L2 Lagrange points. The Earth's moon orbits at 1/5 this distance. Also, asteroids this close to the Earth are likely to either: A planet's "zone of gravitational dominance" can be defined as the maximum stable radius of a moon. An object is defined as a planet if it is large enough to be round and if it is not within the gravitational zone of a larger object.

http://en.wikipedia.org/wiki/Hill_sphere http://en.wikipedia.org/wiki/Lagrangian_point