Tidal interaction
Three-body problem
The smallest distance at which a satellite under the influence of its own gravitation and that of a central mass about which it is describing a Keplerian orbit can be in equilibrium. This does not, however, apply to a body held together by the stronger forces between atoms and molecules. At a lesser distance the tidal forces of the primary body would break up the secondary body. The Roche limit is given by the formula d = 1.26 R_M (ρ_M/ρ_m)^(1/3), where R_M is the radius of the primary body, ρ_M is the density of the primary, and ρ_m is the density of the secondary body. This formula can also be expressed as: d = 1.26 R_m (M_M/M_m)^(1/3), where R_m is the radius of the secondary. As an example, for the Earth-Moon system, where R_M = 6,378 km, ρ_M = 5.5 g cm^(-3), and ρ_m = 2.5 g cm^(-3) is 1.68 Earth radii.
Roche radius
Roche limit