Fr.: rayon de Roche
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 RM (ρM/ρm)1/3, where RM is the radius of the → primary body, ρM is the → density of the primary, and ρm is the density of the secondary body. This formula can also be expressed as: d = 1.26 Rm (MM/Mm)1/3, where Rm is the radius of the secondary. As an example, for the Earth-Moon system, where RM = 6,378 km, ρM = 5.5 g cm-3, and ρm = 2.5 g cm-3 is 1.68 Earth radii.
Named after Edouard Albert Roche (1820-1883), the French astronomer who first calculated this theoretical limit in 1848; → limit.