An Etymological Dictionary of Astronomy and Astrophysics
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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.

Named after Edouard Albert Roche (1820-1883), the French astronomer who first calculated this theoretical limit in 1848; → limit.