Roche's Limit

Roche's limit [′rō·shəz ‚lim·ət]

(astrophysics)

The limiting distance below which a satellite orbiting a celestial body would be disrupted by the tidal forces generated by the gravitational attraction of the primary; the distance depends on the relative densities of the bodies and on the orbit of the satellite; it is computed byR= 2.45(Lr), whereLis a factor that depends on the relative densities of the satellite and the body,Ris the radius of the satellite's orbit measured from the center of the primary body, andris the radius of the primary body; if the satellite and the body have the same density, the relationship isR= 2.45r.

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Roche’s Limit 

the critical distance from a planet inside which, because of the destructive action of gravitational forces, satellites cannot exist. Roche’s limit was investigated by the French astronomer E. Roche (1820–83), who established that for fluid satellites this limit is A = 2.5R, where R is the radius of the planet. Since Saturn’s rings lie within Roche’s limit (the radius of the outer edge of the outer ring is equal to 2.3 times the planet’s equatorial radius), Roche concluded that the rings consist of small solid particles (1848). This was later confirmed by other investigators.

The action of gravitional forces on a solid satellite was studied by H. Jeffreys (1947), who ascertained that the internal stresses necessary to break up a solid satellite can arise only when the dimensions of the satellite are large. Thus, for a solid satellite approaching the surface of Jupiter to break up, the satellite’s diameter must be at least 400–500 km.

G. A. CHEBOTAREV