“Roche's Limit”

Abstract

WITH reference to Prof. G. H. Darwin's notes (NATURE, March 16, p. 460) on the investigations of M. Roche as to the smallest distance from its primary at which a satellite can exist, does not the distance given—viz. 2˙44 times the radius of the primary—refer to the case of the satellite having the same density as its primary? In Note 3 Prof. Darwin warns the reader that Roche's limit depends, to some extent, on the density of the planet. Suppose the density of the planet to remain the same while that of the satellite is taken at double. In this case the tidal or differential influence of the planet on the two halves of the satellite will have doubled, while the gravitational attraction of the two halves of the satellite on each other will have become fourfold; and generally, the power of the planet to pull the satellite asunder will be inversely as the density of the satellite, and directly as the density of the planet.