Introduction to Classical Mechanics · Problem 10.31
Relativity (Kinematics) — Morin
Physics — Mechanics · roche-limit
Problem
A small spherical rock covered with sand falls in radially toward a planet. Let the planet have radius R and density ρp, and let the rock have density ρr. It turns out that when the rock gets close enough to the planet, the tidal force ripping the sand off the rock will be larger than the gravitational force attracting the sand to the rock. The cutoff distance is called the Roche limit. Show that it is given by (note the lack of dependence on the rock's radius)
d=R(ρr2ρp)1/3.