Introduction to Classical Mechanics · Problem 10.32
Relativity (Kinematics) — Morin
Physics — Mechanics · roche-limit-with-rotation
Problem
If an object orbits a planet in a nonspinning manner (such as the seat of a ferris wheel), then the Roche limit is the same as for the radially falling object in the previous exercise (as you can show). However, show that if an object orbits a planet in such a way that the same side always faces the planet, then the Roche limit is given by
d=R(ρr3ρp)1/3.