or, Tides on Steroids
Tides scale as M/r3. What happens when a moon gets too close to a massive planet?
Let's say (incorrectly) that the moon gets disrupted when the gravitational force holding the moon together is exceeded by the tidal force exerted by the planet:
in other words,
Redefine mass in terms of size and average density:
Inserting these in and doing some algebra, we get
which we solve for a limiting distance before tidal disruption occurs:
A more careful treatment first calculated by Edouard Roche (1820-1883) gives the Roche Limit: