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:

and 

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: