**or, Tides on Steroids**

Tides scale as M/r^{3}. 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**: