# How Wide is Earth's Roche Limit?

My question is simple:

Given the gravitational relationship between Earth and the moon, how wide is Earth's roche limit? How close does the moon have to orbit before getting disintegrated by Earth's gravitational pull, and how far does it have to orbit before being free from Earth's orbit entirely?

• The Roche limit and formulae for its calculation are given at en.m.wikipedia.org/wiki/Roche_limit – ProfRob Feb 3 '17 at 8:41
• I'm more concerned about the Seveneves possibility :-) – Carl Witthoft Feb 3 '17 at 12:33
• @RobJeffries It wasn't straightforward. – JohnWDailey Feb 3 '17 at 15:07
• In what way? $R_{\rm roche} = r_m (2M/m)^{1/3} = 9500$ km. There are uncertainties depending on exactly how the Moon's mass is distributed and its rigidity. Is that what you are asking about? How accurately do you need the answer? – ProfRob Feb 3 '17 at 15:18
• How close does the moon have to be to Earth before getting disintegrated, and how far does it have to be to Earth before drifting away to freedom? – JohnWDailey Feb 3 '17 at 15:21