Question

Write an expression for the potential energy of a body of mass m in the gravitational field of the earth and moon. let me be the earth's mass, mm the moon's mass (where 81 m m e m = ), r the distance from the earth's center, and r the physics 113p, summer 2015 study guide module 9 © 2015 university of rochester 4 all rights reserved distance from the moon's center. the distance between earth and moon is about 384,400 km.

Answer 1

Attraction forces subtract one to each other....and there is a point where such forces are perfectly equal...such point is such that its distance from earth c.o.m. is √81 = 9.00 times greater than its distance from moon c.o.m. 
Generic point gravity g can be evaluated this way 
ge = Me*G/de^2 
gm = Mm*G/(3.844*10*8-de)^2 
g = ge-gm 
ge/gm = 81*(1-d)^2/d^2 
if ge/gm = 1, then : 
de^2 = 81(1-de)^2