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.

Attraction forces subtract one to each otherand 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

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -