Newtonian mechanics of Gravitational energy

 
Gravitational attraction. Two masses in space each exert a force on the other. The magnitude of this force depends on the product of their masses and the

Newtonian mechanics

According to classical mechanics, between two or more masses (or other forms of energy–momentum) a gravitational potential energy exists. Conservation of energy requires that this gravitational field energy is always negative.[2]
Particularly, between any two point masses m and M (this works for the spherical bodies also), there always exists a gravitational force of F = GmM/r^2 where r is the distance between their centers. Increasing the distance from r = r_0 to r = r_1 reduces the force, but, since forces in Newton mechanics indicate how much potential energy is lost over space, F = - {dU \over dx}, this separation requires \int_{r_0}^{r_1}{mMG\over r^2} dr = \left . {mMG\over r} \right \vert _{r_1}^{r_0} = {mMG\over r_0} - {mMG \over r_1} = E of energy. Performing positive work equal to E units of energy, we can recede objects from r0 to r1 special units apart. By performing positive work equal to E = {mMG / r_0} , the second term vanishes and objects are infinitely separated (r_1 = \infty). Because gravitational force stops pulling objects together at that distance, E = {mMG / r_0} is known as gravitational binding energy, which is infinite at r_0 = 0 since the gravitational force is infinite there[citation needed].