Replacing M with d M , R with a 2 − − x 2 , and p with p + x in the 'disc' equation yields: d E = ( 2 G [ 3 M ( a 2 − − x 2 ) ] 4 a 3 ) a 2 − − x 2 2 ⋅ ⋅ ( 1 − − p + x ( p + x ) 2 + a 2 − − x 2 2 ) d x Simplifying, ∫ ∫ d E = ∫ ∫ − − a a 3 G M 2 a 3 ( 1 − − p + x p 2 + a 2 + 2 p x ) d x Integrating the gravitational field of each thin disc from x = − − a to x = + a with respect to x , and doing some careful algebra, yields Newton's shell theorem: E = G M p 2 where p is the distance between the center of the spherical mass and an arbitrary point P . The gravitational field of a spherical mass may be calculated by treating all the mass as a point particle at the center of the sphere.