Substituting in d M and integrating both sides gives the gravitational field of the disk: E = ∫ ∫ G M p ⋅ ⋅ 2 y d y R 2 ( p 2 + y 2 ) 3 / 2 Adding up the contribution to the gravitational field from each of these rings will yield the expression for the gravitational field due to a disc. This is equivalent to integrating this above expression from y = 0 to y = R , resulting in: E disc = 2 G M R 2 ( 1 − − p p 2 + R 2 ) To find the gravitational field at point P due to a sphere centered at the origin, an infinite amount of infinitely thin discs facing P , each with a radius R , width of d x , and mass of d M may be placed together.