Here is the first part of the question: If there is an object of mass m at the center of the earth, how much work does it take bring that object up a shaft to the surface? Edit: Earth is uniform density. Do I integrate g(r) = -GMr/R^3 with respect to 'r' to get the change in gravity from the center of the Earth to the surface and then solve from R-0. If so I get a solution of -GM/2R, and that doesn't look at all right to me. The second half of the question relates back to the first part and asks if mass m is dropped from the surface down a mineshaft to the center of the earth, what will its speed be when it reaches the center. Again, since gravity is changing with respect to the radius, how do I get a solid answer?