1. The problem statement, all variables and given/known data At what distance r inside the Earth is the gravitational force due to Earth the same as at the distance r = 4RE (where the latter distance is clearly outside Earth)? Assume uniform density of Earth. 2. Relevant equations conservation of energy? TME = GPE + KE 3. The attempt at a solution At first I thought I could do conservation of energy and set both GPE's equal to each other and solve for a new Radius, but this is not working out well. Is there something I need to do involving the density of Earth and the mass? I really have no idea. Thanks for any help!