1. The problem statement, all variables and given/known data A constant-density planet of radius R has a gravitational acceleration ag = as at its surface. There are two distances from the center of the planet at which ag = as/2. Show that the ratio of these distances may be given by R = 2√2 2. Relevant equations ag= GM/R2 ρ=M/V 3. The attempt at a solution This is my attempt at approaching the problem. Given that there are two distances I'm thinking that one of the distances is inside the planet while the other would be outside. I know that this is a constant density planet therefore in some fashion I must use a density equation. The problem I'm receiving though is that when I setup the ratio I simply get 1 GM/R2 = GρV/2r2 GM/R2 = Gρ(4/3)∏r13/2r12 2M/R2 = ρ(4/3)∏r1 3M/2∏R2ρ=r1 At this point I simply do the same thing for r2 then set the ratio. This definitely doesn't feel right and I think I'm missing a key understanding to be able to completely understand this problem completely. Another idea I had was that the Rs must vary depending on where in relation I'm talking about. Could it be that the radii is R-r1 and R+r2? Any help is much appreciated.