1. The problem statement, all variables and given/known data 2. Relevant equations See below 3. The attempt at a solution My book derives the period of oscillation through the tunnel: T = 2pi/w = 2pi*sqrt(m/k) = 2pi*sqrt(3/(4pi*G*p)) = sqrt(3pi/(G*p)) Where p is the density of the asteroid, and G is the Newton's gravitational constant. I know that the orbit velocity is found by equating the gravity force to the necessary centripetal force: mg = mv^2/r v = sqrt(r*g) So the period is 2*pi*r/v = 2pi*sqrt(r/g) I know these two periods are equal. Can anyone help me with putting them and similar terms and proving that they are?