1. The problem statement, all variables and given/known data Consider a ring-shaped body in a fixed position with mass M. A particle with mass m is placed at a distance x from the center of the ring and perpendicular to its plane. Calculate the gravitational potential energy U of the system (the picture has a small sphere travelling towards the center of a ring perpendicular to the ring's plane). 2. Relevant equations Fg = (G*m*M)/r^2 Fg*r = U = (G*m*M)/r, where r is the radius, and G = 6.67*10^(-11) (gravitational constant) 3. The attempt at a solution Let r be the hypotenuse of a right triangular distance to any part of the ring and a be the distance from the center of the ring to join the hypotenuse. x will make the 90° angle with a. So, I thought that I would multiply the perpendicular component of force to the perpendicular distance x to get a function for gravitational potential energy, F(perpendicular component) = (G*m*M)/(x^2) = (G*m*M)/(r^2 - a^2), where x^2 = r^2 - a^2. Then, U = (G*m*M)/(r^2 - a^2)*(r^2 - a^2)^(1/2) = (G*m*M)/(r^2 - a^2)^(1/2). But apparently this is wrong. The right answer is U = (G*m*M)/(r^2 + a^2)^(1/2), the same as my answer except for the +. I just don't understand why my answer is not right.