Two neutron stars are separated by a distance of 10^13 m. They each have a mass of 10^30 kg and a radius of 10^5 m. They are initially at rest with respect to each other. (a) How fast are they moving when their separation has decreased to one-half its initial value? My answer is 3.652 x 10^3 m/s , and it is wrong again (sigh). here is my computations 1/2(mass)(final velocity)^2 - G(M1)(m2)/Final distance = 1/2(mass)(initial velocity)^2 - G(M1)(m2)/(initial radius) Since they are initially at rest, the vi term is zero, and that kinetic energy term vanishes. Then i plug in the values and solve for final velocity: 1/2(10^30)(final velocity)^2 - (6.67x10^-11)(10^30)^2/(5x10^12) = -(6.67x10^-11)(10^30)^2/(10^13) so I isolate for final velocity and i get (final velocity)^2 = 1.33 x 10^7 and i get final velocity = 3.652 x 10^3, when i input it it says it is wrong. Can someone help me, where did i go wrong? I did it multiple times already.