An exploding star: A planet of mass m is in a circular orbit about a star of mass M at an initial distance of r. The non-rotating star then explodes and ejects half of its mass radially outward in a symmetric fashion with none of its ejecta hitting the planet. After the star's explosion find the new radius of the planet about the star. I got a response with
mrw^2 = GMm / r^2 ,
w^2 = GM / r^3
but could not figure out how to derive the expression. Is it using Conversation of Energy? I understand the Conservation of Momentum part, just didn't get how to obtain the velocity part. Could you please break down the components/energy equation?