I recently did an exercise where I had to calculate the total energy needed to separate the stars completely from each other - i.e. make the distance between them infinity. One then had to calculate the potential energy between them as well as their kinetic energies. But theres something I don't get here - why do you have to use the kinetic energy in the calculations too. Couldnt you imagine a situation where the kinetic energy was the same after they had been separated by a distance of infinity.