Hello everyone. The following is from the practice test given to me for my intermediate mechanics final. I'm, at the moment, completely lost on what to do. If you have even just a few ideas of what I should be doing they would be apperciated. If you want to give a detailed solution it would be wonderful. Problem: The relative coordinate of a system of two masses, m and M, is moving in a circular orbit of radius r_0 because of the mutual gravitational attraction. Suddenly the particle with mass m receives a kick in negative radial direction. As a consequence of this kick, the particles approach each other until the centrifugal force finally repels them again. What radial velocity, v_0 as a result of the kick is necessary to have the particles approach each other to a minimum distance of 10% of r_0? Is the new trajectory a circle, ellipse, parabola or hyperbola? Thank you for your time.