Suppose you have a star of mass M and a planet of mass m orbiting around it. The orbit is circular. m<<<M. U of course is -GmM/r^2. E of course is going to be -U/2 and kinetic energy U/2 due to the virial theorem. What would happen if the mass of the star suddenly doubles? This is a practice test question. Now, if it doubles, the kinetic energy is going to stay the same because the angular momentum won't suffer a torque (because force is radial). However U will double. So we are going to have a new E of -3/2U where U=-GmM/r^2. Now this seems clear to me however. The test then asks the for the kind of orbit the planet is going to experience. The question does not make sense because if it was circular before, and now E is more negative, then the eccentricity will be an imaginary number so it would not be physically possible. Now, I did a similar homework problem to this but the star instead halves. If the star halves and the orbit was originally circular, E is gonna be 0 so the orbit will be a parabola and unbound. However, here I am experiencing instead that the star doubles, so E is going to be more negative than before. What am I supposed to answer here?