In the figure here, a space shuttle is initially in a circular orbit of radius r about Earth. At point P, the pilot briefly fires a forward-pointing thruster to decrease the shuttle’s kinetic energy K and mechanical energy E. (a) Which of the dashed elliptical orbits shown in the figure will the shuttle then take? (b) Is the orbital period T of the shuttle (the time to return to P) then greater than, less than, or the same as in the circular orbit?
Hello. I have a major trouble understanding this question. How do we know that the space shuttle passes throught the point P after losing speed ? Also, the lower orbits must have greater speeds. Doesn't that mean the pilot must increase the shuttle's kinetic energy to go to lower orbits ? Appreciate any help! Thanks!