1. The problem statement, all variables and given/known data A satellite of mass m is in an elliptical orbit around the Earth, which has mass M and radius R. The orbit varies from closest approach of 'a' at point A to maximum distance of 'b' from the center of Earth at point B. At point a the speed of the satellite is vo. Assume Ug = 0 when masses are an infinite distance apart. Express your answers in terms of vo, a, b, m, M, R, and G. A. Write the definite integral (including limits) that can be evaluated to show that Ug at distance r from the center of the Earth is given by Ug = -GMm/r B. Determine the total energy at A. C. Determine the angular momentum at A. D. Determine the velocity at B. As the satellite passes point a, it changes to a circular orbit of radius a around the center. E. Determine the speed. F. Determine the work done by a rocket engine to make this change happen. 2. Relevant equations Fg = GMm/r f = GM/r2 g = Fg/m U = -GMm/r E = K + U = 1/2mv2 - GMm/r 3. The attempt at a solution For a. I wasn't sure where to start. What am I supposed to do, reverse-derive the equation? If so could someone show me how because I really don't know. b should just be E = mvo2/2 - GMm/r but I'm not sure this seems to easy. c like b I already know that the equation is mvoa but again it seems to easy that it's just asking to repeat an equation I learned in class, there must be a catch. d I thought v1r1 = v2r2 therefore vb = voa/b would work but my teacher said this was the answer: vb = square root of (vo2 + 2GM(1/b - 1/a)) I plugged in numbers and the % difference between the equations was approximately 1.8%. How did he get that equation? Why isn't mine right? e my book says that v = square root of (GM/r) so I put square root (GM/a) but again it just seems way too easy. f not sure where to start.