1. The problem statement, all variables and given/known data A rocket ship is in circular orbit of radius R around a planet. Its velocity is doubled by a sudden engine burst. Calculate the furthest distance from the planet on the new trajectory. 2. Relevant equations Elliptical energy equation: E = Ek +Ep = -GMm/2a (a=semi major axis) With Ek = (1/2)mv^2 and Ep = -GMm/R 3. The attempt at a solution Sorry for not being very user friendly. From applying the elliptical energy equation to the initial circular orbit, I deduced (1) v^2 = GM/R where v = initial velocity, M = mass of planet. After the impulse, I have: (2) E = (1/2)*m*(2v)^2 -GMm/R = -GMm/2(r+R) where r = length to planet from furthest distance Combining (1) and (2) gives r = -2R I have two questions in regards to this: 1) Is the method correct? 2) If the answer is right, how is it possible that I get a negative value? Does this just mean it is taken in the 'negative' direction to the original 'R'? Thanks, and sorry for the lack of friendliness in the equations again.