1. The problem statement, all variables and given/known data If the Apollo vehicle is initially in a circular low Earth orbit with altitude h0 = 320 km and it is suddenly accelerated to a new (tangential) velocity of 10.8 km/s, determine the radial position, r, at apogee, the eccentricity of the new orbit and the period of this orbit. ---- I was confused by the wording but just to be clear it starts in a circular orbit and ends in an elliptical orbit of velocity 10.8km/s. 2. Relevant equations Eccentricity: e = (rap - rper)/(rap + rper) 3. The attempt at a solution I think there must be a relation between starting in a circular orbit and ending in an elliptical one. Is it possible that the nearest the Apollo vehicle will come to the Earth under this orbit is 320km? And only the aphogee requires calculation? I'm mainly asking this to see if anyone knows the relationship between the Mass of Earth (negligible Apollo mass) and velocity of orbit. I've had a quick google but unfortunately can't find it! Thanks!