1. The problem statement, all variables and given/known data An eﬃcient way to reach the Moon is to ﬁrst put the spacecraft in a low circular Earth orbit (radius r0, speed v0). The speed is then boosted to vp giving an elliptical orbit with apogee at the Moon’s orbit, ra, and perigee at r0. Show that: (vp/v0)^2=2ra/(r0+ra) 2. Relevant equations http://en.wikipedia.org/wiki/Vis-viva_equation 3. The attempt at a solution Using the Vis Viva equations, I found: vp^2=GM((2/r0)-(1/ra)) v0^2=GM((2/r0)-(1/r0))=GM(1/r0) so (vp/v0)^2=((2/r0)-(1/ra))/(1/r0) Which simplifies to (2ra-r0)/ra, which isn't right. Where did I go wrong?