(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Elliptical orbits question

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