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- Homework Statement
- A rocket is in elliptic orbit around the Earth. To put it into an

escape orbit, its engine is fired briefly, changing the rocket’s

velocity by ΔV. Where in the orbit, and in what direction, should

the firing occur to attain escape with a minimum value of ΔV

- Relevant Equations
- Vesc = sqrt(2Gm/r)

I am really lost on how to deal with this. Since this is an elliptic orbit, the mechanical energy is negative. For the rocket to escape orbit, we have to get the mechanical energy to be equal to or greater than zero. I thought at first that it would escape in the perigee, since that's where the rocket's velocity is fastest, so it would need the minimum nudge ΔV to make it escape. However, the apogee also has the highest gravitational potential energy, so the rocket would require a lower velocity to escape. Either way, it is at one of the end-points, but I am not sure which and how to prove it.