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csmiller1993

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**Summary::**A question on a recent exam was, "At what eccentricity does an orbit experience a velocity at periapsis that is twice the velocity an apoapsis?" I don't know why the provided solution is correct.

On a recent exam, one of the questions was "At what eccentricity does an orbit experience a velocity at periapsis that is twice the velocity an apoapsis?"

In the exam solutions, the given answer is e = 3/5. with the following as the justification:

e + 1 = 4 - 4e

e = 3/5

I'm not sure where the professor got this relation. When I attempt to solve this problem I end up with e = 1/3. My work is attached. Am I missing something or is the professor wrong? I emailed her and she simply said to check my derivation. I've solved it with the vis viva equation as well and still came out to 1/3. Other students have also reported that they got 1/3.

Thanks in advance!