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Homework Statement
A satellite moves in an elliptic orbit with eccentricity e=1/2 around a planet which it was launched. When it arrives at an apsis( a radial turning point), its velocity is suddenly doubled. Show that the new orbit will be either parabolic or hyperbolic depending on which of the turning points the velocity doubling occurs.
Homework Equations
if the E<0 and e<1, the orbit is an ellipse
if E>0 and e>1 the orbit is a hyperbola
The Attempt at a Solution
I tried to solve this question, but I got stuck and couldn't get anywhere cause I wasn't sure what to do.