Orbits: Firing satellite to Moon

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Homework Statement


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Homework Equations


The Attempt at a Solution


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Parts I'm unsure of:
Sketching of graphs in (a) and (b). I know increasing its energy will shift the entire graph upwards. But does it shift it rightwards if the angular momentum is increased?

Last part, they said to ignore the gravitational effects of the moon. But clearly the satellite does not go into an elliptical orbit, as without the moon it's just going to go to a maximum distance, then come back in a straight line. By this analogy, the satellite is just going to be at rest at rmax. Thus the relative velocity is going to be simply the velocity of the moon.

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Discussion

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opinions on the last 3 parts, anyone?