Imagine a spherical, nonrotating planet of mass M, radius R, that has no atmosphere. A satellite is fired from the surface of the planet with speed vo at 30 degrees to the local vertical. In its subsequent orbit the satellite reaches a maximal distance of 5R/2 from the center of the planet. Using the principles of conservation of energy and angular momentum, show that vo - (5GM/4R)^1/2(adsbygoogle = window.adsbygoogle || []).push({});

This is what I've done so far and it's not right:

E=1/2 mv^2 - GMm/2R = GMm/4R

1/2mv^2-GMm/2(5R/2) = GMm/4(5R/2)

1/2mv^2-GMm/5R = 2GMm/20R

1/2v^2 = 3GM/10R

.:v = (3GM/5R)^1/2

Clearly, this isn't the answer I should be getting. Does anybody know where I'm going wrong?

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# Homework Help: Conservation of Energy and satellite

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