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Question

A space ship of mass m is in circular orbit of radius 2Rc, about the earth of mass M and radius Rc. Find the energy required to transfer the space ship to circular orbit of radius 3Rc.

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Solution

Initial potential energy Ui=GMm2Rc
Final Potential energy Uf=GMm3Rc
Difference in energy UfUi=GMm6Rc

this difference in energy is needed to be provided to transfer the ship to the new orbit. So answer is GMm6Rc

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