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

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Solution

Initial potential energy $U_{i} = \frac{- G M m}{2 R_{c}}$
Final Potential energy $U_{f} = \frac{- G M m}{3 R_{c}}$
Difference in energy $U_{f} - U_{i} = \frac{G M m}{6 R_{c}}$

this difference in energy is needed to be provided to transfer the ship to the new orbit. So answer is $\frac{G M m}{6 R_{c}}$

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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.

Initial potential energy Ui=−GMm2RcFinal Potential energy Uf=−GMm3RcDifference in energy Uf−Ui=GMm6Rcthis difference in energy is needed to be provided to transfer the ship to the new orbit. So answer is GMm6Rc

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