# A space vehicle of mass m is in a circular orbit of radius 2Re about the earth (mass me). What is the work done by an external agent to transfer it to an orbit of radius 4Re.

Work done here is the difference in energies at the two orbits.
So,
$W=\frac{G{m}_{e}m}{2\left(2{R}_{e}\right)}-\frac{G{m}_{e}m}{2\left(4{R}_{e}\right)}=\frac{G{m}_{e}m}{8{R}_{e}}$

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