What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ?

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Quantrex Academy · Accepted Answer

Correct answer: C. 5 GmM 6 R

As we know,
Gravitational potential cnergy

= \dfrac{- GMm}{r}

and orbital velocity,

{v}_{0} = \sqrt{GM / R + h}

{E}_{f} = \dfrac{1}{2}{mv}_{0}^{2} - \dfrac{GMm}{3R} = \dfrac{1}{2}m\dfrac{GM}{3R} - \dfrac{GMm}{3R}

= \dfrac{GMm}{3R}\left(\dfrac{1}{2} - 1\right) = \dfrac{- GMm}{6R}

{E}_{i} = \dfrac{- GMm}{R} + K

{E}_{i} = {E}_{f}

Therefore minimum required energy,

K = \dfrac{5GMm}{6R}

What is the minimum energy required to launch a satellite of mass m...

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