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 ?

Question

Aicharya · Accepted Answer

As we know,
Gravitational potential cnergy

= \frac{- GMm}{r}

and orbital velocity,

v_{0} = \sqrt{GM / R + h}

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

= \frac{GMm}{3 R} (\frac{1}{2} - 1) = \frac{- GMm}{6 R}

E_{i} = \frac{- GMm}{R} + K

E_{i} = E_{f}

Therefore minimum required energy,

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

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M…

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