Potential energy of a satellite having mas

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Potential energy of a satellite having mass $‘m’$ and rotating at a height of $6.4 \times {10^6}\,m$ from the earth surface is

A

$ - 0.5\,mg{R_e}$

B

$ - mg{R_e}$

C

$ - 2\,mg{R_e}$

D

$4\,mg{R_e}$

Potential energy of a satellite having mass $‘m’$ and rotating at a height of $6.4 \times {10^6}\,m$ from the earth surface is

Potential energy = $\frac{{ - GMm}}{r} $

$= \frac{{GMm}}{{{R_e} + h}} $

$= \frac{{ - GMm}}{{2{R_e}}}$

$= - \frac{{gR_e^2m}}{{2{R_e}}}$

$= - \frac{1}{2}mg{R_e}$

$ = - 0.5mg{R_e}$