A satellite of mass $m$ is placed at a distance $r$ from the centre of earth (mass $M$). The mechanical energy of the satellite is
A satellite of mass $m$ is placed at a distance $r$ from the centre of earth (mass $M$). The mechanical energy of the satellite is
$ - \frac{{GMm}}{r}$
$\frac{{GMm}}{r}$
$\frac{{GMm}}{{2r}}$
$ - \frac{{GMm}}{{2r}}$
A satellite of mass $m$ is placed at a distance $r$ from the centre of earth (mass $M$). The mechanical energy of the satellite is
Mechanical energy $=K.E+U$ (kinetic energy $+$ potential energy)
$U=-\frac{G m M}{r}$
$K \cdot E=\frac{1}{2} m v^{2}$
$K . E=\frac{1}{2} \frac{G m M}{r}$
$M . E=K . E+U$
$=-\frac{G m M}{r}+\frac{1}{2} \frac{G m M}{r}$
$M . E=-\frac{G m M}{2 r}$
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