If r represents the radius of the orbit of

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If $r$ represents the radius of the orbit of a satellite of mass $m$ moving around a planet of mass $ M$, the velocity of the satellite is given by

A

${v^2} = g\frac{M}{r}$

B

${v^2} = \frac{{GMm}}{r}$

C

$v = \frac{{GM}}{r}$

D

${v^2} = \frac{{GM}}{r}$

If $r$ represents the radius of the orbit of a satellite of mass $m$ moving around a planet of mass $ M$, the velocity of the satellite is given by

Given, $M$ is mass of planet, $m$ is mass of satellite, $r$ is radius of orbit.

Let, $v$ be velocity of the satellite

Now, for the satellite to revolve in the orbit the centripetal force must be balanced by gravitational force i.e.,

$F_{c}=F_{g} \rightarrow(1)$

we know that,

$F_{c}=\frac{m v^{2}}{r}$ and $F_{g}=G M m r^{2}$

substituting these values in $(1)$

$\frac{m v^{2}}{r}=\frac{G M m}{r^{2}}$

After solving this equation we get

$v^{2}=\frac{G M}{r}$

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