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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
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Verified Answer
The correct answer is:
$v^2=\frac{G M}{r}$
Given, $\mathrm{M}$ is mass of planet, $\mathrm{m}$ is mass of satellite, $\mathrm{r}$ is radius of orbit.
Let, $\mathrm{v}$ 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.,
$\mathrm{F}_{\mathrm{c}}=\mathrm{F}_{\mathrm{g}} \rightarrow(1)$
we know that,
$\mathrm{F}_{\mathrm{c}}=\frac{\mathrm{mv}^2}{\mathrm{r}} \text { and } \mathrm{F}_{\mathrm{g}}=\mathrm{GMmr}^2$
Substituting these values in (1),
$\frac{\mathrm{mv}^2}{\mathrm{r}}=\frac{\mathrm{GMm}}{\mathrm{r}^2}$
After solving this equation we get
$v^2=\frac{G M}{r}$
Let, $\mathrm{v}$ 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.,
$\mathrm{F}_{\mathrm{c}}=\mathrm{F}_{\mathrm{g}} \rightarrow(1)$
we know that,
$\mathrm{F}_{\mathrm{c}}=\frac{\mathrm{mv}^2}{\mathrm{r}} \text { and } \mathrm{F}_{\mathrm{g}}=\mathrm{GMmr}^2$
Substituting these values in (1),
$\frac{\mathrm{mv}^2}{\mathrm{r}}=\frac{\mathrm{GMm}}{\mathrm{r}^2}$
After solving this equation we get
$v^2=\frac{G M}{r}$
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