A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$. The value of $x$ is ______ , where $M$ and $R$ are the mass and radius of earth, respectively. ( G…

Question

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$. The value of $x$ is ______ , where $M$ and $R$ are the mass and radius of earth, respectively. ( G is the gravitational constant)

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { orbital velocity } v_0=\sqrt{\frac{\mathrm{GM}}{4 \mathrm{R} / 3}}=\sqrt{\frac{3 \mathrm{GM}}{4 \mathrm{R}}} \ & 	ext { Angular momentum of satellite }=\frac{\mathrm{M}}{2} \mathrm{v}_0 \frac{4 R}{3} \ & =\frac{M}{2} \cdot \sqrt{\frac{3 \mathrm{GM}}{4 \mathrm{R}}} \cdot \frac{4 \mathrm{R}}{3} \ & =M \sqrt{\frac{\mathrm{GMR}}{3}} \ & x=3\end{aligned}$

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$…

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