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(D) The orbital velocity of a satellite is given by $v = \sqrt{\frac{GM}{r}}$,where $M$ is the mass of the Earth.$1$. Kinetic Energy $(K)$: $K = \frac

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Frequency of revolution varies as $1/r^{3/2}$

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(D) The orbital velocity of a satellite is given by $v = \sqrt{\frac{GM}{r}}$,where $M$ is the mass of the Earth.$1$. Kinetic Energy $(K)$: $K = \frac{1}{2}mv^2 = \frac{GMm}{2r}$. Thus,$K \propto \frac{1}{r}$.$2$. Angular Momentum $(L)$: $L = mvr = m \sqrt{\frac{GM}{r}} \cdot r = m\sqrt{GMr}$. Thus,$L \propto \sqrt{r}$.$3$. Linear Momentum $(p)$: $p = mv = m\sqrt{\frac{GM}{r}}$. Thus,$p \propto \frac{1}{\sqrt{r}}$.$4$. Frequency of revolution $(n)$: The time period $T = \frac{2\pi r}{v} = 2\pi \sqrt{\frac{r^3}{GM}}$. The frequency $n = \frac{1}{T} = \frac{1}{2\pi} \sqrt{\frac{GM}{r^3}}$. Thus,$n \propto \frac{1}{r^{3/2}}$.

$A$ satellite is orbiting the earth in a circular orbit of radius $r$. Which of the following is true?

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