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Satellites

The orbital v...

Question

The orbital velocity of a satellite at point $B$ with radius $r_{B}$ is $v$ . The radius of point $A$ is $r_{A}$ .When satellite is at $A$ , the orbit is increased in radial distances uniformly, so that $r_{A}$ becomes $1.2 r_{A}$ , find the orbital velocity at $(1.2 r_{A})$

\frac{v r_{B}}{r_{A} \sqrt{1.2}}

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\frac{v r_{A}}{1.2 r_{B}}

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\frac{v r_{B}}{1.2 r_{A}}

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\frac{v r_{A}}{r_{B} \sqrt{1.2}}

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Solution

The correct option is A $\frac{v r_{B}}{r_{A} \sqrt{1.2}}$
For two points on same orbit
$L = m v_{A} r_{A} = m v r_{B}$
$v_{A} = \frac{v r_{B}}{r_{A}}$
For two points on different orbits.
$v = \sqrt{\frac{G M}{r}}$
$\frac{v_{n}}{v_{A}} = {(\frac{r_{A}}{1.2 r_{A}})}^{\frac{1}{2}}$
$v_{n} = v_{A} {(\frac{r_{A}}{1.2 r_{A}})}^{\frac{1}{2}}$
$v_{n} = \frac{v r_{B}}{r_{A}} {(\frac{r_{A}}{1.2 r_{A}})}^{\frac{1}{2}} = \frac{v r_{B}}{r_{A} \sqrt{1.2}}$

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