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

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$\frac{{vr}_{A}}{r_{B} \sqrt{1.2}}$

$\frac{{vr}_{B}}{r_{A} \sqrt{1.2}}$

$\frac{{vr}_{A}}{1.2 r_{B}}$

$\frac{{vr}_{B}}{1.2 r_{A}}$

answer is A.

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Detailed Solution

For two points on same orbit L = ${mv}_{A} r_{A} = {mvr}_{B}$

$v_{A} = \frac{{vr}_{B}}{r_{A}} - - - - - - (i)$

For two points on different orbits.

$v = \sqrt{\frac{GM}{r}} \frac{v_{0}}{v_{A}} = {(\frac{r_{A}}{1.2 r_{A}})}^{\frac{1}{2}}$

$v_{0} = v_{A} {(\frac{r_{A}}{1.2 r_{A}})}^{\frac{1}{2}} = \frac{{vr}_{B}}{r_{A}} {(\frac{r_{A}}{1.2 r_{A}})}^{\frac{1}{2}} = \frac{{vr}_{B}}{r_{A} \sqrt{1.2}}$

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