The radii of circular orbits of two satellites A and B of the earth are ' 4 R ' and ' R ' respectively, where R is the radius of earth. If the speed of satellite B is 6 V , then th

Question

The radii of circular orbits of two satellites A and B of the earth are ' 4 R ' and ' R ' respectively, where R is the radius of earth. If the speed of satellite B is 6 V , then the speed of satellite A will be

TestHub · Accepted Answer

The orbital speed of a satellite is given by $v = \frac{GM}{r}$ .

This implies $v \propto \frac{1}{r}$ .

For satellites $A$ and $B$ , the ratio of their speeds is:

$\frac{v _{A}}{v _{B}} = \frac{r _{B}}{r _{A}}$

Given $r_{A} = 4 R$ , $r_{B} = R$ , and $v_{B} = 6 V$ :

$\frac{v _{A}}{6 V} = \frac{R}{4 R} = \frac{1}{2}$

$v_{A} = \frac{6 V}{2} = 3 V$

Answer: 3 V

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