First slide

Motion of planets and satellites

Question

Two satellites of masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ are revolving round the earth in circular orbits of radius $r_{1}$ and $r_{2} (r_{1} > r_{2})$ respectively. Which of the following statements is true regarding their speeds $v_{1} a n d v_{2}$ ?

Easy

A

$v_{1} = v_{2}$
B

$v_{1} < v_{2}$
C

$v_{1} > v_{2}$
D

$\frac{v_{1}}{r_{1}} = \frac{v_{2}}{r_{2}}$

Solution

$v = \sqrt{\frac{G M}{r}} \Rightarrow v \propto \frac{1}{\sqrt{r}} i f r_{1} > r_{2} t h e n v_{1} < v_{2}$
Orbital speed of satellite does not depends upon the mass of the satellite

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