First slide

Motion of planets and satellites

Question

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1%, its speed will

Moderate

A

increase by 1%
B

increase by 0.5%
C

decrease by 1%
D

decrease by 0.5%

Solution

$v \propto \frac{1}{\sqrt{r}}$
% increase in speed $= \frac{1}{2}$ (% decrease in radius)
$= \frac{1}{2} (1 %) = 0 .5 %$
i.e., speed will increase by 0.5%.

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