A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R . The period of the second satellite is larger than that of th

Question

A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R . The period of the second satellite is larger than that of the first one by approximately

TestHub · Accepted Answer

In the problem orbital radius is increased by $1 %$
Time period of satellite $T \propto r^{3 / 2}$

$\Rightarrow \frac{∆ T}{T} = \frac{3}{2} \times \frac{∆ r}{r}$
Percentage change in the time period
$= \frac{3}{2}$ [ $%$ change in orbital radius]
$= \frac{3}{2} (1 %) = 1.5 %$

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