First slide

Motion of planets and satellites

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

Moderate

A

0.5 %
B

1.0 %
C

1.5 %
D

3.0 %

Solution

In the problem, the orbital radius is increased by 1%
Time period of satellite, $T \propto r^{3 / 2}$
Percentage change in time period
$= \frac{3}{2} (% change in orbital radius) = \frac{3}{2} (1 %) = 1 .5 %$

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