First slide

Motion of planets and satellites

Question

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a satellite orbiting a few hundred kilometres above the earth’s surface $(R_{Earth} = 6400 km)$ will approximately be

Moderate

A

1/2 h
B

1 h
C

2 h
D

4 h

Solution

$\frac{T_{2}}{T_{1}} = {(\frac{r_{2}}{r_{1}})}^{3 / 2} \Rightarrow T_{2} = 24 {(\frac{6400}{36000})}^{3 / 2} ≅ 2 hour$

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