Question

A geo-stationary satellite orbits around the earth in a circular orbit of radius $36000km$. Then, the time period of a spy satellite orbiting a few $100km$ above the earth's surface ($R_{earth}=6400km$) will approximately be -

• A. $1/2hr$
• B. $1hr$
• C. $2hr$
• D. $4hr$

Answer 1

The correct option is C $2hr$

Satellite orbits in a radius of $36000㎞R_1=36000㎞$

$R_{earth}=6400㎞,R_2=6400$

By Lepler's third law, we know that

$T^2\propto R^3$

Also we know that time period of geostationary satellite is $24h$

$T_1=24h$

$\therefore {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^3$

$\Rightarrow \frac{{\left(24\right)}^2}{{\left(T_2\right)}^2}={\left(\frac{36000}{6400}\right)}^3$

$T_2=24{\left(\frac{6400}{36000}\right)}^{3/2}$

$T_2=2h$