Question

A and B are two satellites revolving around the Earth in a circular orbit of radius R and 9R, respectively. If the time period of satellite A is 1 hour, then what will be the time period of satellite B?

• A. 3 hours
• B. 9 hours
• C. 18 hours
• D. 27 hours

Answer 1

The correct option is D 27 hours

Given:
Radius of orbit of satellite A (R${}_A$) = R
Radius of orbit of satellite B (R${}_B$) = 9R
Time period of satellite A (T${}_A$) = 1 hour

From kepler's laws, we know that
$\frac{T_A}{T_B}=(\frac{R_A}{R_B}{)}^{\frac{3}{2}}$
$\frac{1}{T_B}=(\frac{R}{9R}{)}^{\frac{3}{2}}$
$\frac{1}{T_B}=(\frac{1}{3}{)}^3$
$\frac{1}{T_B}=\frac{1}{27}$

$\Rightarrow T_B=27hours$