Question

Satellite A is 5 times farther from a planet than satellite B. If it takes satellite A 22 weeks to complete a full orbit around the planet, how long will it take satellite B to travel around the planet once?

Answer 1

This question can be solved by Kepler's Third law of planetary motion which cites that The square of time period of a planet is directly proportional to cube of it's mean distance 

For Satellite B, 
Mean distance = x
Time period = yweeks 

For Satellite A, 
Mean distance = 5x 
Time period = 22 weeks. 

Now, 

$( \frac{t_{1} }{t_{2}} ) ^{2} = ( \frac{d_{1}}{d_{2} } )^{3}$


(y/22)² = (x/5x)³

y²/22² = 1/125

y² = 484/125

y = 1.96 ≈ 2 weeks.

Therefore, Satellite B takes 2 weeks to complete one revolution