Question

Satellite A is 7 times farther from a planet than satellite B. If it takes satellite B 4 weeks to complete a full orbit around the planet, how long will it take satellite A 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 = 4weeks 

For Satellite A, 
Mean distance = 7x 
Time period = y weeks. 

Now, 

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

(4/y)² = ( x/7x)³

16/y² = 1/343

y = 74 weeks.

Therefore, Satellite A takes 74 weeks to complete one revolution around the planet.