Question

Satellite A, at a distance of 6.0 units, orbits a planet in 2.0 weeks. Satellite B orbits it in 7.0 weeks. How far is it from the planet?

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 A,
Mean distance = 6 units.
Time period = 2 weeks

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

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

(2/7)² = (6/x)³

4/49 = 216/x³

4x³ = 216*49

4x³ = 10584

x = 13.79 units ≈ 14 units .

Satellite B is at a distance of 14 units from the planet.