Question

The formula to find the period of orbit of a satellite around a planet is T2=(4π2GM)r3 where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant. If you are given all the values except r, how do you rewrite the formula to solve for r?

Answer 1

The formula of the 3rd Kepler`s Law:
$T ^{2} = \frac{4 \pi ^{2}r ^{3} }{GM}$
$4 \pi ^{2} r ^{3} = T^{2}GM \\ r^{3} = \frac{T ^{2} GM}{4 \pi^{2} } \\ r = \sqrt[3]{ \frac{T ^{2}GM }{4 \pi ^{2} } }$