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) = (4 \pi ^(2)r ^(3) )/(GM)`

`4 \pi ^(2) r ^(3) = T^(2)GM \\ r^(3) = (T ^(2) GM)/(4 \pi^(2) ) \\ r = \sqrt[3]{ (T ^(2)GM )/(4 \pi ^(2) ) }`