Question

PLEASEEE HELP!!!! 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 answer is r = ∛(T²GM/4π²)

T² = (4π²/GM)r³

Divide both sides by 4π²/GM
T²/(4π²/GM) = (4π²/GM)r³/(4π²/GM)
T² * GM/4π² = r³
r = ∛(T²GM/4π²)