the formula to find the period of orbit a satellite around a planet is T^2 = (4pi^2/GM) r^3 where r is the orbits mean radius. If you are givin all the values except r, how do you rewrite the formula to solve for r

The correct answer is r = ∛GM*T²/4π²

Step-by-step explanation:

Let's rewrite the formula to find the period of orbit of a satellite around a planet, to solve for r, this way:

T^2 = (4pi^2/GM) r^3

T² = (4π²/GM) * r³

r³ = T² / (4π²/GM)

r³ = T² * GM/4π²

r³ = GMT²/4π²

∛r³ = ∛GM*T²/4π²

r = ∛GM*T²/4π²

The correct answer is r = ∛GM*T²/4π²