Question

The formula to find the period of orbit of a satellite around a planet is 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

r=

Explanation:

4 PIE SQUARED
`\sqrt[3]{\frac{GMT^(2) }{4\pix^\pi {2}  } }`

Answer 2

From my website, I have an online Kepler's Third Law calculator.
The formula is G · m · t² = 4 · π² · r³
I had to solve I have the formula solved for 'r', 't' and 'm' and I made a graphic of all three formulas. (see attached).
Anyway, since the formula is G · m · t² = 4 · π² · r³ then we can solve for 'r'

r³ = (G · m · t²) / (4 · π²) and therefore
r = cube root [(G · m · t²) / (4 · π²)]