Mathematics
superjosh
9

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?

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joycesouza

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)]

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