The formula to find the period of orbit of a satellite around a planet is T2 = (4π2GM) r^3 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?

Question

Mathematics

Javion

21 November, 07:00

The formula to find the period of orbit of a satellite around a planet is T2 = (4π2GM) r^3 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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Douglas Lin · Answer 1

The formula to find the period of orbit of a satellite around a planet is T^2 = (4π^2/GM) r^3 where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant. To find the value of r, we rewrite r^3 = (T^2GM/4π^2) or r = (T^2GM/4π^2) ^ (1/3)