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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?

Respuesta :

HomertheGenius
The formula of the 3rd Kepler`s Law:
[tex]T ^{2} = \frac{4 \pi ^{2}r ^{3} }{GM} [/tex]
[tex]4 \pi ^{2} r ^{3} = T^{2}GM \\ r^{3} = \frac{T ^{2} GM}{4 \pi^{2} } \\ r = \sqrt[3]{ \frac{T ^{2}GM }{4 \pi ^{2} } } [/tex]

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