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17 May, 18:59

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

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  1. 17 May, 22:25
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    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
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