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21 March, 01:24

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

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  1. 21 March, 03:36
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    160 days

    Explanation:

    Using the equation

    rA^3/TA^2 = rB^3/TB^2

    Where rA is radius of Moon A = R

    TA is Time for moon A complete one orbit = 20 days

    rB is radius of Moon B = 4R

    TB is Time for moon B complete one orbit = ?

    Therefore

    rA^3/TA^2 = rB^3/TB^2

    R^3/20^2 = (4R) ^3/TB^2

    Cross multiply to solve for TB, then we have

    TB^2 * R^3 = (4R) ^3 * 20^2

    TB^2 * R^3 = 64 * R^3 * 400

    TB^2 * R^3 = 25600 * R^3

    Divide both sides by R^3

    TB^2 = 25600

    Square root both sides

    TB = sqrt 25600

    TB = 160days
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