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14 February, 14:47

Given: G = 6.672 * 10-11 N · m2 / kg2 Io, a satellite of Jupiter, has an orbital period of 1.24 days and an orbital radius of 4.11 * 105 km. From these data, determine the mass of Jupiter. Answer in units of kg.

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  1. 14 February, 15:44
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    Mass of Jupiter = 4.173*10^15kg

    Explanation:

    Using Kepler's 3rd law, it states that the orbital period T is related to the distance, r as:

    T^2 = GM/4 pi * r^3

    Where G = universal gravitational constant

    r = radius

    M = masd of jupiter

    Rearranging the formular to make M the subject of formular

    T^2 * 4 pi = G M * r^3

    (T^2 * 4 pi) / (G * r^3) = M

    (1.24^2 * 4 * 3.142) / (6.672*10^-11) (4.11*10^8) ^3

    M = 19.32 / 6.672*10^-11) (4.11*10^8) ^3

    M = 19.32 / 4.63 * 10^15

    M = 4.173*10^15kg
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