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.

Question

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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Verity 3 years 2021-08-25T10:30:25+00:00 1 Answers 2 views 0

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  1. kimcuc
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    2021-08-25T10:31:30+00:00
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    Answer:

    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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