Calculate the location xcm of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at x=

Question

Calculate the location xcm of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at x=0 and the Moon is located in the positive x direction.

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Calantha 4 years 2021-08-06T08:05:24+00:00 1 Answers 169 views 1

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  1. Neala
    0
    2021-08-06T08:06:56+00:00
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    Answer:

    4.6\times 10^3 km

    Explanation:

    We are given that

    Mass of Earth,M=6\times 10^{24} kg

    Mass of moon,m=7.35\times 10^{22} kg

    x_1=0

    Distance between Earth and moon,x_2=3.80\times 10^5 km

    We have to find the location of the center of mass of the Earth- Moon system.

    Position of center of mass of Earth-Moon system

    x=\frac{Mx_1+mx_2}{m+M}

    Using the formula

    x=\frac{6\times 10^{24}\times 0+7.35\times 10^{22}\times 3.8\times 10^5}{6\times 10^{24}+7.35\times 10^{22}}

    x=4.599\times 10^3 Km\approx 4.6\times 10^3 km

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