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5 September, 13:23

During a solar eclipse, the moon (of mass 7.36 * 1022 kg), Earth (of mass 5.98 * 1024 kg), and Sun (of mass 1.99 * 1030 kg) lie on the same line, with the moon between Earth and the Sun. What gravitational force is exerted on the moon by the Sun? The universal gravitational constant is 6.673 * 10-11 N · m 2 / kg2, the Earth-moon distance is 3.84 * 108 m, and the Earth-Sun distance is 1.496 * 1011 m. Answer in units of N.

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  1. 5 September, 17:00
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    Newton's law of gravitation states that the force exerted by a body on another body is calculated as below:

    F = GM1•M2 / r²

    Where

    Mass of moon is

    Mm = 7.36 * 10²² kg

    Mass of earth is

    Me = 5.98 * 10²⁴kg

    Mass of sun

    Ms = 1.99 * 10^30 kg

    Gravitational constant

    G = 6.673 * 10^-11 Nm²/C²

    Earth-moon distance is

    Rem = 3.84 * 10^8 m

    Earth-Sun distance is

    Res = 1.496 * 10¹¹ m

    So, distance from the sun to the moon can be calculated using

    The distance from the sun to the moon is the difference between the distance from the earth to the sun and distance from the earth to the moon

    Rms = Res - Rem

    Rms = 1.496 * 10¹¹ - 3.84 * 10^8

    Rms = 1.49216 * 10¹¹ m

    Gravitational force exerted by the moon on the sun can be calculated using

    Fms = G•Mm•Ms / Rms²

    Fms = 6.673 * 10^-11 * 7.36 * 10²² * 1.99 * 10^30 / (1.49216 * 10¹¹) ²

    Fms = 4.39 * 10^20 N

    Then, the gravitational force exerted on the moon by the sun is 4.39 * 10^20N

    Extra ...

    We can also calculate the force exerted on the earth by the sun using

    Fes = G•Me•Ms / Res²

    You can compute that by inserting the parameters above

    Also we can find the force exerted by earth on the moon using

    Fem = G•Me•Mm / Rem²

    You can also compute this
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