? asked in 教育及參考書標準及測試 · 1 decade ago

AL PHY gravitational force 問題 有ans要解題

What is the difference between the acceleration of the earth towards the sun when an eclipse of the sun occurs and when an eclipse of the moon occurs?Give your answer in terms of mass of the earth(Me) , mass of moon (Mm) ,radius of earth's orbit about the sun (R),radius of moon's orbit about the earth(r).

Ans:2GMm/(r^2)

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  • 1 decade ago
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    Gravitational force on the Earth towards the Moon

    = GMmMe / r2

    Acceleration of the Earth towards the moon

    = (GMmMe / r2) / Me

    = GMm / r2

    Let k be the acceleration of the Earth towards the Sun.

    When an eclipse of the Sun occurs, the moon is between the Earth and the Sun. The gravitational force on the Earth by the Moon and the Sun are in the same direction.

    When an eclipse of the Moon occurs, the Earth is between the Moon and the Sun. The gravitational force on the Earth by the Moon and the Sun are in the opposite direction.

    Hence, the difference

    = (k + GMm / r2) - (k - GMm / r2)

    = 2GMm / r2

    Source(s): Myself~~~
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