As a moon follows its orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitati

Question

As a moon follows its orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitational force by 12.7%. Find the ratio rmax/rmin, where rmax is the moon’s maximum distance from the center of the planet and rmin is the minimum distance.

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Ngọc Khuê 4 years 2021-07-20T13:27:28+00:00 1 Answers 90 views 0

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  1. thienthi
    0
    2021-07-20T13:29:12+00:00
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    Answer:

    rmax/rmin = √1.127

    Explanation:

    F = GmM / r²

    As the masses can be assumed to be constant, the force between the two is proportional to the inverse of the square of the distance between them

    (Fmax – Fmin) / Fmin = 0.127

               (Fmax – Fmin) = 0.127Fmin

           1/rmin² – 1/rmax² = 0.127(1/rmax²)

                          1/rmin² = 0.127(1/rmax²) + 1/rmax²

                          1/rmin² = 1.127(1/rmax²)

                  rmax²/rmin² = 1.127

                     rmax/rmin = √1.127 ≈ 1.06160256…

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