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Zepler [3.9K]
3 years ago
12

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

um 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.
Physics
1 answer:
professor190 [17]3 years ago
8 0

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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Explanation:

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Applying<u> Natural Logarithm</u> on both sides of the equation (2):

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According to the Natural Logarithm rules xln(e)=x, so (4) can be written as:

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Finally:

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3 years ago
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