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.

Answer 1

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...