As a moon follows its orbit around a planet, the maximum grav- itational force exerted on the moon by the planet exceeds the minimum gravitational force by 11%. 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.

The gravitational force exerted on the moon by the planet when the moon is at maximum distance  is

where G is the gravitational constant, M and m are the planet and moon masses, respectively. This is the minimum force, because the planet and the moon are at maximum distance.

Similary, the gravitational force at minimum distance is

And this is the maximum force, since the distance between planet and moon is minimum.

The problem says that  exceeds  by 11%. We can rewrite this as


Substituing the formulas of Fmin and Fmax, this equation translates into

and so, the ratio between the maximum and the minimum distance is

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