33. III As a moon follows its orbit around a planet the maximum gravitational force exerted on the moon by the planet exceeds the mini- mum gravitational force by 11% Find the ratio r_(max)/r_(min) where r_(max) is the moon's maximum distance from the center of the planet and r_(min) is the minimum distance.

To solve this problem, we can use the formula for gravitational force, which is given by Newton's law of gravitation: where is the gravitational force, is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of the two objects.In this case, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitational force by 11%. Therefore, we can write: Substituting the formula for gravitational force, we have: We can cancel out the common factors and from both sides of the equation: Taking the reciprocal of both sides, we get: Taking the square root of both sides, we get: Therefore, the ratio is: This is the ratio of the moon's maximum distance from the center of the planet to its minimum distance.