Final answer:
The maximum and minimum values for the gravitational force that Earth and Mars exert on each other can be determined by calculating the force between them at their closest approach (opposition) and farthest separation (conjunction).
Step-by-step explanation:
The maximum and minimum values for the gravitational force that Earth and Mars exert on each other can be calculated using Newton's Law of Gravitation. The formula for gravitational force is F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the centers of the objects.
Since the masses of Earth and Mars remain constant, the maximum gravitational force occurs when the distance between them is minimized (closest approach), and the minimum gravitational force occurs when the distance between them is maximized (farthest separation). The maximum force would be when Earth and Mars are at opposition, approximately 401 million km apart. The minimum force would be when Earth and Mars are at conjunction, approximately 78 million km apart.
So, the maximum and minimum values for the gravitational force between Earth and Mars are determined by the distances between them, and the actual values can be calculated using the gravitational constant and the masses of the two objects.