Final answer:
The gravitational force between two masses where one mass is doubled and the distance is doubled will be half as great as the original gravitational force.
Step-by-step explanation:
When the distance between two point masses, m and M, is increased to 2d and the mass m is doubled to become 2m, the gravitational force between them changes according to the universal law of gravitation, which states that the gravitational force (F) is directly proportional to the product of their masses (m & M) and inversely proportional to the square of the distance (d) between them. This relationship is given by the formula F = G(m & M)/d², where G is the gravitational constant. Initially, the force is F = G(m & M)/d², and after the changes, the new force becomes F' = G(2m & M)/4d² due to doubling of one mass and the square of the distance. The '2' from the increased mass in the numerator is canceled out by one '2' from the denominator, leaving the new force at G(m & M)/2d², which is half of the initial gravitational force. Thus, the gravitational force will be half as great after the changes.