Final answer:
The correct scenario that would result in the greatest gravitational force between two objects is C, where you halve the distance between the objects while keeping their masses constant. This results in a gravitational force that is four times stronger due to the inverse square law of gravitation.
Step-by-step explanation:
Gravitational force plays a significant role in understanding how objects exert forces on each other due to their mass. According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Thus, when you double the mass of both objects (scenario A), the gravitational force becomes four times stronger because the force depends on the product of the two masses. On the other hand, if you double the mass of one object (scenario B), the gravitational force only doubles, since only one of the contributing masses has changed.
However, when considering changes in distance, if you halve the distance between two objects (scenario C), the gravitational force increases by a factor of four, since the force is inversely proportional to the distance squared. This means that halving the distance actually has a greater impact on increasing the gravitational force than simply doubling the mass of one or both objects. Therefore, the correct answer is scenario C, as halving the distance between two objects will result in the greatest increase in gravitational force. Increasing the distance, as in scenario D, would drastically decrease the gravitational force, specifically by a factor of nine if the distance is tripled.