Final answer:
The gravitational force between two bodies with masses of 100 kg and 400 kg, the same distance apart, is four times greater than the force between bodies with masses of 100 kg and 200 kg.
Step-by-step explanation:
When comparing the gravitational force between two bodies, it is essential to use Newton's law of universal gravitation, which states that the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The gravitational force (F) is given by the equation:
F = G * (m1 * m2) / r^2
where G is the gravitational constant (6.674 × 10^-11 N·m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between their centers. For the first scenario with masses of 100 kg and 200 kg, the force can be calculated and used as a reference. For the second scenario, when one mass is doubled to 400 kg and the other remains at 100 kg, the product of the masses becomes four times greater. Since distance remains constant, the force, according to Newton's formula, also becomes four times stronger compared to the initial scenario.