When considering two bodies of different masses and distances between them, which scenario produces the strongest gravitational attraction according to Newton’s law?

According to Newton’s law of universal gravitation, the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This can be expressed with the formula ( F = G \frac{m_1 m_2}{r^2} ), where ( F ) is the gravitational force, ( G ) is the gravitational constant, ( m_1 ) and ( m_2 ) are the masses of the two bodies, and ( r ) is the distance between their centers.

When analyzing the provided scenario, having a significantly larger mass close to a smaller mass results in a greater gravitational attraction for several reasons. First, the larger mass contributes substantially to the product ( m_1 m_2 ), thus increasing the force. Additionally, the closeness of the two masses minimizes the distance ( r ), which appears in the denominator squared. Since gravitational force decreases with the square of the distance, reducing the distance significantly amplifies the gravitational attraction due to the nature of the ( 1/r^2 ) dependence.

In contrast, scenarios involving equal and smaller masses that are far apart or both masses being equal and far apart would result in