According to Newton's Law of Gravity, how do mass and distance affect the gravitational attraction between two objects? $F=\frac{G{m}_1{m}_2}{r^2}$

• A. The gravitational force $F$ increases with increasing mass and decreases with increasing distance.
• B. The gravitational force $F$ increases with both increasing mass and increasing distance.
• C. The gravitational force $F$ decreases with both increasing mass and increasing distance.
• D. The gravitational force $F$ decreases with increasing mass and increases with increasing distance.

Answer: (A)

Verified step by step guidance

1. Start by recalling Newton's Law of Universal Gravitation, which states that the gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers. This can be expressed mathematically as: $F=\frac{Gm{1}_{}m{2}_{}}{r^2}$, where G is the gravitational constant.
2. Understand the relationship between mass and gravitational force: As the masses of the objects (m1 and m2) increase, the gravitational force between them also increases. This is because the force is directly proportional to the product of the masses.
3. Consider the effect of distance on gravitational force: As the distance (r) between the two objects increases, the gravitational force decreases. This is due to the inverse square relationship, meaning the force is inversely proportional to the square of the distance.
4. Analyze the options given in the problem: The correct interpretation of Newton's Law of Gravity is that the gravitational force increases with increasing mass and decreases with increasing distance.
5. Conclude by selecting the correct answer based on the analysis: The gravitational force increases with increasing mass and decreases with increasing distance, which aligns with the mathematical expression and conceptual understanding of Newton's Law of Universal Gravitation.