If the distance between two objects is increased by two times, the gravitational force between them will

According to Newton's Law of Universal Gravitation, the gravitational force (F) between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers. This relationship is mathematically expressed as F = G(m1m2)/r², where G is the gravitational constant [1]. Because of this inverse-square relationship, any change in distance has a squared effect on the force in the opposite direction. If the distance between two objects is increased by two times (doubled), the new force becomes proportional to 1/(2r)², which simplifies to 1/4r². Consequently, the gravitational force decreases by a factor of four. This principle confirms that as objects move further apart, the attractive force between them weakens significantly.

Sources

1. [1] https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:types-of-interactions/x215e29cb31244fa1:newton-s-law-of-universal-gravitation/a/newtons-law-of-universal-gravitation