Question

Two stars are near each other, and experience gravitational force between them. What happens if the distance between them is decreased by a factor of two?

a) Gravitational force decreases by a factor of two
b) Gravitational force increases by a factor of two
c) Gravitational force remains the same
d) Gravitational force becomes zero

Answer 1

The gravitational force between two stars increases by a factor of four if the distance between them is halved, due to the inverse square relationship outlined by Newton's law of universal gravitation.

Step-by-step explanation:

The question relates to how the gravitational force between two stars changes if the distance between them is altered. According to Newton's law of universal gravitation, the force of gravity is directly proportional to the product of the masses involved and inversely proportional to the square of the distance between their centers. Therefore, if the distance between two stars is decreased by a factor of two, the gravitational force between them increases by a factor of four, not two. This is because the force varies as the inverse square of the distance between them, so when the distance is halved, the inverse square is (1/2)^2, which is 1/4 the original distance, meaning the force increases by a factor of four (the inverse of 1/4).