What happens to the gravitational force between two objects if the distance between them triples?

(1 point)

The force increases by a factor of 9.

The force decreases by a factor of 9.

The force increases by a factor of 3.

The force decreases by a factor of 3.

1 answer

The gravitational force between two objects is described by Newton's law of universal gravitation, which states that the force \( F \) is inversely proportional to the square of the distance \( r \) between their centers:

\[ F \propto \frac{1}{r^2} \]

If the distance between the two objects triples (i.e., becomes \( 3r \)), the new gravitational force \( F' \) can be expressed as:

\[ F' \propto \frac{1}{(3r)^2} = \frac{1}{9r^2} \]

This shows that the new force \( F' \) is \( \frac{1}{9} \) of the original force \( F \):

\[ F' = \frac{F}{9} \]

Therefore, if the distance between the two objects triples, the gravitational force decreases by a factor of 9.

The correct answer is: The force decreases by a factor of 9.