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

Question

(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.

Answer 1

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 $F^{\prime }$ can be expressed as:

$$F^{\prime }\propto \frac{1}{(3r{)}^2}=\frac{1}{9r^2}$$

This shows that the new force $F^{\prime }$ is $\frac{1}{9}$ of the original force $F$:

$$F^{\prime }=\frac{F}{9}$$

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.