If the separation between two fixed-mass objects is increased to three times its original distance, how does the gravitational force between them compare to the original force?

If the separation between two fixed-mass objects is increased to three times its original distance, how does the gravitational force between them compare to the original force?

• A. One-third as great
• B. Nine times greater
• C. One-ninth as great
• D. Original force

Answer: (C)

Gravitational force between two masses follows the inverse-square law: F is proportional to 1 over the distance squared, r^2. If the separation is increased by a factor of 3, the distance becomes 3r. The new force is F' = F0 / (3^2) = F0 / 9. So the force is one-ninth as great as the original.

Gravitational force between two masses follows the inverse-square law: F is proportional to 1 over the distance squared, r^2. If the separation is increased by a factor of 3, the distance becomes 3r. The new force is F' = F0 / (3^2) = F0 / 9. So the force is one-ninth as great as the original.