If the distance between two masses is tripled, how does the gravitational force

If the distance between two masses is tripled, how does the gravitational force change?

If the distance between two masses is tripled, how does the gravitational force change?

Step 1: Understand that gravitational force (F) between two masses depends on the distance (r) between them.
Step 2: Remember the formula for gravitational force: F ∝ 1/r². This means that the force is inversely proportional to the square of the distance.
Step 3: If the distance (r) is tripled, we can express this as r becomes 3r (where r is the original distance).
Step 4: Substitute 3r into the formula: F ∝ 1/(3r)².
Step 5: Calculate (3r)², which equals 9r².
Step 6: Now the formula looks like this: F ∝ 1/(9r²).
Step 7: This means that the new gravitational force (F') is F/9, where F is the original force.
Step 8: Conclude that if the distance between the two masses is tripled, the gravitational force becomes one-ninth of the original force.

Inverse Square Law – The gravitational force between two masses is inversely proportional to the square of the distance between them.