What is the equation for gravitational force?

What is the equation for gravitational force?

• A. F = (m1 + m2) / r^2
• B. F = G m1 m2 r
• C. F = G (m1 m2) / r^2
• D. F = G (m1 + m2) / r

Answer: (C)

Gravity follows an inverse-square relationship: the force between two masses grows with the product of their masses and falls off with the square of the distance between them. This is captured by F = G (m1 m2) / r^2, where G is the gravitational constant. The product m1 m2 shows that larger masses pull harder, and the 1/r^2 term shows that doubling the distance reduces the force by a factor of four. The units also line up correctly: G has the appropriate units to make F come out in newtons when m1 and m2 are in kilograms and r is in meters. Other forms don’t fit because they either add the masses instead of multiplying them, place distance in the numerator (which would mean the force increases with distance), or omit the square on distance (which would change how the force weakens with distance and wouldn’t match observations).

Gravity follows an inverse-square relationship: the force between two masses grows with the product of their masses and falls off with the square of the distance between them. This is captured by F = G (m1 m2) / r^2, where G is the gravitational constant. The product m1 m2 shows that larger masses pull harder, and the 1/r^2 term shows that doubling the distance reduces the force by a factor of four. The units also line up correctly: G has the appropriate units to make F come out in newtons when m1 and m2 are in kilograms and r is in meters.

Other forms don’t fit because they either add the masses instead of multiplying them, place distance in the numerator (which would mean the force increases with distance), or omit the square on distance (which would change how the force weakens with distance and wouldn’t match observations).