The equation for the law of universal gravitation is
where **F** is the attractive force between masses **m**_{1} and **m**_{2} separated by distance **d**. **G** is the universal gravitational constant and relates **F** to the masses and distance as the constant π similarly relates the circumference of a circle to its diameter. By substituting changes in any of the variables into this equation, we can predict how the others change. For example, we can see how the force changes if we know how either or both of the masses change, or how the distance between their centers changes. Suppose, for example, that one of the masses somehow is doubled. Then substituting 2m_{1} for m_{1} in the equation gives
So we see the force doubles also. Or suppose instead that the distance of separation is doubled. Then substituting 2d for d in the equation gives
And we see the force is only ¼ as much. |