If you have a rope around a soccer ball and the moon, which rope would have to increase in length more to create a one meter gap between the rope and the soccer ball/moon?
They would both increase length by 2 ? meters. Since Circumference = Diameter * ?, when they increase in length it is true that Circumference = (Diameter + 2) * ?. Distribute the ? and you get Circumference = Diameter * ? + 2 * ?.