As we have stated since the beginning of the semester, the gravitational force acting on an object on the surface of the Earth can be calculated as `\vec{F}_{g} = m\vec{g}`.   But what about the gravitational force between the Earth and the moon?  Or the Earth and the sun?  Clearly, there is a gravitational force that keeps the Earth orbiting the sun, but how do you calculate its magnitude?

We have talked about Newton’s three laws of motion.  Now it is time to introduce his fourth major law, the Universal Law of Gravitation.  The Law of Gravitation explains the rules that govern the gravitational interaction between two point particles.  Of course, the Earth, the sun, and the moon aren’t point particles, but because the distances between objects within the solar system are much larger than the size of the objects themselves, they can be modeled as point masses.  This will let us use the Universal Law of Gravitation to describe not just the interactions between small masses, but also the interactions that determine how satellites orbit planets and planets orbit the sun.