If you want to understand all the best physics jokes (yes, these do exist), you should probably know about the spherical cow and the three-body problem.

Before looking at the three-body problem, let's start of with something simpler---the two-body problem. Suppose I have two objects (two stars would work) that are both moving and both interacting with each other.

The goal is to find an expression for the position of both objects (that are interacting gravitationally) for all future times. I'm not going to go through a full derivation, but solving the two-body problem isn't impossible. Here's what you do.

- In order to keep track of both stars, you would need six coordinates. There are three coordinates for the location of each star (assuming we don't care about their rotational orientation).
- We can make this a three-coordinate problem by considering the motion relative to the center of mass of the two-star system. This means the problem can be reduced to two problems. There is the motion of the center of mass (which isn't too interesting) and then a reduced mass (a combination of the two stars) orbiting the center of mass.
- In the reduced mass system, there is only the gravitational force pulling towards the center of mass. There is no torque on the reduced mass. This means that the angular momentum vector is constant. So, we can pick a plane of motion to coincide with the x-y plane. This means that we only need two coordinates to describe this system (we are getting somewhere).
- When you get to the actual physics (in Lagrangian mechanics) you can create a potential due to the angular motion (we can call this the centrifugal potential). This means that you will have a gravitational plus centrifugal potential and turn it into a 1-D problem (only motion in the r direction).