# Three is a big number

Carrying on the big number theme I will now tell you that three is a good working approximation to infinity. Yes, three, you know, the number that comes after two.  As in one, two, infinity.

So you are thinking I’ve finally lost my marbles.

Well, consider this problem.

We know how a single object moves. Newton worked it out, and gives us some nice laws for it. What about if we put a second object next to it, and have the two attract by gravity? Like a planet orbiting a star. Newton worked that one out too. If one is much smaller than the other, it will orbit in an ellipse. But strictly, they both move in ellipses, about their centre of mass.

What if we throw in a third object?  Like a big planet orbiting a binary star. What happens then? The exact answer to this has escaped the best mathematicians and physicists, including geniuses like Poincare and Lagrange.  In fact, in some cases it can be shown that the behaviour is chaotic – there are no repeating orbits; we will never get the objects to return to their starting points with the same velocities.  Put in more objects and it just gets worse.

Thus three objects might as well be an infinity, as far as calculating their movement goes. QED.

(For a nice demo of orbiting bodies, see this applet. I suggest looking at their in built examples).