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Carbonated_Brains · 05-31-2004, 04:22 PM

Let's see how badly I can mangle physical theory based on my memory of high school.

So you've got one body floating in space. It's simple to demonstrate it's position and behaviour; if nothing acts upon it, it just sits there.

Two bodies in space. When they have a gravitational effect on each other, they trace out an ellipse. Their motions can be predicted and explained analytically using mathematics. Newton solved the 2 body problem.

Add a third body? The math goes to hell. It is generally thought that the three body problem lends itself to chaos theory, and that there is no analytical way to describe the movements of three bodies insofar as how they act on each other. It was originally postulated that one could predict the future of an object's motion assuming you knew the forces acting upon it, but the three body problem proved this to be false; and essentially gave birth to the idea of chaos theory.

In 1912, Karl Sundman developed a convergent infinite series as a solution to the restricted three body problem. Problem is, getting it to any level of precision required something on the order of 10^8,000,000 terms, and his solution is of little practical use.

I always was fascinated by the fact that science cannot explain something as "seemingly" simple as how three objects affect one another.

05-31-2004, 04:22 PM	#18
Carbonated_Brains Does it show up here when I type? Join Date: Oct 2003 Location: Between the smoky layers of a prosciutto sandwich! Posts: 355	Let's see how badly I can mangle physical theory based on my memory of high school. So you've got one body floating in space. It's simple to demonstrate it's position and behaviour; if nothing acts upon it, it just sits there. Two bodies in space. When they have a gravitational effect on each other, they trace out an ellipse. Their motions can be predicted and explained analytically using mathematics. Newton solved the 2 body problem. Add a third body? The math goes to hell. It is generally thought that the three body problem lends itself to chaos theory, and that there is no analytical way to describe the movements of three bodies insofar as how they act on each other. It was originally postulated that one could predict the future of an object's motion assuming you knew the forces acting upon it, but the three body problem proved this to be false; and essentially gave birth to the idea of chaos theory. In 1912, Karl Sundman developed a convergent infinite series as a solution to the restricted three body problem. Problem is, getting it to any level of precision required something on the order of 10^8,000,000 terms, and his solution is of little practical use. I always was fascinated by the fact that science cannot explain something as "seemingly" simple as how three objects affect one another.