EDUPA: The Three Body Problem

The Problem:

The first topic of the evening I will talk about is the well-known three body problem. More an interesting case in classical mechanics than necessarily one of astrophysics-exclusive applications: this problem refers to the complete solution of motion three objects which both emit and impart a force upon one another. The classic example of this is three bodies in space, each with a certain mass and gravitational field.

The physics:
This problem primarily revolves around Newton's second equation, F=ma, and the universal law of gravitation (F=G*M_1*M_2/R^2). The most important part here, of course, is the R^2 dependency of this interaction. Since we are looking at three bodies, each body will have a constantly changing and updating radius in relation to the others. This is a problem, as any time the relationship between them changes, the force changes direction and strength. Essentially, updating the radius term for any of these bodies would change the effect felt by both the other bodies. Even if the simulation does a good job of modeling and averaging the steps taken by these, the finite nature of these steps as done by a computer would mean that they must still happen sequentially. This compounds any error, and leads to an inaccurate measurement.

Why does it matter?
The modeling of this will help astrophysicists to better understand the way that planets move, allowing them to solve many more complicated systems than we currently are able to. The solution to this has applications in computing and numerical analysis as well. By devising a way to make a true integration of the motion, one would also find a way to make computations that can occur simultaneously and without error. Assuming a solution to the three body problem would extrapolate to n-body problems, it could have applications to fields such as biology, chemistry, and materials science to explain molecular interactions as well.

Who is going to solve it?
From what I have found, there are no major publications of people actively working on this problem. It seems to be something more of a mathematical anomaly than an area of active physics. There are many programmers probably working on similar methods, but I couldn't find recent works on the subject.

What I think:
The non-linear nature of this problem seems like something that functional programming could potentially solve. By passing terms that are not by nature finite, it could be one way to resolve the dependency issues inherent to the problem. Time to start studying my lambda calculus!