Orbital mechanics is complex and contains many non-intuitive examples of bodies in motion. It also contains a number of intractable problems that so far have defied analytical solutions. One of the best known is the problem of three non trivial masses orbiting one another. Solutions exist for several limited cases such as one of the bodies being of insignificant mass. A general case solution also exists from almost 100 years ago but converges so slowly that it is useless in practice. No usable general case purely analytical solution is known.

One of the reasons is that the three body system exhibits highly chaotic behaviour. It is extremely sensitive to tiny changes in conditions. It also exhibts strange attractors that have a tendency to eject one body with the result being a very stable two body system and one rogue body. Both of these situtations are demonstrated in the model parameters supplied with the simulation. I will be interested to know if anybody can find an initial setup that runs longer than mine.

I have modeled this using Google SketchUp version 7.1 and the latest version of SketchyPhysics ver 3.2. At this time that is the only combination of software that will work reliably. It will run on SU8 but it will also invariably crash, sooner or later.



The simulation is very simple to run. When you first load it hide the splash screen by clicking on the screen and then right click and select hide. You may adjust the starting parameters by simply moving the bodies around. Be careful if you save a configuration to not overwrite the original since you will have to download it again to recover the initial configuration. SketchyPhysics has limits that make it difficult or impossible to model inelastic collisions and still run on an average computer. Because of that collisions are modeled as perfectly elastic. This however brings a problem which is a result of the granularity of the simulation producing wrong answers when relative velocities are very high and position changes per frame are large. In some encounters the math will "blow up" and the bodies will rocket off into the distance with a large excess of velocity. This isn't a shortcoming of just this simulation as it applies to all numerical methods that use this approach to the problem. The use of very high powered computers removes the problem from consideration for non-relativistic solutions but it is still an ongoing issue in the simulation of bodies orbiting close to the event horizon of a black hole.

The simulation may be downloaded here:

http://sketchup.google.com/3dwarehou...22578eaa9892aa

I'm afraid that SketchUp 7.1 is no longer available so if you don't have it you can use SketchUp 8 but it will crash unpredictably.

SketchyPhysics 3.2 is available here

http://code.google.com/p/sketchyphys...2.exe&can=2&q=