Doug Hamilton as a nifty Astronomy Workshop web page, with lots of fun little tools….

I can guess why anyone with limited time might not want to risk editing Wikipedia. The finer the sculpture, the more likely it is to have its nose knocked off by drunken 16-year-old vandals. The “no original research” policy is infinitely regressive. There’s no mechanism to identify authority whatsoever.

You might consider adding a taunting footnote, in hopes that a seasoned warrior will see it and brave the gauntlet.

Not a lot of people know that there is an exact perturbation expansion solution to the three body problem, but it has rather poor convergence…

It isn’t quantum physics that is the oddity, but actually classical physics! The normal teaching of Newtonian physics (at least at low levels) falsely claims/indoctrinates the persistent lie that it allows the positions of the planets to be exactly calculated (determinism) when it does not if you have 3+ bodies, which you do. Richard P. Feynman conceded this in his book QED:

‘when the space through which a photon moves becomes too small (such as the tiny holes in the screen) … we discover that … there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that … interference becomes very important.’

The interference is due to many vacuum virtual charges:

‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs.’ — I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

The duration and maximum range of these charges is easily estimated: take the energy-time form of Heisenberg’s uncertainty principle and put in the energy of an electron-positron pair and you find it can exist for ~10^-21 second; the maximum possible range is therefore this time multiplied by c, or 10^-12 metre. This is far enough to deflect electrons but not enough to be observed as vacuum radioactivity. Like Brownian motion, it introduces chaos on small scales, not lare ones:

‘… the Heisenberg formulae can be most naturally interpreted as statistical scatter relations, as I proposed [in the 1934 book 'The Logic of Scientific Discovery']. … There is, therefore, no reason whatever to accept either Heisenberg’s or Bohr’s subjectivist interpretation …’ — Sir Karl R. Popper, Objective Knowledge, Oxford University Press, 1979, p. 303.

The Schroedinger wave equation arises naturally from a sea of particles because we know that you get waves in particle-based fluids: http://feynman137.tripod.com/#b

nuclear physics is inherently quantum mechanical, so you can’t get away with using the cold determinism of classical mechanics and hope to get answers corresponding to what experimentalists observe–you run into all sorts of odd probleems having to do with the indistinguishability of particles inside the nucleus, as well as the probabilistic nature of quantum mechanics.

This is a slightly different issue than the one above: Einstein was looking for a universe that was neither expanding nor contracting. By adding a cosmological constant, and fine-tuning the mass in the universe, this can be done pretty easily within GR–simply write down the standard cosmology that prefers no direction nor any position (as modern cosmologists do when taking their first, most basic run through things), and then set all the time derivatives equal to zero. This ends up giving you a set of relationships betwene the CC, the density of the universe, and the pressure of the matter in the universe.

It is a perfectly legitimate solution in the presence of a CC. However, a slight bump of this system leads not to a transition to chaos, but rather will cause the universe to either contract or to expand. Therefore, the Einstein static universe ends up beng akin to blaancing an egg on the top of a basketball–not impossible, per se, but it is essentially impossible to do perfectly enough to get the system to stay like that.

But you wouldn’t really consider the system chaotic–it would still remain a well-defined robertson-walker-desitter universe and would still be relatively close to the original system in the parameter space, at least initially. Late observers will be able to deduce the initial conditions of the system. Chaotic systems are much more uppity and difficult to manage.

The latter three tend to resemble a logarithmic spiral that may relate to the ‘Mice Problem’
http://mathworld.wolfram.com/MiceProblem.html

Yet all the multiple body systems would appear to likely have some type of radial symmetry that may resemble a ‘Superellipse’.
http://mathworld.wolfram.com/Superellipse.html

Nami– I don’t know anything about work with non-inverse-square force laws, but then again I wouldn’t.

None of these solutions is at all stable! Or realistic. But they are interesting and fun.

I just found this simulator program that “looks” great. I haven’t yet downloaded it, but will be doing soon. I came across this while searching for the program you mentioned. I’d really love to a non-inverse square universe.

http://gravit.slowchop.com/

If one adds a simplistic directional value to the system, then it cannot surely evolve ? all the above solutions are not really ideal?, for instatnce the first “figure-of-eight” is background independant.

If one was to find 21 point masses evolving thus, anywhere other than in a computer generated program, I would be amazed!

Their mutual Newtonian gravitational attraction, is realistically to “clinical”? . Example, any Cosmic background Expansion paramiter would nullify the systems evolution?

Even a simplistic 2-body system cannot evolve as an isolated system indefinate ?

Again, the input of the constrained orbits in the last box is neat, and is based on the unchanging Mathematics of Isolated Systems, which are not “Relative” to change !

Still cool to look at though.