Looks Like Critical Mass is about 15 J's

I got my first three baseline simulations done. I used the same distances as found in our Solar system. First, Jupiter was made 1 Jupiter mass, Saturn 2Js, Uranus 4Js and Neptune 8 Js. Now it took a reasonable length of time to collapse. By fortunate good luck, that was about 62,000 years. I let it run longer just to watch it, but by 62 ky there were serious distortions like orbits crossing each other and extreme eccentricity. Saturn wound up the inner planet about half way into the asteroid belt with an aphelion a little under Jupiter's original orbit. Neptune kicked up surprisingly high.

Next, the mass ordering was reversed, Jupiter 8 Js, Saturn 4Js, Uranus 2Js and Neptune 1J. I thought it might be stabler. That lasted 91 ky before it looked totally weird. This time, due to the perburbations of the type modeled by Kevin at Chiron, it looked like Uranus was going to wind up a roaster. It had gotten in quite close to the Sun. Earth's orbit was cranked about 60 or 70 degrees to the invarient plane, perihelion about 50 Gm and aphelion about 250 Gm.

Then I assigned each planet 3.75 Jupiter masses and it lasted 82 ky. Jupiter and Saturn's orbits seemed to touch when viewed from the poles and the other two were out there a little beyond the Kuiper Belt.

Kevin had put a standard disclaimer that said his simulation was only good for about 100,000 years. That's pretty close to consensus for how far you can trust simulations and Kevin's right, but I don't know if he is talking about trying to find Chiron in a telescope after that time, in which case his timeframe surely works, or if he is just wanting a representative case to show how orbits can become very eccentric and shrink drastically. If you're trying to do the demonstration then at least 10 and maybe a hundred times that would probably do.

One source of error is that I can't get to the pause button fast enough for several years to go by and for Jupiter to achieve a full orbit. That clock starts fast! I guess I need to have a simulation paused at, say, April 1, 2012 and make sure they all start from there. I guess such a massive error might throw the length these things last off by several thousand years.

It was mere good fortune that I chose mass values that seemed to be critical for the distances found in our solar system. Now I am in a position to try to answer Vagueofgodalming's query about distances. But I don't know how long I should run it before I declare it "stable". I will try twice the distances. If that "looks" stable I will divide that by the square root of two, then the square root of two, etc.

In all these simulations with the different masses, I noticed that Uranus had the least stable orbit when the simulations first started, even though the distributions were different every time. The lines representing Uranus's orbit were up to about 5 mm apart on my monitor over a single orbit.

Tony Dunn's program has a "plot/don't plot" button and it's very good for following chaotic simulations. The idea here is that the machine calculates all the positions on the board and then creates a graphic display. It you hit "don't plot", then it stops making graphic displays every 30th of a second and as a result, the machine runs much faster. You can turn it on for 167 years and then turn it off and thousands of years will go by in a minute or so. Sometimes the planets enter stable circular phases and the plots are almost superimposed, while other planets show precession or large changes in orbital elements. It's real fun to watch ;)

:D

-Michael C. Emmert