Thank you for the replies.

I'm not trying to model the whole solar system. I'm only trying to see if a fully formed Uranus & Neptune can peacefully co-exist for 100,000 years while seperated by only 1 AU. Originally, I did have Jupiter and Saturn in the simulation, I placed them at 5 & 8 AU as shown in the Nature diagram. This is just beyond the 2:1 resonant point. You have to look really close at figure 1 so see that Saturn migrates ever so slightly towards Jupiter which brings it into the 2:1 resonant point, where their combined gravity will now point in a specific direction rather than random directions at conjunction, as Ken describes.

With Jupiter and Saturn in the simulation, the results were similar, and the chaos in Uranus' and Neptune's orbits began right away. Wanting to know the sourse of chaos-producing pertabutions, and suspecting that Uranus & Neptune were doing it to each other, I deleted Jupiter and Saturn.

I used a timestep of 65K seconds, less than 1 day. I only need to go 500 - 1000 years to get my results.


The problem with the planetary disk condensing the way it is is that orbital periods are quite slow at the distances of Uranus & Neptune, and the disk material is theorized to have been too thin at that distance that the lifetime of the solar system is not long enough to have allowed Uranus & Neptune to accrete. This suggests they formed closer to the Sun, and migrated out to their current positions.

In the particular case of this Nature paper, the author's concern about the planets forming in their current locations is that it doesn't explain the tilts of the gas giants, especially Uranus. If Uranus were knocked on its side by a giant collision, there's no reason to believe that the orbital planes of its moons would have enough time over the life of the solar system to catch up with the planet's equator. So he speculates that if Uranus got tipped on its side gradually over the course of hundreds of thousands of years, that the moons orbital planes would be able to keep pace with the changing orientation of Uranus' equator. Although he doesn't say so in the paper, it seems to me that unlike the impactor theory, the planatary pertubation theory would provide torque to the planes moons' orbits as well as Uranus' equator.

Although no amount of modeling can forsee what may have actually happened in the early years of this system, that's not really the goal of these kinds of simulations. These simulations are only trying to spot trends. The author performed about 30 different simulations varying his starting conditions each time. He's not trying to find the smoking gun that says "Jupiter started exactly here, Saturn exactly there, this produces the exact obliquities observed today." He's simply trying to show that close planetary encounters can affect the obliquities of the planets, and that a 2:1 Jupiter Saturn orbital period ratio can disrupt the orbits of Uranus and Neptune enough to cause these close planetary encounters.

I'm glad you've got the Nature paper, Grant. It makes it much easier to discuss. The part you quote is followed by:

"...( the disk is assumed to start just beyond the initial orbit of the outermost planet)..."

which I take to mean that Uranus & Neptune were not in the disk at the time. And the part you quote is preceeded by the description of the changes in their orbits and obliquities following the migration of Jupiter and Saturn into the 2:1 resonance.

So I think the part you quote is referring to how their orbits circularized into the orbits we see today, [i]after[/] Saturn migrated beyond the 2:1 resonant point, rather than how they remained circular during the first 100,000 years before any of them ventured out into the planetisimal disk.

As Ken pointed out, the dynamical friction would have to be very strong to continuously circularize the orbits of planets that are pumping full AUs into each others perihelions and aphelions every 500 years.