# Would a spherically distributed solar system inevitably become flat, i.e., develop a plane of the ecliptic?

Notes

1. I have tagged this as hard science - If it turns out that current science has no research on the subject or cannot cope with calculations about this sort of system, I may relax this to science-based and allow informed speculation.

2. Some people might object that I have used the idea of gods in a hard science question. The gods are merely a fiction to 'explain' how the system might have come about - they are not essential. Feel free to ignore the god aspect and imagine that this solar system came about by natural forces.

Setup

Some young gods are playing at solar systems. One has the idea that, instead of the usual boring flat system, their system should be spherical.

They start with a Sun-like star then add asteroids and planets orbiting it every which way. Some orbits are at right-angles to each other or any other arbitrary angle. Some orbits are in similar planes but in opposite directions.

The young gods set this in motion and sit back in glee to watch the chaos that results. Near misses, weird non-elliptical orbits and, best of all, the occasional huge planetary collision.

Question

Presumably the solar system will eventually form some stable configuration. Will this inevitably be a standard flat system with all planets orbiting in the same direction or could there conceivably still be orbits in opposing directions and non-colliding orbits at up to 90 degrees from one another?

Assumptions

2. You may assume pretty much any starting configuration and velocity of orbiting bodies (OBs), as long as they tend to remain within the spherical radius of Sol's flat system.

3. The total mass and distribution of elements of OBs is the same as in our solar system.

4. Optionally you may assume the same planets (Earth, Mars etc.) and asteroids that we have, only orbiting in 3D instead of 2D.

5. Gods are not essential to the question, they are just there to give a motivation for the starting conditions. You may assume that this system came about by chance, however unlikely that may be.

• I don't believe that I can provide an actual answer of sufficient quality, but: 1) Retrograde orbits are a thing. Even if all planets are in (more-or-less) a single plane, they need not all orbit in the same direction. 2) Within the last several days, I read an article about astronomers observing a stellar system in which planets orbited in multiple planes, so it would seem that this is also a thing that can happen, if you can avoid problems with everything crashing together and destroying each other. – Dave Sherohman Sep 12 '20 at 11:03
• @Dave Sherohman - This sounds very interesting. Note that for hard science you don't necessarily have to provide the mathematics yourself. References to reputable sources is also an option, and this of course includes astronomical observations. If you feel inclined to work this comment into an answer (or even partial answer) I would be very grateful. – chasly - supports Monica Sep 12 '20 at 11:09
• Catch some rogue planets, have it collide with another system etc. As far as know, systems form flat, they don't become flat. Have things happen later that give you strange orbits. I'm not an astronomer, sorry if there is some weird phenomenon I'm missing that flattens orbits in basically vacuum, but I wonder if your starting point is wrong. – Raditz_35 Sep 12 '20 at 12:44
• The system won't ever become a "regular" system with all the major bodies orbiting in the same direction more or less in the same plane unless those same gods resurrect Sir Isaac Newton PRS and compel him to repeal the law of conservation of angular momentum. (Really, "hard science"?) – AlexP Sep 12 '20 at 13:11
• @Alex - hard science doesn't mean hard in the sense of advanced or difficult. It means that the answers should provide hard evidence. For example explaining the the application of Newton's laws to the problem. What is easy for some people is difficult for others. P.S. If you believe that, then what is the final configuration going to look like? – chasly - supports Monica Sep 12 '20 at 13:54

The question of stability will produce very different answers depending on the exact parameters of the system, but it seems that there are regions in parameter space of stability and regions of parameter space of instability.

The one example of confirmed significant non-coplanarity I know of is $$\upsilon$$ Andromedae A, a system containing three (and perhaps four) giant planets. A number of groups have suggested that planets c and d share a significant mutual inclination; some of the best evidence comes from McArthur et al 2010, who calculated a mutual eccentricity of $$29\pm1^{\circ}$$. As $$\upsilon$$ And has an age of $$\sim$$3 billion years, we can see that significantly evolved systems can harbor non-coplanar planets.

The question, though, is whether the current arrangement is stable, and if so, what mechanism is responsible. The authors found that the current inclinations and eccentricities can be maintained for c and d for a period of $$\sim$$100,000 years (at which point their simulations terminated), although the system exists on the very edge of stability in parameter space. A few tweaks to the initial conditions could lead to damping of the inclination of simply a catastrophic disruption of the system.

Libert & Tsiganis 2009 argued that, as with certain other planetary systems, the Kozai mechanism could lead to a stable configuration if the mutual inclination of c and d was $$\sim45^{\circ}$$ - although their nonrelativistic analysis may well be incomplete. This might require interactions with the other star in the system, $$\upsilon$$ And b. Other groups considered planet-planet scattering, which would still be an option in a one-star system.

In short: it seems quite possible that the system will never flatten out. If the planets have always had such a high mutual inclination, then it's clear that that can persist for billions of years, i.e. most of a roughly Sun-like star's lifetime. In that case, the answer to your question is likely no: A non-coplanar system does not necessarily have to evolve into a fplane.

### Chaotic initial placement of an N-body system results in everything in the sun or oort cloud.

So, no. It wont be planar.

I've ran a few N-body simulations trying to see what I can get to form, and randomly placing bodies (using c++'s std::normal_distribution) always resulted in a chaotic explosion. Doesn't matter if I modelled 10 bodies or 100 bodies or 1000. Doesn't matter what I used for their initial velocities, masses, and positions. They always blew up. The closer the mean start point was to the sun the sooner the system blew up. Many hit the sun or left the solar system (depending on the config), the rest settled into 100-1000yr elliptical orbits.

Simulation models interactions at a resolution of 1 hour. The tail shows the last 30 weeks travels

Here's a typical first year:

A typical 100th year:

A typical 500th year:

Here's one after 1000 years. I included the plane Z=0 to show that they aren't forming a planar system.

Basically they exploded, and tended to slow down a long way out. Typical distances for that final shot are 10^12 to 10^15m, which is past pluto and in the oort cloud. Orbital periods were in the hundreds or thousands of years.

Your gods will be waiting a long time for subsequent impacts. I stopped the simulation at 100,000 years, because I needed the computer to do actual work again. At this point its basically simulating the comet orbits.

So, your gods should know that they should keep their solar system formation to rotating pools of gas clumping together if they want anything interesting to happen.

(Apologies for the Z/N/E axis, I hacked this into some mining software I'm developing and forgot to change the axes)

• This is an interesting result, but I wonder whether the conclusions hold for truly astronomical timescales (i.e. billions of years). The orbits might be eccentric and highly inclined for now, but subsequent passes close to the parent star could eject them from the system, and dynamical interactions with other bodies might mean that the orbits are completely unstable. – HDE 226868 Sep 12 '20 at 14:18
• @HDE226868 I can't prove they don't - but my gut is telling me it's unlikely. "Chaos + Chaos = Order" doesn't seem likely. – Ash Sep 12 '20 at 14:23
• How many bodies are you simulating? What is their mass? And I hate to ask it, but how much can we trust the simulator? Simulators are notoriously sensitive to CPU precision limitations and whenever I see a chaotic explosion like this I wonder if the precision errors contributed to the problem. – JBH Sep 12 '20 at 15:18
• Sorry, I just remembered you tried a variety of quantities, masses, etc. Sorry. Anyway, what simulator did you use? What computing platform? Thanks. – JBH Sep 12 '20 at 15:25
• Windows, C++, x64. Intel I9. 64-bit data types. I hacked a hand-made N-body simulator it into some software my company is developing. – Ash Sep 12 '20 at 15:31