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five planet system (Read 14820 times)
EDG
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five planet system
10/11/06 at 18:13:49
 
Here's a fun one to try... (rightclick and save target, it's a gsim file)
5-planet system
 
 
Inner/Outer Reach values is from Jones et al. papers:  
http://arxiv.org/abs/astro-ph/0603200
and  
http://adsabs.harvard.edu/abs/2005astro.ph..3178J
 
What's interesting about this system is that I ran it for about 8 hours last night (3.5 million years simulation time) and I lost all the planets except the innermost one!
 
However, when I removed GG4 (the green one) and ran it today for 9 hours with a 3 day timestep, all the planets were still there after 35 million years of simulation time. So it looks like the green one is the kicker that sends it over the edge.  
 
Looking at the stats below, you'll notice that GG4's aphelion is within GG5's "Reach" (defined in the Jones papers linked below). "Gravitational Reach" indicates the 'ejection zone' of a gas giant - if a less massive object is in that region then it'll be tossed out of the system.  
 
And sure enough in a five system run, GG4 is tossed out. Unfortunately, this happened while I was asleep Wink. What I think happened is that GG4 and GG5 started interacting after about 2.5 million years (which is when I went to bed), one got tossed out but in the process the other must have had a close pass with one of the inner GGs, and got tossed out as well, making the inner system unstable so that 2 and 3 got eventually tossed out later on.
 
GG2 and GG3 aren't the most stable system either, there's a fair bit of natural wobble in GG3's orbit so I would have said that those were the next most likely to get tossed out anyway... but given that after 35 Ma these two are still here if GG4 isn't, implies that it's fairly stable to me.  
 
Anyway, from the calculated Reach limits, my money was on GG4 being the troublemaker, and sure enough when it's removed the system lasts a lot longer - so I think that's a fairly decent vindication of the gravity simulator program Wink.  
 
----------------------
Stats:
F7 V primary: 1.177 solar masses, 2.02988 solar radii, 1.6657 solar luminosity
 
GG1 (purple):
semimajor axis: 6.218 AU
eccentricity: 0.064
mass: 0.309 MJ
radius: 62067.5 km
hill sphere:  0.272 AU
inner reach: 4.458 AU
outer reach: 7.433 AU
perihelion: 5.817 AU
aphelion: 6.618 AU
4:1 resonance: 2.467 AU
2:1 resonance: 3.917 AU
 
 
GG2 (red):
semimajor axis: 11.814 AU
eccentricity: 0.003
mass: 0.279 MJ
radius: 46636.0 km
hill sphere:  0.499 AU
inner reach: 10.280 AU
outer reach: 13.348 AU
perihelion: 11.777 AU
aphelion: 11.851 AU
4:1 resonance: 4.688 AU
2:1 resonance: 7.442 AU
 
 
GG3 (yellow):
semimajor axis: 15.358 AU
eccentricity: 0.037
mass: 0.136 MJ
radius: 41673.0 km
hill sphere:  0.511 AU
inner reach: 12.741 AU
outer reach: 17.463 AU
perihelion: 14.785 AU
aphelion: 15.930 AU
4:1 resonance: 6.095 AU
2:1 resonance: 9.675 AU
 
GG4 (green):
semimajor axis: 27.644 AU
eccentricity: 0.097
mass: 0.028 MJ
radius: 20116.0 km
hill sphere:  0.542 AU
inner reach: 22.259 AU
outer reach: 31.945 AU
perihelion: 24.969 AU
aphelion: 30.319 AU
4:1 resonance: 10.970 AU
2:1 resonance: 17.414 AU
 
 
GG5 (blue):
semimajor axis: 38.702 AU
eccentricity: 0.115
mass: 0.075 MJ
radius: 27734.0 km
hill sphere:  1.053 AU
inner reach: 27.912 AU
outer reach: 46.330 AU
perihelion: 34.233 AU
aphelion: 43.170 AU
4:1 resonance: 15.359 AU
2:1 resonance: 24.380 AU
 
----------------------
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Re: five planet system
Reply #1 - 10/12/06 at 00:01:44
 
Quote from Mal   on 10/11/06 at 18:13:49:
Here's a fun one to try... (rightclick and save target, it's a gsim file)...

You can also set up a file association between Gravity Simulator.  Then you can run any .gsim file on your computer or on the web by simply clicking and choosing Open.  To set up the file association, browse to a folder containing a .gsim file.  Right click on it, choose Open With.  Click "Choose Program", browse to gravitysimulator.exe, choose it and check "always use the selected program to open this type of file".
 
Quote:
Unfortunately, this happened while I was asleep
 Gotta hate that.  No wonder you're trying to get the autosave to work.  See the other thread where you reported the problem.
 
Thanks for the links to the papers.  The formulas derived on page 6 should be very useful.  The 2nd link only lets me get the abstract, so I'll have to look up this one in the library.
 
There's a new term I've recently learned.  "Dynamically Full" is used to describe a star system that is maxed-out in how many planets it can hold.  Our solar system is dynamically full.  A planet placed between any 2 other planets would not be stable.  It sounds like your 5-planet system is beyond dynamically full.  
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Re: five planet system
Reply #2 - 10/12/06 at 03:48:56
 
I've been running your sim.  The fun stuff starts at about 3.6 million years.  The orbits of gg4 and gg5 are about to intersect.
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Re: five planet system
Reply #3 - 10/15/06 at 11:46:54
 
I've been running the sim for a few days now and @ TS=16384 its been completely stable for 6 myr.
 
I'm thinking that the only reason it flew apart at the higher TS was the accumulation of errors.
 
 
(7 am 10/16/2006)
8 Myr = still stable, although 2 & 3 are starting to approach much closer, as are 4 & 5.  I suspect if it was run at even slower TS's < 1024s we might even eventually end up with [2,3] and [4,5] in that they would coalesce together.  I will continue to observe it for a few more days yet.
 
(9 pm 10/16/2006)
only been running it part of the day today due to working on other projects.  but I'm up to 9 Myr and it's still stable.  I'm going to let it run overnight full throttle and see what its like in the morning.
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« Last Edit: 10/16/06 at 19:15:17 by abyssoft »  
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Re: five planet system
Reply #4 - 10/15/06 at 13:39:31
 
Quote from abyssoft   on 10/15/06 at 11:46:54:
I've been running the sim for a few days now and @ TS=16384 its been completely stable for 6 myr.

I'm thinking that the only reason it flew apart at the higher TS was the accumulation of errors.

lol... I've been doing the same.  You've got me beat by a few hundred thousand years.  I might pump it up to 64K since you're doing 16K.
 
Simulations like this are very sensitive to chaos.  If you think of all the orbital elements, a small difference of say 1% in eccentricity, inclination, LAN, Per, SMA will only cause a small difference in the size, shape and orientation of the orbit.  But a 1% difference in SMA will cause a 1.5% difference in period, which means a ~1.5% difference in Mean Anomoly.  But unlike the other orbital elements, the 1.5% difference in Mean Anomoly is per orbit, so the error builds. After several orbits, the planet could be anywhere along its orbit. So the first property to suffer in accuracy in simulations such as this is the positioning of the planet in its orbit.
 
Since ejections are caused by close encounters, and close encounters are dependent on planet positioning, I would guess that any difference in time step will lead to different ejection dates.  It's possible that if the simulation were run at a timestep as slow as 512 that we'd see an ejection at 400,000 years. In other words, there may not be a trend that the faster the time step, the quicker the ejection.  But it would be interesting to test that.  If you can, keep up your 16K simulation.  I'll try 64K and see what happens.
 
I think the best we can do in this type of simulation, after running it at various time steps, is to conclude that this system is not stable on timescales greater than a few hundred thousand years.
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Re: five planet system
Reply #5 - 10/15/06 at 20:36:38
 
Here's a 22,500 year slice of the sim at timestep 32K.
 
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Re: five planet system
Reply #6 - 10/15/06 at 20:36:58
 
Problem is, it'd also probably evolve totally differently if one of the planets was a degree further forward or back along its orbit when the simulation started. There's so many variables here it's almost mind-blowing.  
 
EDIT: Heh, posted at the same time there! GG3 (the yellow one) is looking a bit wobbly there!
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Re: five planet system
Reply #7 - 10/16/06 at 18:43:43
 
**edit  changed 32k to 64k **
 
At 64k time step, the fun stuff starts happening around 9 million years into the simulation.
 
On Feburary 20, 9130047, gg1 and gg4 should collide.  At time step 64k, they do not collide as gg4 is travelling much more than the radius of gg1 + radius gg4 combined.  The time step is too fast for this approach, and gg4 skips over gg1.  But in the process, the heaviest acceleration it experiences in the flyby is extrapolated over an entire time step.  gg4 is unnaturally accelerated to an unrealistic velocity and exits the system on a hyperbolic trajectory.
 
Slowing down the time step several decades prior to this encounter changes the dynamis of the flyby.  gg4 completely misses gg1 although its trajectory is noticably bent.  This illustrates how powerful chaos is in these types of simulations, and how at this point we're really just rolling the dice. gg4's fate is that it will get ejected, unnaturally ejected as described above, or collide.  So the conclusion that this system is not stable is still very valid.
 

 
Slowing down the timestep a couple of months before impact yields the same trajectory as the first image, except that it plots more points each time step.  gg4 now travels much less than the combined radius of gg1+gg4 each time step.  This time it can not avoid its destiny, and it collides.

 
Try it yourself.
http://orbitsimulator.com/gravity/simulations/gg4.gsim
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« Last Edit: 10/17/06 at 01:34:48 by Tony »  
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Re: five planet system
Reply #8 - 10/16/06 at 22:12:12
 
that's pretty cool Smiley.
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Re: five planet system
Reply #9 - 10/17/06 at 07:26:09
 
Up to 10.5 myr and still stable, I would have to give a vote to the system is stable, but in order to be sure I want to go to at least 70 myr (1% of the lifespan of the system)
 
I'll continue posting every 5 myr and let ya know how it's coming
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Re: five planet system
Reply #10 - 10/17/06 at 07:31:47
 
Quote from abyssoft   on 10/17/06 at 07:26:09:
Up to 10.5 myr and still stable, I would have to give a vote to the system is stable, but in order to be sure I want to go to at least 70 myr (1% of the lifespan of the system)

I'll continue posting every 5 myr and let ya know how it's coming

 
Well, numerically speaking it shouldn't be stable. GG4 is within the ejection zone of one of the other gas giants - according to the calculations (from papers by Jones etc al) it should be ejected as a result.
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Re: five planet system
Reply #11 - 10/17/06 at 13:19:32
 
Ok I also Decide to Run it @ TS=6 Days; and I must say the results were not what I expected @ all....
 
all numbers listed in x1000 years
0-800 Pretty normal orbits
800-830 feedback between 4,3 and then 5,4 starts
830-980 everything appears stable for the moment
980-1020 can see active gravitational energy transport between 3,4,5 (3 migrates inward, while 5 migrates outward)
1020-1100 orbit of 4 becomes more erratic, procession rate dramatically increased
1100-1150 interactions between 3,4,5 becoming more pronounced and 4,5 gaining eccentricity
1150-1200 this remain relatively unchanged
1200-1400 procession rate for 4 comes to an almost standstill.  3,4 lose some eccentricity
1400-1500 4,5 appear to be building up a resonance feedback
1500-1550 procession of 4 speeds up a little and appears to be undergoing oscillations of  pro and retro grade
1550-1600 orbit of 5 gaining additional eccentricity and starting to take on pluto like characteristics.  Orbit of 4 almost circular
1600-1700 pluto like pattern continues
1700-1800 active gravity transport between 1,2,3 (1 migrating outward, 3 migrating inward)
1800-1850 1 becomes more eccentric, 4 maintains almost circular orbit, 5 continues to gain eccentricity but slowly
1850-2000 things smooth out for a while
2000-2100 occassional interaction between 2,3 appears to be resonance related.
2100-2200 resonance feedback bewtween 2,3 becomes more noticable
2200-2300 4 gaining eccentricity, procession of 5 becomes almost nill
2300-2400 active gravitation energy transport between 3,4,5 again
2400-2500 1,2,4,5 all processing very slowly however 3 is processing wildly >2 deg per rot
2500-2600 4,5 gaining eccentricity, 3 starting to have strong flux in apo and peri distances
2600-2700 4 starts to occassional cross the orbit path of 5
2700-2750 4,5 starting feesback resonance again
2750-2900 procession of 4 speeding up again interaction between 4,5 becoming more pronounced
2900-3000 procession of 4 becomes strongly retrograde
3000-3010 procession of 4 stops
3010-3020 procession of 4 prograde and strong interaction with 3 noticed
3020-3050 3,4 resonant feedback noticed.  procession of 4 gains speed again
3050-3100 3,4 interacting more frequently and the orbit of 4 changing dynamics.
3100-3150 interaction 4,5 causes strong shift in orbit of 5
3150-3170 4 becomes more eccentric and starts to interact more with 5
3170 4 ejected from system after close interaction with 3 followed by strong interaction with 5
3170-3400 3 ocillating wildly in both procession and peri, apo distances.
3400-3500 3 Apo distances and eccentricity fluxing wildly
3500-3600 1,2,3 all gaining eccentricity but 3 gaining the most
3600-3800 ecc of 5 now hovering around .3 (this is interesting later on)
3800-3900 procession of 3 slows, 5 increases and 3 becomes more ecc
3900-4000 system dynamics really start to change quickly now  
4000-4100 3,5 start to interact strongly
4100-4200 procession of both 3,5 greatly accelerated
4200-4220 procession of both 3,5 return to more normal appearance.  strong interaction between 2,3 noted
4220-4320 procession of 3 again accelerating. 3,5 undergo major changes to orbital params (5 migrates inward, 3 outward)
4320-4350 orbital migration reverses
4350-4430 3,5 gain eccentricity. 3,5 resonant feedback on 2 and stronger interactions with 2
4430-4500 chaos reigns, all remaining bodies (1,2,4,5) taking on cometary like orbits
4500-4540 all orbits becoming more erratic
4540-4550 1,2 ejected from the system
4550-4560 3 ejected from the system and  
4560+ 5 remains with a final ecc of .6
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Re: five planet system
Reply #12 - 10/17/06 at 15:45:15
 
Wow, that sounds completely insane Smiley. (thanks for writing all that up!). I think, as Tony says, we can definitely say that this is an unstable system.  
 
By way of comparison, I tried removing GG4 from the mix and things seemed to be a lot more stable. I dunno if anyone has time or inclination to try that after they're done playing with the full five planet system, but it'll be interesting to compare results.  
 
Of course, since this is pretty chaotic, all this depends on where the planets are in their orbits when the simulation starts - is this all just from using the file in the first post? Or have you tried this with the planets starting off in different positions?
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Re: five planet system
Reply #13 - 10/17/06 at 16:07:13
 
currently I'm just playing with your sim
I'm thing about doing a couple more writeup on high TS's on this sim I'm thinking 48 Days for the next one.
 
I'm up to 12 myr on the slower one (16Ks) and it's still stable
I plan on runing it atleast until 70 Myr.  I may run it longer depends on if anything destablizes
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Re: five planet system
Reply #14 - 10/18/06 at 12:49:56
 
It would be nice to make a plot of timescales that a system remains stable vs. time step to study how the time step effects the quality of the data, and the quality of the conclusions.  Any good science experiment needs to know the limits of the equipment.
 
Would anyone be interested in being involved in conducting such an experiment?  Suggestions are welcome.  I was thinking of something similar to what we're doing in this thread, but done in a more organized fashion.
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