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New system - asteroid belts & kirkwood gaps pt. 2 (Read 18471 times)
EDG
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New system - asteroid belts & kirkwood gaps pt. 2
10/05/08 at 15:41:51
 
Here's a brand new system I made in order to see what happens with kirkwood gaps within its asteroid belt. This is actually the one that started off my interest in it, because as it is it has a planet between the 3:2 and 2:1 resonances of the innermost jovian, and that probably shouldn't be there.  
 
Code:
   Num Star	Age    ZMass   Mass	  ZLum	     Lum	   Rad   Met Pha
  2840 G2 V     4.736   0.992   0.992     0.7072248     1.0207404     0.997   2   1
  
ZAMS Inner Zone =    0.704   Current Inner Zone =    0.833
ZAMS Hab Zone   =    1.407   Current Hab Zone   =    1.668
ZAMS Earth Equiv=    0.841   Current Earth Equiv=    1.010
ZAMS Outer Zone =    2.132   Current Outer Zone =    2.562
 
 Habitable
Num    AU	  ecc	 type	mass     den	 rad	  peri	 aph	hill     inner     outer	4:1	 2:1	migrate
 1     0.300     0.044     4.000     0.001  5000.000  4000.000     0.287     0.313     0.002     0.279     0.319     0.119     0.189     0.671
 2     0.570     0.094     4.000     0.001  3500.000  4800.000     0.516     0.624     0.004     0.498     0.635     0.226     0.359     0.671
 3     0.969     0.000     5.000	Planetoid Belt
 4     1.454     0.162     4.000     0.004  3500.000  8000.000     1.217     1.690     0.016     1.107     1.729     0.577     0.916     0.671
 5     2.291     0.030     2.000     0.379  1246.700 51658.500     2.223     2.358     0.113     1.769     2.699     0.909     1.443     0.671
 6     4.123     0.063     2.000     0.350   993.500 54227.500     3.863     4.383     0.199     2.868     4.980     1.636     2.597     0.671
 7     7.834     0.036     3.000     2.123  2340.200 74357.000     7.554     8.113     0.689     4.797    10.181     3.109     4.935     0.671
 8    16.451     0.044     1.000     0.236  1700.280 39746.000    15.726    17.175     0.696    12.944    19.261     6.528    10.363     0.671
 9    24.676     0.025     1.000     0.196  1706.880 37318.000    24.048    25.304     0.981    20.124    28.246     9.792    15.545     0.671
  
1. Orbit = 0.300 AU, Radius = 4000. km, Density = 5000. kg/m3, Mass= .001 MJ, BBTemp=  511.4 K, MMW=   28.35, Atm=   1
2. Orbit = 0.570 AU, Radius = 4800. km, Density = 3500. kg/m3, Mass= .001 MJ, BBTemp=  371.0 K, MMW=   20.40, Atm=  10
3. Orbit = 1.454 AU, Radius = 8000. km, Density = 3500. kg/m3, Mass= .004 MJ, BBTemp=  232.3 K, MMW=    4.60, Atm=  15 


 
Planet 3 is the one that's between the 2:1 and 3:2 resonances... and also is on an eccentric orbit so it actually goes through the asteroid belt too. So it probably isn't really a stable system with this planet there (that said, over about 650 years it seemed stable...)
 
I did two runs with 200 asteroids located at 1.176 +/- 23% AU, with the other planets as shown above (I put all of them in). In the first run I left out the errant planet 3, and it seemed pretty stable. In the second run, I kept planet 3 in there and had a few asteroids tossed into more eccentric orbits. I ran both for about 500 years at 16k timestep (I did them originally at 65k, but that may have been too fast so I re-ran them at a slower one).  
 
Frank - would you be able to do some sma/ecc graphs for the asteroids in this system again at all? I'd be really interested to see if (a) any kirkwood gaps are starting to show up (though that said, the belt is pretty much exactly fills the space between the 4:1 and 2:1 resonances of the inner jovian (Planet 5)) and (b) what effect Planet 3 has on the belt in the second run.  
 
You can download the output files here (showing a and e), they're about 5MB each (zipped) - I'll leave these up for a couple of days:
Run1 (no planet 3): http://www.spicapublishing.co.uk/users/consty/2840nopanth.zip (16k timestep)
Run2 (with planet 3): http://www.spicapublishing.co.uk/users/consty/2840panth.zip (16k timestep)
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« Last Edit: 10/06/08 at 00:49:02 by EDG »  

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Re: New system - asteroid belts and kirkwood gaps
Reply #1 - 10/05/08 at 19:52:57
 
Here's a picture of the second run (with the extra planet in blue) when it starts. As you can see, it goes into the belt (the belt is between 0.909 and 1.444 AU, and the planet's perihelion is 1.217 AU).
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2840.jpg

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Re: New system - asteroid belts and kirkwood gaps
Reply #2 - 10/05/08 at 21:44:04
 
This is the 2nd run with the blue planet, after 510 years at 16k timestep.
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2840b.jpg

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Re: New system - asteroid belts & kirkwood gaps pt
Reply #3 - 10/06/08 at 00:52:05
 
And here's the first run (with no blue planet) after about 531 years. As you can see, it's a lot more stable, and the belt is hardly ruffled at all.
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2840c.jpg

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Re: New system - asteroid belts & kirkwood gaps pt
Reply #4 - 10/09/08 at 00:24:42
 
I'm trying another run with 250 asteroids at 1.3 AU +/- 50% at 16k (no blue planet). The first run didn't really show much because all the asteroids were between 2:1 and 4:1, and all they did was jiggle up and down a bit on the a-e graph (Frank's let me use his graph plotter, which is proving to be interesting!). This new run should have asteroids that go from just inside 4:1 to beyond the 3:2 distance so I should see a more interesting evolution (they go pretty much to the orbit of the second planet, out to just within the innermost jovian).
 
I'll leave it running overnight and I'll try and post some results tomorrow night if I can.
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #5 - 10/09/08 at 18:26:44
 
Here's an sma-ecc plot of the 250 asteroids after about 2800 years at 16k timestep. You can't see it very well but there's a definite disruption around 1.44 AU (the 2:1 resonance with the innermost jovian) and beyond that it's pretty chaotic, but the weird thing is that the entire belt is becoming more eccentric as time goes on as you go further from the star (to the right on the graph - the lefthand blue line is at 0.5 AU, the righthand blue line is at 2.3 AU with 0.2 AU increments in between). The belt started off at 0 ecc, and after 2800 years the main belt is peaking around 0.05 ecc. I wonder if that's because of the other jovians in the system, or if something else is afoot - any ideas as to what could be going on here?
 
I'm not really seeing that eccentricity pumping/surging that was going on in our own solar system either, but I'm not sure if that's because I've got too few asteroids plotted here (maybe I need a few hundred more too see that?).
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« Last Edit: 10/10/08 at 13:57:20 by EDG »  

PicA2840b_txt-6602.gif

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Re: New system - asteroid belts & kirkwood gaps pt
Reply #6 - 10/10/08 at 10:52:10
 
Mal , Is this a picture with or without the extra planet ?  
 
EDIT : is the picture a representation of the files you provided above , or is it a different fileoutput ?
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« Last Edit: 10/10/08 at 14:14:09 by frankuitaalst »  
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #7 - 10/10/08 at 13:47:02
 
it's without the extra planet (I've added labels to the graph, you may have to refresh your browser to see them).
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #8 - 10/10/08 at 14:20:43
 
If the picture above is from the file you provided above , the animation looks as following .  
I think it's normal the eccentricity rises as the  bodies are further from the central sun.  
If you look closely , if possible ,  the particles move initially in a kind of wave .
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no_planet.gif
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #9 - 10/10/08 at 14:27:06
 
Hm I'll have to try that again... the picture isn't from the text files in my first post - it's from a new run of 250 asteroids at 16k for 2800 years that I mentioned a few posts up. I've attached the gsim file.  
 
(how are you making the animationw btw, is that just in an animated gif creator?)
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #10 - 10/10/08 at 14:35:43
 
Quote from Mal on 10/10/08 at 14:27:06:

(how are you making the animationw btw, is that just in an animated gif creator?)

Yes indeed , it takes three programs , first GravSim , then the SMAEccInclViewer and finally a gif creator .  
( Whished all could be done in one program   Smiley)  
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #11 - 10/10/08 at 19:30:35
 
Yeah I ran the original run again for 150 years and got the same results as Frank... completely wacky, what the heck is causing the eccentricity to do that??? It's like there's a wave propagating through it from the sunward end whose frequency increases over time.
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #12 - 10/11/08 at 02:16:39
 
Quote from Mal on 10/10/08 at 19:30:35:
Yeah I ran the original run again for 150 years and got the same results as Frank... completely wacky, what the heck is causing the eccentricity to do that??? It's like there's a wave propagating through it from the sunward end whose frequency increases over time.

I'm glad the programm also runs at your PC .  
Resonances are quite complicated , that's why I wrote this visualisation tool to get some feeling with it . In fact you can compare it with a string of spring masses on which you tug with a force with a given frequency . You'll get also a wave pattern .  
In this case the force however acts in two dimensions and with a 1/rČ scale , creating this weird patterns .  
Maybe you'll find some principles in the work of Murray & Dermott . I haven't looked up yet .  
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #13 - 10/11/08 at 14:58:03
 
Quote from frankuitaalst on 10/10/08 at 14:35:43:

( Whished all could be done in one program   Smiley)  

Me too.  But I've never found a GIF writer for Visual Basic.
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #14 - 10/11/08 at 23:43:43
 
OK, I've kinda figured out how to make the graphs and animate them (thanks to Frank!)...  
 
Here's about 150 years worth of 200 asteroids at 1.176 +/- 23% AU and 16k timestep. This first file is without the blue planet, so the system is as shown below:
 
Code:
   Num Star	Age    ZMass   Mass	  ZLum	     Lum	   Rad   Met Pha
  2840 G2 V     4.736   0.992   0.992     0.7072248     1.0207404     0.997   2   1
  
ZAMS Inner Zone =    0.704   Current Inner Zone =    0.833
ZAMS Hab Zone   =    1.407   Current Hab Zone   =    1.668
ZAMS Earth Equiv=    0.841   Current Earth Equiv=    1.010
ZAMS Outer Zone =    2.132   Current Outer Zone =    2.562
 
 Habitable
Num    AU	  ecc	 type	mass     den	 rad	  peri	 aph	hill     inner     outer	4:1	 2:1	migrate
 1     0.300     0.044     4.000     0.001  5000.000  4000.000     0.287     0.313     0.002     0.279     0.319     0.119     0.189     0.671
 2     0.570     0.094     4.000     0.001  3500.000  4800.000     0.516     0.624     0.004     0.498     0.635     0.226     0.359     0.671
 3     0.969     0.000     5.000	Planetoid Belt
 5     2.291     0.030     2.000     0.379  1246.700 51658.500     2.223     2.358     0.113     1.769     2.699     0.909     1.443     0.671
 6     4.123     0.063     2.000     0.350   993.500 54227.500     3.863     4.383     0.199     2.868     4.980     1.636     2.597     0.671
 7     7.834     0.036     3.000     2.123  2340.200 74357.000     7.554     8.113     0.689     4.797    10.181     3.109     4.935     0.671
 8    16.451     0.044     1.000     0.236  1700.280 39746.000    15.726    17.175     0.696    12.944    19.261     6.528    10.363     0.671
 9    24.676     0.025     1.000     0.196  1706.880 37318.000    24.048    25.304     0.981    20.124    28.246     9.792    15.545     0.671 


 
Here's where the resonances are for the inner jovian (at 2.291 AU)
 
Code:
Res     AU
4:1     0.91
3:1     1.10
5:2     1.24
7:3     1.30
2:1     1.44
5:3     1.63
3:2     1.75
4:3     1.89
5:4     1.97
1:1     2.29 


 
(the blue lines are 0.06 AU apart, starting at 0.9 AU on the left).  
 
The big bulge forming on the right is the 2:1 resonance (which marks the outer boundary of this particular belt). You can see a much smaller bump forming at 1.10 AU, which corresponds to the 3:1 resonance. You can see the 'flicking' starting on the left edge of the belt and working inward during the first few years, and very rapidly the whole belt is jiggling up and down in sma-ecc space.
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