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Kirkwood gaps? (Read 42089 times)
EDG
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Re: Kirkwood gaps?
Reply #15 - 09/23/08 at 21:20:36
 
Here's the #, SMA, Ecc, and Inc for asteroids 300000-399999 in csv format
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« Last Edit: 09/24/08 at 19:29:50 by EDG »  

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Re: Kirkwood gaps?
Reply #16 - 09/23/08 at 21:22:40
 
And here's the #, SMA, Ecc, and Inc for asteroids 400000-423291 in csv format.
 
You can merge them together using Programmer's File Editor, which is a really good, basic text editor (written by someone at my old Uni!) that can open huge text files.  
http://www.lancs.ac.uk/staff/steveb/cpaap/pfe/pfefiles.htm
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« Last Edit: 09/24/08 at 19:30:32 by EDG »  

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Re: Kirkwood gaps?
Reply #17 - 09/23/08 at 21:26:06
 
And here's a table showing all of Jupiter's big resonances:
 
Code:
res  multiple Period(s)  distance(m)  distance(AU)
6:1	0.17	6.24E+07	2.358E+11	1.58
5:1	0.20	7.49E+07	2.662E+11	1.78
4:1	0.25	9.37E+07	3.090E+11	2.07
3:1	0.33	1.25E+08	3.743E+11	2.50
2:1	0.50	1.87E+08	4.904E+11	3.28
3:2	0.67	2.50E+08	5.941E+11	3.97
4:3	0.75	2.81E+08	6.426E+11	4.30
5:4	0.80	3.00E+08	6.709E+11	4.48
1:1	1.00	3.75E+08	7.785E+11	5.20 <<<<<<<<<<<< Jupiter
4:5	1.25	4.68E+08	9.034E+11	6.04
3:4	1.33	5.00E+08	9.431E+11	6.30
2:3	1.50	5.62E+08	1.020E+12	6.82
1:2	2.00	7.49E+08	1.236E+12	8.26
1:3	3.00	1.12E+09	1.619E+12	10.82
1:4	4.00	1.50E+09	1.962E+12	13.11
1:5	5.00	1.87E+09	2.276E+12	15.22
1:6	6.00	2.25E+09	2.571E+12	17.18 

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Re: Kirkwood gaps?
Reply #18 - 09/23/08 at 21:48:28
 
This is interesting - I plotted the first 32,000 asteroids of the 300k group (i.e. numbers 300,000 to 332,000) as a graph of asteroid number vs SMA. You can clearly see some gaps in here. They mostly seem to correspond to the Kirkwood Gaps but I'm not sure what's going on between 2.8 and 3.0 AU. Apparently the 5:2 and 7:3 resonances (which I didn't list on the table are in this region (5:2 is at 2.83 AU and 7:3 is at 2.96) so these are probably responsible for the "thinning out" there - see also the graph at http://en.wikipedia.org/wiki/Kirkwood_gap . I'm not sure what's so special about those particular resonances that they result in gaps though.  
 
I guess those trails of asteroids stretching down toward the sun are the result of specific searches that found a lot of earth-crossers? (because they must be close in asteroid number, and therefore discovery date?).
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sma300k.gif

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Re: Kirkwood gaps?
Reply #19 - 09/23/08 at 22:57:13
 
Quote from Mal on 09/23/08 at 21:17:40:
What might be interesting is to see if including Saturn in the system makes any difference - I think there are some secular resonances (the nu 6 one?) that can affect the inclination - these are mentioned on page 315 of Solar System Dynamics.

I got the asteroid data from astorb.dat , which can be found here: ftp://ftp.lowell.edu/pub/elgb/astorb.html

I stripped out the asteroid number, semimajor axis, eccentricity and inclination and used those to make the graphs. Note that the data contains asteroids outside the main belt, so if you're showing them on a graph and want to focus on the belt you have to trim the range of the graph axes. I'll attach the data in the next posts.
Thanks for the link , I'll add them to my favorites  Smiley.  
Actually the data above include already Saturn as I used the onlyplanets.gsim and added the bodies between mars and jupiter .  
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Re: Kirkwood gaps?
Reply #20 - 09/24/08 at 05:01:18
 
Hallo Mal , can you repost the 400k.zip ?  It contains the 400k.csv instead of the 500k.csv
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Re: Kirkwood gaps?
Reply #21 - 09/24/08 at 05:32:32
 
Here's a picture of the Sma and ecc of the first 400k asteroids Mal provided .  
1 line represents 1AU .  
Eccentricity goes from 0 to 1 .  
Its interesting to see how the planets clear the gaps.  
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PicSmaEccIncl_txt_400k.jpg
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Re: Kirkwood gaps?
Reply #22 - 09/24/08 at 06:14:52
 
Zooming in into the 2 to 3 AU range gives the following picture ....
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PicSmaEccIncl_2to3AU.jpg
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Re: Kirkwood gaps- evolution
Reply #23 - 09/24/08 at 06:51:30
 
The animation herunder shows the evolution of 600 bodies in 3AU+/-40% , as above , but this time with a time-step of 5 years in a SMA-Eccentricity plot .
400 years are simulated in total .  
Again the "stationary" points are planets ( Jupiter at the right ) .  
 
It is clear that some regions are triggered very quickly ( 2.5 Au and 3.25 Au)  
Interesting is the region in the middle between Mars and Jupiter where some bodies seem to decrease their sma and increase their eccentricity ...
 
EDIT : new animation attached
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« Last Edit: 09/24/08 at 11:05:03 by frankuitaalst »  

600BodiesbetweenMarsandJupiter.gif
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Re: Kirkwood gaps - Inclination
Reply #24 - 09/24/08 at 07:25:23
 
The plot herunder shows the Inclination - SMA distribution of the data provided by Mal .  
Max incl is 179.  
Its amazing how there seems to be a stratification .  
Apparently some regions are forbidden ?
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PicSmaEccIncl_txtSMAIncl.jpg
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Re: Kirkwood gaps- evolution
Reply #25 - 09/24/08 at 17:05:13
 
Quote from frankuitaalst on 09/24/08 at 06:51:30:
It is clear that some regions are triggered very quickly ( 2.5 Au and 3.25 Au)
Interesting is the region in the middle between Mars and Jupiter where some bodies seem to decrease their sma and increase their eccentricity ...

EDIT : new animation attached

 
That's mindboggling...!  Shocked
 
I mean, that big "fold up" between 3 and 3.5 AU looks like it's right at the 2:1 resonance, and there's a smaller 'spike' that develops later at 2.5 AU that corresponds to the 3:1 resonance. I wonder why everything's compressing in and folding up on the 2:1 though, or is that just an illusion caused by the animation?  
 
Fascinating stuff! (it's weird, I was never really interested in the Kirkwood Gaps but I'm really getting sucked in by all this now!)
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Re: Kirkwood gaps - Inclination
Reply #26 - 09/24/08 at 17:07:18
 
Quote from frankuitaalst on 09/24/08 at 07:25:23:
The plot herunder shows the Inclination - SMA distribution of the data provided by Mal .
Max incl is 179.
Its amazing how there seems to be a stratification .
Apparently some regions are forbidden ?

 
Yeah, I think some of those are caused by the "nu" resonances that I mentioned earlier. What would be really interesting would be to see how these graphs would look for an asteroid belt in a different system, but I guess we're running into computational problems because there's no way even any current computer could handle running a simulation of 10,000 (never mind 400,000) asteroids before we die of old age... is there??
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Re: Kirkwood gaps?
Reply #27 - 09/24/08 at 19:33:33
 
OK, i've checked and updated the attached files in the earlier posts, they should all be correct now.
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Re: Kirkwood gaps?
Reply #28 - 09/25/08 at 08:10:29
 
Quote from Mal on 09/24/08 at 19:33:33:
OK, i've checked and updated the attached files in the earlier posts, they should all be correct now.

Thanks , I'll integrate yhem into the other fle .  
BTW : the total file in zip has about 6.15 MB. Anyone feels interested to receive it ?  
 
About the output Mal , do you have special wishes about the range of output : is SMA 0 - 7 AU ok ? or should it be larger ?  
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Re: Kirkwood gaps?
Reply #29 - 09/25/08 at 08:36:10
 
Well I'm mostly interested in the main belt... 1.5 to 5.5 AU should be fine to see what's going on there. Thanks!
 
I'd also be curious to see an animation (like your eccentricity one) to see what happens to the inclinations of your bodies between Mars and Jupiter. And also to see what happens to your bodies if you fill the space completely between Mars' and Jupiter's orbits (rather than just fill part of the space between them) to see what happens to bodies that start off closer to the planets.
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