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Kirkwood gaps? (Read 42079 times)
frankuitaalst
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Re: Kirkwood gaps?
Reply #30 - 09/25/08 at 09:44:30
 
Here's the SMA-Ecc distribution of the data provided by Mal ( more than 420000 bodies )
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PicSmaEccIncl_txtSMAEcc.jpg
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frankuitaalst
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Re: Kirkwood gaps?
Reply #31 - 09/25/08 at 09:47:00
 
Same data as above but in SMA- Incl representation ...
The trojans of Jupiter are represented at around 5.1 AU .
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SMAIncl60.jpg
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frankuitaalst
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Re: Kirkwood gaps?
Reply #32 - 09/25/08 at 10:06:02
 
Quote from Mal on 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.

If you want a more "zoomed" picture than provided above it can be made .  
 
I'll try to represent also the inclination . My guess is there will be not much variation while IJup is close to zero .  
If I fill the gap between Jupiter and Mars completely I think the objects close to Jupiter will drift away very quickly .  
I'll give it a try in the weekend .  
Question fo Tony : if I make objects with AU 3 +/-50% will this then result in a range of 1.5 Au to 4.5 AU ?  
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frankuitaalst
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Re: Kirkwood gaps - Inclination
Reply #33 - 09/25/08 at 10:35:34
 
Quote from Mal on 09/24/08 at 17:07:18:

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??

I think you're right .  
But there may be a solution which can reduce the computing time.  
Lets say we want to compute p bodies and add n asteroids ( p=10 , n=10000) .  
The computing time goes up as : T = a. (n+p)*(n+p) , so kwadratic .  
10 times more bodies gives 100 times longer run ...
 
But : if one runs the simulation once with the p bodies and stores the obtained data , then a separate program can calculate an additional body in a time T2= b*p . ( if the asteroid is small it has no influence upon the other bodies , so they don't have to be calculated ; their previous orbits which are known reman valid ) .  
So if we run this program n times we have a total time of : T2 = n*b*p . This is the time to integrate the n asteroids .  
T2/T gives : b*p/(a*n) , or if a=b then : T2/T = p/n .  
If p=10 and n=10000 asteroids then the simulation in this way may be performed 10000/10 = 1000 times faster ...
Of course this requires a lot of reprogramming ....
I think jpl calculates orbits of asteroids in this way , assuming an asteroid doesn't influence the major bodies ...
 
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frankuitaalst
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Re: Kirkwood gaps- Inclination change
Reply #34 - 09/25/08 at 12:11:01
 
Adding the inclination change to the animation gives the following picture :  
Eccentricity in red , inclination in green .  
Animation covers 100 years after the initial circular orbits between Mars and Jupiter .  
Each frame covers 1 year . Total of 100 frames .  
The inclination change is at maximum closer to Jupiter .  
As may be seen the changes in eccentricity appear to come in waves as the eccentricity is pumped up by the resonances .
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SMAInclEvolutionAsteroids.gif
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Re: Kirkwood gaps?
Reply #35 - 09/25/08 at 20:08:30
 
what's causing the "spurts" in eccentricity? It's like there's a rhythmic increase in one set of asteroids, then in another set, then back to the first one... is the periodicity of that down to Jupiter's orbital period or something?
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Re: Kirkwood gaps?
Reply #36 - 09/26/08 at 08:07:48
 
Quote from frankuitaalst on 09/25/08 at 09:44:30:
Here's the SMA-Ecc distribution of the data provided by Mal ( more than 420000 bodies )

 
Is it me or is there a slight clumping of asteroids going between about 1 AU (at zero eccentricity) to 2 AU (at 0.5 eccentricity)?
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frankuitaalst
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Re: Kirkwood gaps?
Reply #37 - 09/26/08 at 11:17:21
 
Quote from Mal on 09/25/08 at 20:08:30:
what's causing the "spurts" in eccentricity? It's like there's a rhythmic increase in one set of asteroids, then in another set, then back to the first one... is the periodicity of that down to Jupiter's orbital period or something?

It's intruiging isn't it ? I don't know exactly what happens here but my guess is that these bodies which are in a 1:2 resonance to Jupiter get a boost every time they are close to Jupiter , increasing their eccentricity ..
Those which are lagged for 180 get also a boost , but later .  
This might explain the waves ??
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frankuitaalst
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Re: Kirkwood gaps?
Reply #38 - 09/26/08 at 13:19:44
 
What causes the spurts as Mal asked ? Sure some resonance interaction, or the lack of at other distances .
But its very hard to visualize this .  
Is a body at a certain position changing its eccentricity or does it change its sma over time ?  
Both .  
The animation in annex shows the variation of SMA/Year as a function of SMA of the above simulation .  
One can see  bodies having the same SMA at a certain time can decrease or increase their SMA .  
The plot is centered on dSMA/year =0 .  
The resonance mechanism must be very complex .  
I can only draw one conclusion : the dynamical behaviour becames stronger the more the body is near to Jupiter .  
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0p155AUJupiterdSMAanim.gif
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Re: Kirkwood gaps?
Reply #39 - 09/26/08 at 14:59:30
 
That's bizarre... it looks like there's a central core that oscillates a small amount around 0 there, but as you get toward Jupiter the rest of the asteroids fluctuate in a more extreme way. I have no idea what's going on there - and there doesn't seem to be a link to the resonant distances either.
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Re: Kirkwood gaps?
Reply #40 - 09/29/08 at 23:11:02
 
OK, I just made my computer cry a bit...  
 
I've now got a text file about 200 years of sma, ecc, and inc data for 500 asteroids between Mars and Jupiter (2.8 AU +/- 40%, starting at ecc 0 an inc 0 on 1/1/2005, set at uniform distribution), sampled every 150 days. I started with the fullsystem.gsim, deleted everything except the 8 planets (and Pluto) and added the 500 asteroids. I also, for a twist, replaced Mars with another Jupiter, so there's a Jupiter inside and outside the belt. I just wanted to see if that had any effect.
 
Unfortunately I have no idea what to do with the data. I have a big 17MB text file that compresses down to about 7 MB (too big to attach), and my text editor (that has been known to handle 1GB text files) actually crapped out on opening the file, which was weird!  
 
So... frank, can I send this to you somehow and you can maybe work your graph magic on it? I'd be curious to see how this looks.
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« Last Edit: 09/30/08 at 18:37:09 by EDG »  

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frankuitaalst
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Re: Kirkwood gaps?
Reply #41 - 10/01/08 at 13:15:08
 
yes you can send it to me by mail . I think my mail can handle 10MB . The visualisation program can handle more than 40MB , so I guess this is not a problem .
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« Last Edit: 10/01/08 at 22:31:47 by frankuitaalst »  
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Re: Kirkwood gaps?
Reply #42 - 10/01/08 at 23:47:09
 
OK, frank - thanks! Check your PMs, I've put it on an FTP site for you to download (easier that way!).
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frankuitaalst
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Re: Kirkwood gaps?
Reply #43 - 10/02/08 at 04:01:50
 
Here's the plot you requested showing the e vs Sma over the 200 years .  
The asteroids seem to have a hard time  Smiley
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frankuitaalst
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Re: Kirkwood gaps?
Reply #44 - 10/02/08 at 09:10:58
 
An animation over the first 50 years shows that the asteroids below 2AU are unstable from the beginning .  
Further around 3.5AU there is some kind of resonance .
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FullsystemAnimEcc.gif
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