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New system - asteroid belts & kirkwood gaps pt. 2 (Read 18404 times)
EDG
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #30 - 10/15/08 at 08:49:15
 
This is the same graph with a max eccentricity of 0.3... I've drawn a white line in - is it me or can you draw a line between the jovian and the deflected sunward part of the outer belt?
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #31 - 10/16/08 at 09:04:17
 
This graph (using the new beta) shows:
 
An inner belt of 250 massless point asteroids (2.87 - 5.3 AU)
A jovian of 0.379 MJ, at 2.291 AU with an ecc of 0.1  
An outer belt 250 massless point asteroids (0.58 - 1.61 AU).  
 
I recalculated the inner and outer edges of the "gap" around the jovian based on its new eccentricity, which is why the extent of the belts isn't the same as before when it was 0.03.  
 
I'm not sure why the inner edge of the outer belt is so ragged while the outer edge of the inner belt is so sharply defined. It could be that the calculated "outer reach" of the jovian is too low (I used the formula from this Jones/Sleep/Underwood paper which you can download by clicking the PDF Version link at the top of the page. TBH I'm surprised they're giving it away for free!).
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #32 - 10/16/08 at 11:18:30
 
Cheesy Ty for the wonderful link it will help me a lot with my sims
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #33 - 10/16/08 at 12:44:41
 
yah, it's a good paper for worldbuilders Smiley.
 
I should see if I can get some orbital dynamics postdocs on here... I'd love to know what they think of some of this stuff.
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #34 - 10/16/08 at 13:00:53
 
Quote from Mal on 10/13/08 at 12:33:44:
- just like the interior resonances closest to the jovian were angled inwards. Again, could this be down to the eccentricity of the jovian?

I think this must be the result of the resonances themselves .  
I got the same result in other simulations with 0 eccentricity of the Jupiter planet .  
See the post on Dynamics of Resonances .  
 
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« Last Edit: 10/16/08 at 22:57:22 by frankuitaalst »  
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #35 - 10/16/08 at 22:56:11
 
Quote from Mal on 10/15/08 at 08:49:15:
This is the same graph with a max eccentricity of 0.3... I've drawn a white line in - is it me or can you draw a line between the jovian and the deflected sunward part of the outer belt?

I think there's some parabolic relationnship between a and e of a body in resonance with the main body . The parabola bends inwards for inner bodies and outwards for outer bodies ( see the latest posts in the Dynamic of resonances thread for 1:2 and 2:1 resonances ) . Saying the kissing line goes through the main planet can hold , but depends on the place where you start the parabola .  
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« Last Edit: 10/17/08 at 11:47:30 by frankuitaalst »  
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #36 - 11/02/08 at 15:33:22
 
Something a bit different here:
 
This is a graph showing 150 years of evolution of a belt of 500 massless point asteroids that start off linearly distributed between 3.0 and 5.0 AU within Jupiter's orbit in our own solar system (all other bodies have been removed except for Jupiter and the Sun). So the belt starts just within the 2:1 resonance and goes out almost to Jupiter's orbit at 5.204 AU.  
 
As you can see, the results are rather... explosive - the belt is quickly torn apart and asteroids are sent scattering all over the place. I think this confirms that it's definitely impossible for a planet to form within this region close to a jovian - all the planetesimals would be in orbits that are too unstable (and if I left this running long enough I suspect that the belt would dissipate eventually).  
 
The big peak on the left is the 2:1 resonance. I think the "wall" to the right of that (beyond which everything goes crazy) is actually roughly where the 3:2 resonance is.
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #37 - 11/03/08 at 17:57:27
 
The SMA/Ecc graphs are pretty good for showing how the eccentricity gets pumped, but I'm still not sure where there are actual gaps in the belt (or maybe 150-200 years is too short a timescale for that to happen). Right now it looks like things are keeping the same SMA but increasing their eccentricity... What would be the best way to find out if the SMA itself is changing?
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #38 - 11/05/08 at 11:31:42
 
Quote from Mal on 11/03/08 at 17:57:27:
The SMA/Ecc graphs are pretty good for showing how the eccentricity gets pumped, but I'm still not sure where there are actual gaps in the belt (or maybe 150-200 years is too short a timescale for that to happen). Right now it looks like things are keeping the same SMA but increasing their eccentricity... What would be the best way to find out if the SMA itself is changing?

In this case I think you can use the time feature which allows you to plot the SMA vs time. The viewer also outputs the MeanSMA as a time series . This might be helpful ...
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Re: New system - asteroid belts & kirkwood gaps pt
Reply #39 - 11/05/08 at 13:01:16
 
Quote from Mal on 11/02/08 at 15:33:22:
Something a bit different here:
As you can see, the results are rather... explosive - the belt is quickly torn apart and asteroids are sent scattering all over the place. I think this confirms that it's definitely impossible for a planet to form within this region close to a jovian - all the planetesimals would be in orbits that are too unstable (and if I left this running long enough I suspect that the belt would dissipate eventually).

The big peak on the left is the 2:1 resonance. I think the "wall" to the right of that (beyond which everything goes crazy) is actually roughly where the 3:2 resonance is.

Amazing plot Mal .  
Jupiter has a strong disturbing effect . I think you might get a simular result if you put the bodies between Jupiter and Saturn  
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