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Ring system modelling (Read 2957 times)
frankuitaalst
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Ring system modelling
08/27/07 at 12:42:09
 
In an attempt to simulate the formation of a ring system : in the follwing sim a small body system was created with in total 70 small bodies ,orbiting a central star .  
The small bodies were placed at 1 AU +/- 0.03 AU .  
So in each "of the 7 "rings" contains 10 bodies .  
A planet of 100 Earth masses was added at a distance of 1.5874 AU .  
So there must be a 1:2 resonance to the central ring .  
I hoped to get some gap in the ring system , similar to the Encke gap in the Saturn system .  
What happens is that the moonlets mix in some way and tend to create some gaps ...
But the gaps are not coherent in this sim and are due to the changing excentricities ...
The sim was run for about 150 years and 1 screenshot covers 5 years .  
I tried to post the .gsim file also but I guess only one annex is allowed .
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EDG
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Re: Ring system modelling
Reply #1 - 08/27/07 at 17:55:10
 
You're actually making an asteroid belt here (so I'd expect to see something like the Kirkwood Gaps eventually) rather than a ring system. I don't know if there's functionally much that's different though, beyond the fact that the distances/scales are much larger for an asteroid belt.
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Tony
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Re: Ring system modelling
Reply #2 - 08/27/07 at 18:36:43
 
I don't think the Kirkwood Gap is a gap in the traditional sense.  Rather, it is a gap in a table of semi-major axes.  So it's likely you'll never see a gap in your animation.  I believe the real Kirkwood Gaps have pleanty of stuff in them.  It's just that there's a lower-than-normal amount of asteroids whose semi-major axes reside in the resonant areas.  But there's pleanty of asteroids with semi-major axes outside the resonant areas, with eccentricities so their orbits carry them through the "gap", making the gap appear populated.  But if you actually wanted to see the gap, you'd have to make a scatter plot of semi-major axes.  This might be tricky to do as-is, since Gravity Simulator will give you your semi-major axes across a row rather than a column, and the row will contain object names, semi-major axes, and a blank column.  Does anyone know of a way in Excel to delete every 3rd column, and then transform the row to a column? I could always write a patch to the beta version to output the data in an Excel-friendly format.  Let me know if that would help.
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EDG
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Re: Ring system modelling
Reply #3 - 08/28/07 at 00:42:45
 
I think Tony is right about what the gaps are. The SSD book shows a plot of semimajor axis (x) vs eccentricity (y) that shows the gaps quite well.  
 
Some more data output options would be nice. To get that graph, you'd have to be able to specify a time and then output the semimajor axis and eccentrity for any specified objects (e.g. all the asteroids) at that instant. I guess if you could specify a range of times you might be able to see how the gaps evolve over time, which would be pretty cool.  
 
What would be quite interesting is the ability to show graphs in gravsim itself. Instead of showing the orbits (which is basically x/y/z coordinates over time) you could show other 'phase spaces' (like the graph on page 457 of SSD, which shows a.sinW vs a.cosW - if you show that over time then you can see the bands evolving.
 
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frankuitaalst
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Re: Ring system modelling
Reply #4 - 08/28/07 at 10:00:34
 
Theres a way in Excel : if you have  
Planet ,5,  ,Planet ,6,   ,  
you can use the sort funktion and press options .
Instead of using then sorting top down you use left right .  
After sorting you should become then :  
Planet ,Planet,  ,   , 5, 6,  
Then you can delete the colums .  
To make a graph you have the option to use the rows instead of the colums , so no need to transform rows in colums.
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frankuitaalst
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Re: Ring system modelling
Reply #5 - 08/28/07 at 12:10:59
 
Wondering whether a 1:2 resonance asteroid belt system is stable or not I made the following sim :  
Central sun , 1 planet 50 Earth Masses at 1.5874 Au (T=2 Y) and two asteroid rings , each consisting of 30 asteroids with mass 1000 kg . First ring is at 0.985 AU , the second at 1.015 AU .  
So , both rings are close to the resonance orbit of 1 AU .  
What will happen ? Will they clear out the gap between them or will they fill the gap ?  
The answer is amazing , I don't understand . I'll post the Gif file asap .  
Heres to .gsim file .
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frankuitaalst
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Re: Ring system modelling
Reply #6 - 08/28/07 at 12:27:40
 
Heres the animated gif , covering 50 years of simulation of the above .gsim ...
Screenshot was made every 0.5 years ( quarter of an orbit of the planet ) .  
The system starts with two rings , and they keep separated , however soon the orbits become somewhat elliptical , with moving point of apogee.  
Result is that the system seems to "vibrate" .  Huh
The vibration is at its maximum at about 26 years and then .... at about 50 years we get a circular system again ...Someone has an explanation ?  
( to speed up the system I omitted some screenshots after 30 years )
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frankuitaalst
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Re: Ring system modelling
Reply #7 - 08/28/07 at 13:51:44
 
I tried the same sim as above , but put the two "rings" at 0.99 and 1.01 AU , thus closer to each other .  
Both rings contain 30 bodies .  
As above I got also a resonance , almost mixing the bodies , but .... after about 50 years the picture shows the initial conditions again ... To be honest ...I don't understand this fully .
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