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Ring System (Read 4351 times)
shellandtube
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Ring System
09/19/07 at 21:13:05
 
In order to model the formation of a ring system I created a sim that has a satellite breaking up at the Roche limit. I created a clump of particles halfway between Jupiter and Io. The sim has 300 fragments all orbiting together within a sphere approx 3000km in diameter. The sphere quickly breaks up and forms a ring that over time gradually becomes broader. Over time i might expect to see signs of gaps appearing due to resonance with the moons. I have just left the 4 gallilean moons.
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Tony
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Re: Ring System
Reply #1 - 09/19/07 at 21:30:34
 
Your simulation reminds me of one I described on the Space.com forum, of what would happen to an asteroid that was nuked to prevent an Earth collision.  The fragments spread out in the orbit, similar to your ring-particle simulation:
 
http://uplink.space.com/showthreaded.php?Cat=&Board=askastronomer&Number =746189&Search=true&Forum=All_Forums&Words=apophis&Match=Entire%20Phrase&Searchpage=0&Limit=25&Old=1year&Main=745291
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shellandtube
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Re: Ring System
Reply #2 - 09/19/07 at 21:40:34
 
To keep it as accurate as possible all of the fragments in the clump are orbiting jupiter. Not a central fragment. BTW nice sim Tony it illustrates well the need to fragment as early as possible.
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shellandtube
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Re: Ring System
Reply #3 - 09/19/07 at 21:42:33
 
Have just noticed that my ring system is pulsing. i.e the "average" SMA is increasing and decreasing.
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Re: Ring System
Reply #4 - 09/19/07 at 22:44:14
 
Concerning the pulsations I had the same experience , see the posts under "ring system modelling ".
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shellandtube
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Re: Ring System
Reply #5 - 09/19/07 at 23:10:08
 
This system is pulsing with a shorter period. Here is a graph of SMA of 2 random particles over about 80 days.
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Re: Ring System
Reply #6 - 09/19/07 at 23:44:20
 
This is a fun simulation to watch.  Let it run overnight to see how it evolves.
 
Semi-major axis, like most orbital elements, is an oscillating orbital element.  As a ring particle has a conjunction with Io, Io's gravity vector opposes Jupiter's gravity vector.  For that instant, it is as if Io didn't exist, and the particle simply orbited a less-massive Jupiter.  As it approaches and receedes from conjunction, other axes come into play.
 
In the top graph, you've got two cycles:  one with a period of about 3 days, and a larger one with a period of about 40 days.  See if the shorter one matches the frequency of Io encounters, and the larger ones matches an Io encounter while Io is aligned with Europa or Ganymede.
 
One way to test this is to eliminate Io and try it again.  See how this affects your graph.  Then you can include Io but eliminate Europa, or eliminate both of them... the list goes on.  You can even try eliminating the Sun to see what effect, if any, the solar tide has.
 
Another neat thing to try is to eliminate everything but Jupiter and 1 test particle.  In theory, there should be no change of SMA.  Your graph should be a perfect flatline.  So any changes you have can be attributed to numerical error, possibly from a large time step.  But it should be much smaller than the 6000 km swing you are currently experiencing.
 
How often is the data sampled?  If your value is large, you can get artifacts in your data.
 
I doubt you'll ever see a gap (but I could be wrong).  As long as your objects have any eccentricy to them, they will travel through the gap.  This is similar to the gap in the asteroid belt.  It is not a visible gap, rather it is just a gap in a table of data of semi-major axes.  There are pleanty of objects with other SMAs and some eccentricity passing through the gap all the time.  I think the visible gaps in Saturn's rings are caused by shepard moons that actually orbit in the gap.
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frankuitaalst
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Re: Ring System
Reply #7 - 09/20/07 at 09:17:00
 
Nice simulation ! How did you create the exploding body ?
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shellandtube
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Re: Ring System
Reply #8 - 09/21/07 at 23:37:20
 
Been away a couple of days.
Tony I sampled every day for 100 days.
Frankuitaalst I just created 300 objects and picked the orbital parameters to create a random clump confined to the area that approximated an orbiting satellite. Each fragment was 1E19 Kg and 0km in diameter to avoid collisions.
If the centre of the body is 300,000 km from centre of jupiter and i want a sphere of 3000 km diamter i set the sma to 300,000 +/- 0.5% to give values 1500km either side.
Using simple trig I calculated the angle A (arctan 1500/300000) = 0.29 degrees
This gave me the variation in inclination, i chose 1 degree +/- 29%
So strictly its not quite in the ecliptic but close enough.
I then set LAN and AP to 0 +/- 0 and set the mean anomoly to 1 degree +/- 29%
This gives me my sphere of fragments that are all in orbit around jupiter and is the best approximation to the break up of a satellite i can come up with. In the initial conditions it approximates a singly body and breaks up due to tidal forces and interaction of the fragments.
 
Still I was suprised how quickly the ring formed.
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Tony
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Re: Ring System
Reply #9 - 09/21/07 at 23:53:06
 
You couldn't have sampled every 100 days if your simulation only ran for 80 days.  At best, you'd have 1 data point.
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shellandtube
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Re: Ring System
Reply #10 - 09/22/07 at 00:18:45
 
Quote from shellandtube on 09/21/07 at 23:37:20:
Tony I sampled every day for 100 days.

A sample every 24 hours (1 day) for 100 days ie hundred samples. When i did the picture i could get only get 80 days on.
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shellandtube
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Re: Ring System
Reply #11 - 09/22/07 at 10:48:31
 
Quote from Tony on 09/19/07 at 23:44:20:
 I think the visible gaps in Saturn's rings are caused by shepard moons that actually orbit in the gap.

 
That is the case for keeler gap and encke division in the outside of the A ring.
Some of the inner gaps and ringlets are maintained by mean motion resonance with some of the larger moons in particular titan. The page on wikipedia suggests a lot of the structure of the rings is due to interactions with the satellites. It was an effect similar to this i was hoping to see in my simulation.
http://en.wikipedia.org/wiki/Rings_of_saturn .
 
Might create a sim tomorrow with lighter fragments initially in perfectly circular orbits and see what happens.
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frankuitaalst
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Re: Ring System
Reply #12 - 10/08/07 at 13:25:11
 
In the next sim I created a ring system just in the middle of Venus and Earth ie at 129 AU +/- 2% .  
360 small bodies .  
Just wondering what would happen . Can Earth or Venus disrupt the system and attract some ?  
In this simulation covering about 90 years some "clumps" are generated which come and disappear.  
The firts part of the picture is made in rotating frame to Earth , the last part in rotating frame to one of the bodies .  
The last part is interesting as the bodies seem to play "accordeon" .  
Why is this ? Is it the ring structure that causes this or the presence of the planets ?
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ErathVenusAst.gif
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Re: Ring System
Reply #13 - 10/08/07 at 13:29:26
 
To find out why the asteroids contract all the planets were deleted in the next sim and just a ring system was made at 1AU .  
The system is remarkable stable . There almost is no sign of any contractions .
So I guess the disturbing influence of the other planets must have caused or initiated the contractions .
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