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Saturnian Trojans ? (Read 1512 times)
frankuitaalst
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Saturnian Trojans ?
02/23/09 at 11:59:38
 
There are as far as I know no known Trojans to Saturn ( and Uranus ) ; Jupiter has numerous Trojans while Neptune has only 6 trojans , all of them leading .  
Why doesn't Saturn has no detected Trojans ?  
I remember a statement Saturnian Trojans are only stable over longer time periods in certain (Inc, Ascending node ) regions .  
Here's a simulation of 25 leading and 25 trailing trojans to Saturn. They were originally placed around the L4 and L5 point , at zero inclination .  
Screenshots were taken each 145 years ( about 5 Saturnian years ) .  
The whole simulation was run for about 30.000 years .  
Blue bodies are leading , green are trailing .  
Trojans of Saturn indeed seem to be unstable ( even in this small amount of time ) .  
Jupiter seems to pump up the eccentricity of the trojans little by little , till the orbits really suddenly get a boost in eccentricity resulting in varying major-axes .  
Finally the orbits get out of their horseshoe and will be wildly scattered over the solar system .  
It's amazing to see how the leading trojans ( the blue ones ) seem to be more stable than the trailing ones .  
 
I tried to stabilise the orbit of Saturn in rotating frame but unfortunately this wasn't a succes .  
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SaturnTrojans145yFrame.gif
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atomic7732
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Re: Saturnian Trojans ?
Reply #1 - 02/23/09 at 14:28:02
 
Frank could you run it longer to see the orbits scatter?
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Tony
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Re: Saturnian Trojans ?
Reply #2 - 02/23/09 at 15:28:17
 
To stabalize Saturn, use the "Calibrate" button on the "Rotating Frame Adjustment" interface.  Click Calibrate.  The mouse turns to crosshairs.  Then click Saturn.  Wait a few minutes and click Saturn again.  This tells Gravity Simulator how far Saturn drifted and sets a new rotating period based on this.  To fine-tune it, just do it again.
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atomic7732
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Re: Saturnian Trojans ?
Reply #3 - 02/23/09 at 17:25:19
 
Quote from Tony on 02/23/09 at 15:28:17:
To stabalize Saturn, use the "Calibrate" button on the "Rotating Frame Adjustment" interface.  Click Calibrate.  The mouse turns to crosshairs.  Then click Saturn.  Wait a few minutes and click Saturn again.  This tells Gravity Simulator how far Saturn drifted and sets a new rotating period based on this.  To fine-tune it, just do it again.

But do you slow it down to actually click on saturn or just near saturn?
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Tony
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Re: Saturnian Trojans ?
Reply #4 - 02/23/09 at 18:40:34
 
You need to click exactly on Saturn.  If Saturn is tracing an oval, choose the same part of the oval for both clicks:  Leading Edge, Trailing Edge, or Center, whichever you can more precisely identify.  This tells Gravity Simulator how fast Saturn is drifting so it can compensate.
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frankuitaalst
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Re: Saturnian Trojans ?
Reply #5 - 02/24/09 at 12:30:49
 
I've managed to keep Saturn still . Thanks for the hint Tony .  
For those who want to try the simulation : simulation starts some years after the initial setup .  
I've run it at 30000 seconds , but reduced it when the system gets crazy to 16000 seconds.  
 
Edit : running the application longer than 30.000 years where the trailing trojans become unstable I noticed also the leading trojans become unstable after about 68000 years .  
Does anybody has an idea what's causing the difference ?  
 
Edit2 : Question for Tony : I thought to reverse the simulation in order to observe the stability differences  back in time and wanted to make some screenshots , but GravSim didn't make screenshots in reverse mode . Did I do something wrong ?
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frankuitaalst
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Re: Saturnian Trojans ?
Reply #6 - 02/25/09 at 13:34:06
 
I've outputted the data of the above simulation uo to 40.000 years , about 10.000 years after the scattering of the trailing Trojans and made the following Sma,Ecc and Sma,Inc plots .
The graphs clearly show how the asteroids are scatterd troughout the solar system .  
The scatterig starts where the body of the tree diverges into the branches to the left and right .  
It's amazing how the bodies which started  at zero eccentricity and  zero inclination are scattered not only in sma but also in inclination .
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SaturnTrojansEvolutionSMa_and_Inc.gif
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