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Jupiter's Trojan Asteroids (Read 16569 times)
Tony
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Jupiter's Trojan Asteroids
07/11/08 at 19:49:15
 
Jupiter has a large population of Trojan Asteroids orbiting its Lagrange 4 and Lagrange 5 points. The asteroids orbiting the L4 point are known as the Greek camp, while the ones orbiting the L5 point are known as the Trojan camp. The simulation http://orbitsimulator.com/gravity/simulations/jupitertrojans.gsim contains 872 Greek and Trojan asteroids, the total population known as of 2006. Because of the large number, it is not recommended that you run it with Gravity Simulator 2.0. Rather, visit the message board and get the latest Beta version and use the Preferences menu to set the "Do Events" interval to 1, or the simulation may freeze.
 
When you run this simulation, try turning on the trails and set the rotating frame period to Jupiter's period in the View menu to watch the asteroids trace tadpoles around Jupiter's L4 and L5 points.

 
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frankuitaalst
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Re: Jupiter's Trojan Asteroids
Reply #1 - 05/25/10 at 12:04:11
 
Tony , how did you manage to get all this data in your sim ?  
In the meantime the number of trojan asteroids is getting as high as more than 4000 ! .  
( ref : http://www.cfa.harvard.edu/iau/lists/JupiterTrojans.html)  
In the baut forum there's nowadays a thread going on about 3D visulistaion of the orbits of these bodies .  
Here's a representation of about 3000 of them simply generated as an Excel picture .  
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Jupiter_Trojans_as_per_20100104.jpg
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frankuitaalst
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Re: Jupiter's Trojan Asteroids
Reply #2 - 05/25/10 at 12:14:07
 
I've been trying to get some 3D visualisation of the orbits of the trojans .  
It's not easy to choose a good vantage point because the asteroids show a lot of dynamics .  
Viewed from the sun and looking at Jupiter for instance some would disappear behind the screen ....  
To overcome this I've choosen here the vantage point of an "Anti-Jupiter " ie a fictious body just opposite to Jupiters position to the sun .  
In the next animation the 16 earliest trojans are shown .  
Each frame covers 11.86 years.  
L4 is represented in red , L5 in green .  
For reference Earths orbit is shown in blue , in order to get some scaling to the picture .  
It may be clear that the trojans really aren't in the L4 and L5 points
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16_Jup_Trojans_from_antiJup.gif
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Tony
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Re: Jupiter's Trojan Asteroids
Reply #3 - 05/25/10 at 17:33:13
 
Quote from frankuitaalst on 05/25/10 at 12:04:11:
Tony , how did you manage to get all this data in your sim ?
In the meantime the number of trojan asteroids is getting as high as more than 4000 ! ...

I used Horizons Automator, which is a stand-alone program I use to generage many of my gsim files.  I posted it here a while back, but I think most people had trouble with it.
 
I really like your 3-d view.  It truly shows the shape of the trojan populations.
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frankuitaalst
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Jupiter's Trojan Asteroids
Reply #4 - 05/28/10 at 13:34:29
 
Thanks Tony ,  
Hereby another visualisation of 1000 of these Trojans in a perspective view as per 2010 01 04.  
Get your blue/red glasses  
The vantage point is a probe circling at 10 times the Jupiter distance and looking towards the sun ( at the center ).  
The probe takes 1 screenshot every 2 , so the animation takes 180 pictures in order to circle fully aroud .  
In this way we get a view from all sides .  
I had to magnify the objects sizes in order to make them visible . Jupiter appears here as the big dot , which was also magnified , however the perspective was maintained.  
For this animation I took the above database , selected the asteroids with ephemeris on 20100104 , and ran a special viewer in Pbasic.  
It's a pitty I had to reduce the number of Trojans , reduce the number of frames by a factor of 2 and had to reduce the screenwidth in order to get the file fit to the 1MB limit .
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1000_JupiterTrojansAround.gif
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Tony
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Re: Jupiter's Trojan Asteroids
Reply #5 - 05/28/10 at 14:18:44
 
You can always email me your larger file.  I know how to bend the rules!
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frankuitaalst
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Re: Jupiter's Trojan Asteroids
Reply #6 - 05/29/10 at 02:19:52
 
Thanks to Tony the full animation with 3000 Trojans in a larger frame can be found here:
http://www.orbitsimulator.com/gravity/simulations/users/frank/3000JupiterTrojans Anim.gif
It is clear in this picture that the leading population has more bodies than the trailing one .  
It also seems that the leading population is more centered to the ecliptic than the trailing .  
AFAIK the reason for this is unknown .  
 
Edit : if the animation shows some white lines and ghost rectangles it helps when you maximize the screen
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« Last Edit: 05/29/10 at 03:23:28 by frankuitaalst »  
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frankuitaalst
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Re: Jupiter's Trojan Asteroids
Reply #7 - 08/30/10 at 14:24:43
 
Still fascinated about the dynamics of the Jupiter trojans I took the time to run the .gsim Tony made in the first post above .  
It took about one hour to run it for 1 Jupiter year .  
Hereunder is the result in animated gif , showing the swarm of trojans in jupiters rotating frame.
Enjoy ...
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GravSim_JupiterTrojans_1Jup_Rev.gif
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frankuitaalst
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Re: Jupiter's Trojan Asteroids
Reply #8 - 08/30/10 at 14:58:14
 
Fortunately I used the "output file" feature while running the sim and kept track of the orbital elements of the above population .  
In the Sma vs Eccentricity chart the movement of the Trojans looks as following  
Most of the populatiion seems to wander in the Sma direction backward and forward . There seems to be little change in eccentricity
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JupiterTrojans_Sma_vsEcc_Evol_.gif
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frankuitaalst
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Re: Jupiter's Trojan Asteroids
Reply #9 - 09/02/10 at 04:10:20
 
I've been investigating the dynamics of the trojans somewhat further .  
In the next animation it is clear that the Argument of Perifocus and the Length of Ascending Nodes are variing very liitle .  
Some trojans however tend to oscillate in the ArgPerifocus ( shown in abscis)
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Jupiter_Trojans_Arg_vs_LAN.gif
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Re: Jupiter's Trojan Asteroids
Reply #10 - 01/28/11 at 16:36:10
 
Quote from frankuitaalst on 08/30/10 at 14:58:14:
Fortunately I used the "output file" feature while running the sim and kept track of the orbital elements of the above population .
In the Sma vs Eccentricity chart the movement of the Trojans looks as following
Most of the populatiion seems to wander in the Sma direction backward and forward . There seems to be little change in eccentricity

I particularly like this animation. The motion strongly suggests circular motion viewed from within the plane.
 
Try graphing SMA against θJupiterθasteroid. (Of course, make sure you mod the latter so it is within the range -180 - 180.) I'm pretty sure this will give you two swarms; one at 60 and one at -60, rotating in opposite directions.
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