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Jupiter, Earth's savior? (Read 15315 times)
frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #15 - 10/03/07 at 23:12:23
 
The picture hereunder gives the same simulation as above (3:2 resonance with Jupiter ) . Sim was run for 125 years .  
In order to get an impression how the particles behave the orbit was created by 4 circle segments of 90 each of a different color .  
After some time 3 knots are created which wind up and unwind as they orbit. By chance 2 knots are positionned at the intersection of 2 different colors . Following the simulation on screen it's nice to see how the particles do not mix up .  
The winding up is really that big that nearly a full quarter segment lies in one knot  Roll Eyes.
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color32Jupiter.gif
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #16 - 10/06/07 at 19:28:13
 
Asteroids on a 2:1 resonance to Jupiter are shown here ...
Their orbit comes close to Saturn ( yellow dot )in this rotating frame to Jupiter ( pink dot at 10 'o clock ) .  
The influence of Saturn is really big . In this timeframe of 50 years Saturn strips away a lot of asteroids , creating a gap . Creation of the gap is a matter of just a couple of years .
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2ResonJup.gif
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Tony
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Re: Jupiter, Earth's savior?
Reply #17 - 10/06/07 at 19:36:02
 
That last one was quite interesting.  You might want to set the rotating frame period to Saturn's orbital period and try it again.  It looks like the particles trailing Saturn after the gap are in L4 tadpole orbits or perhaps horseshoe orbits.
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #18 - 10/07/07 at 03:20:32
 
Good idea ...  
Heres a gif for the fisrt 75 years in Rotating frame to Saturn ( yellow dot at the right ) .  
Saturn steals two times material from the ring in this timeframe. Its action on the ring is rather violent as the material is ejected far away .  
Interesting is to follow the "tail" of the gap going upwards  after the fisrt encounter .  
The tail seems to sweep several times ...as if the animal was wounded.  
I'll post the second part of the sim , also 75 years .  Some horseshoe structure is visible there .
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Saturn2ResJup.gif
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #19 - 10/07/07 at 03:30:38
 
Heres the second part of the simulation , also covering 75 years .  
I can't detect yet any horseshoe orbits to Saturn .  
But interesting is the cloud of objects which release at the top just after the beginning .  
They "lift off" and start to move anti-clockwise , accelerating and decelerating .  
Looks as if they are in a horseshoe orbit around Jupiter . Do they ?  
Would be funny : Jupiter gets horseshoe asteroids with the help  of Saturn .
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Saturn2ResJup2.gif
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #20 - 10/07/07 at 05:11:29
 
Nopes ... no trojans for Jupiter either . I ran the sim for more than 250 years . Although Jupiter has a big influence there s no building of trojans. I think the original distance from the ring ( and thus also the momentum ) is just to big . Same may be true for Saturn . What do you guys think ?  
Heres the .gsim file .  
I ran it at 32000 sec , reducing speed to 8000 for a while when saturn was close
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shellandtube
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Re: Jupiter, Earth's savior?
Reply #21 - 10/07/07 at 05:46:11
 
Frankuitaalst, I am running a similar sim but with the asteroids in a slightly elliptical orbit (SMA 7AU and e=0.18). Just set it running, if i see anything of interest i will post about it. The eccentricity will alter the relative velocity of the asteroids and the gas giants and i expect it to provide slightly different results.
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shellandtube
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Re: Jupiter, Earth's savior?
Reply #22 - 10/07/07 at 06:44:07
 
Here is a screenshot from the sim i mentioned above. Its in a rotating frame locked to saturn. I am not quite sure how to interpret it. Any help guys?
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asteroids0001.GIF

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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #23 - 10/07/07 at 11:43:40
 
You have the Trails on ? What you see is normal I think . What timestep do you use ? I didn't go further than 32000 ( in order not to throw out any objects )
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Re: Jupiter, Earth's savior?
Reply #24 - 10/08/07 at 12:44:40
 
about 8100 for the timestep and yes the trails are on. i changed the doEvents interval and Plot count to make it run quicker i think it was every 150 itererations. I expected to see the loops but some of them were strange. There was 1 that looped around a point at least twice and then moved off. It's not in this pic though. Could it have been a temporary trojan? The point it was circling seemed to be a little more than 60 degrees ahead and on its second loop the loop was larger and more elliptical. After that it moved away and i lost it in bulk. I looked for the position of jupiter just after i lost it and think jupiter would have been close by when it destabilized.
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #25 - 10/08/07 at 13:35:02
 
It may be possible that you had a temporary trojan . Trojans are however hard to get out of a bunch of "random" bodies . If the velocities and positions don't match ...theres little chanche to get a stable trojan . I whished I knew how to create one .
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Re: Jupiter, Earth's savior?
Reply #26 - 10/08/07 at 15:11:47
 
I only noticed it when I turned the trails on, it only made 2 loops then dissapeared. How long it had been there I couldn't say. My thinking is when jupiter passed it destabilized it so it may well be possible that a previous passage of jupiter caused it to become a trojan. The page on wikipedia about trojans is useful.
http://en.wikipedia.org/wiki/Trojan_asteroid
 
My best guess to create one artificially would be to create a bunch of 50 or so objects such that they where all close to the sma of jupiter say +/- 1% and 60 degs in front (or behind) also +/- a few degrees. If you then run the sim with rotating frame to jupiter you might get lucky. I think a trojan would just orbit around the L4 or L5 point in a rotating frame? I guess you would know more than me. I gather from your posts that you work in some related field. Whereas I am a chemical engineer and this is just a hobby.
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Re: Jupiter, Earth's savior?
Reply #27 - 10/08/07 at 19:46:16
 
So I took my own advice and tried it out. created 50 objects sma 5.204 +/- 1% and spread them out at 60 degrees behind +/- 1.2 degs. I ran the simulation for 300 years. The objects spread out a couple of degrees either side of 60 and pretty much stayed there. The bunch expanded and contracted over 25 years or so but remained in the vicinity of the lagrange point. Does this make them all trojans? From the wikipedia definition in the above link it does.
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #28 - 10/08/07 at 22:57:39
 
Sure , this is definitively a way to make trojans, or at least some of them . In a three body system trojans stay at their position . Due to perturbations of other planets trojans tend to make orbits around their stable point . This orbits are dynamically stable , meaming the orbit can change but will not drift off.  
Problem is : how do trojans arrive at their stable point from elsewhere. What orbit should they have so that at some time they are captured as a trojan ?  I was never able to simulate such thing. Anybody does ?  
Creating a ring of bodies as seen in the previous posts hasn't yet created trojans till now.  
To answer your question : I'm not profesionally involved in astronomy or something like that . I'm a mechanical engineer and work in the field of anaerobic digestion . Astronomy is just a strng interest of mine.  
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Re: Jupiter, Earth's savior?
Reply #29 - 10/08/07 at 23:04:31
 
Quote from frankuitaalst on 10/08/07 at 22:57:39:
Due to perturbations of other planets trojans tend to make orbits around their stable point

The other planets have nothing to do with it.  Delete them and you'll see.
 
If you place an object directly on the L4 or L5 in a perfectly circular orbit, it will not drift.  But if you nudge it a little, so its velocity is no longer perfect, it will circle the L point regardless of whether other planets exist or not.
 
Also, if you place an object near an L4 or L5 point, but not directly on it, it will also orbit the L point, regardless of whether other planets exist or not.
 
The perturbations from the other planets will, however, make it impossible to set up the perfect L4 or L5 scenerio.  But even if they don't exist, you can still have objects orbit the L4 and L5 points.
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