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Jupiter, Earth's savior? (Read 15298 times)
shellandtube
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Re: Jupiter, Earth's savior?
Reply #30 - 10/08/07 at 23:13:17
 
I am involved with the manufacture of nylon polymers. Jupiters trojans could have formed at the same time as the planet and become locked there as it started accumulating gas and became massive. Or they might be the remnants left over from the formation of the inner planets gradually pushed out by the solar wind or who knows?
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Re: Jupiter, Earth's savior?
Reply #31 - 10/09/07 at 01:11:27
 
That's one theory for the trojans of Neptune.  I don't see why it wouldn't apply to Jupiter as well.  They were planetesimals that were co-orbital with the planetesimals that formed Jupiter, but got locked into Jupiter's L4&5 points when Jupiter's mass became significant.
 
I doubt the solar wind is strong enough to push anything more massive than gas and microscopic grains.  Even if it was, the result would not be a wider semi-major axis, but a higher eccentricity.
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #32 - 10/09/07 at 08:55:18
 
Quote from Tony on 10/08/07 at 23:04:31:

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.

You're right . I formulated the sentence poorly .  
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #33 - 10/09/07 at 09:09:50
 
Heres a simulation of 100 Asteroids in the leading L-point of Jupiter with a tolerance of +/- 1% in both AU and Anomaly . Simulation spans 25 years. Asteroids tend to spread out but look stable .  
BTW : looks as if Mercury resonances to Earth at nearly 1:4 , as the screenshots were made every 90 days.
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100TrojansJup.gif
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shellandtube
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Re: Jupiter, Earth's savior?
Reply #34 - 10/09/07 at 11:05:14
 
Thats what I got in my sim. I ran it longer and found that they spread and contracted over time. Mine was also the trailing L point but that shouldnt make any difference.
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Re: Jupiter, Earth's savior?
Reply #35 - 10/09/07 at 13:10:15
 
Wondering if also Saturn can hold Trojans ( according to literature there are no trojans discovered... ) I ran the sim herunder .  
Two times 50 asteroids were located in the L - point . The blue have a spread of1% the orange ones have a spread of 2% . The sim was run for 100 years . It's nice to see how the orange spread more than the blue over time .  
Trojan behaviour seems to be possible over this timescale , but I wonder why the asteroids drift so quick (maybe I didnt give the 2% inclinaton ) .  
Question to Tony : I positioned them to the M Value of Saturn +60 degrees . Was this correct ?
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SaturnTrojans.gif
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Re: Jupiter, Earth's savior?
Reply #36 - 10/09/07 at 14:21:39
 
From the first pic it doesnt look like they are 60 degrees behind. They are drifting away from saturn moving towards 60 degs. I run a sim and pause when the planet of interest is either to the left or right of the sun (0 or 180 degs respectively) and then create with a man anomoly +/- 60 from 0 or 180.
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Re: Jupiter, Earth's savior?
Reply #37 - 10/09/07 at 20:06:44
 
Moving off topic for a sec, I was reading about Hill sphere's and Roche limits and came across something interesting. It was suggested that if a body had enough tensile strength to pass beyond the roche limit it would reach a point where objects not bound to the surface would be pulled off by the gravity of the larger body. By considering the gravitational forces I came up with a formula to calculate the SMA of the orbit at which the 2 gravitational forces where equal. This assumes both bodies remain spherical and that the definition of SMA is from the centre of mass of each object.
Putting in the numbers I got a value of 17800km for the earth moon system which is a gap of 9300km from surface of earth to surface of moon!
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #38 - 10/10/07 at 04:27:26
 
Yes I noticed also that the 60 offset wasn't visible on the screen , that's why I ask Tony if I did it right .  
Nevertheless : heres the same sim but run for 500 years in steps of 5 years .  
One can notice that some asteroids drift away.
Look whats happening to the end of the sim : the asteroids come close to Saturn and move back in a different orbit . Seems as a horseshoe path was created .  
I think I didn't get the L-point from the beginning as I took the actual value of the SMA of Saturn instead of the mean SMA.    
I think however Saturn is capable to sustain coorbitals , although none have been found till now.
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SaturnTrojans3.gif
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #39 - 10/10/07 at 11:08:56
 
I think you derived the equation to calculate the distance at which a body feels an equal but opposite attraction from 2 other bodies . This means that in this position the body doesn't feel any external force , so even a droplet of water (if not evaporating ) would remain a droplet .  
A body in this point remains here if both planets also remain at their position .
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« Last Edit: 10/10/07 at 13:58:37 by frankuitaalst »  
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shellandtube
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Re: Jupiter, Earth's savior?
Reply #40 - 10/10/07 at 13:22:56
 
Yeah to calculate the point the equation is based on the exact balance of forces and yes exactly at the point there is no net force. I ought to have said anything inside the orbit above or just to go all the way put a "less than" in the equation.
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Re: Jupiter, Earth's savior?
Reply #41 - 11/12/07 at 11:31:49
 
Thread restored
There's a few threads that were generating error messages when viewed, including this one.  This thread should work again.
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Re: Jupiter, Earth's savior?
Reply #42 - 11/13/07 at 21:26:22
 
Quote from Tony on 11/12/07 at 11:31:49:
Thread restored
There's a few threads that were generating error messages when viewed, including this one. This thread should work again.

 
Huzzah! Good work, Tony! Smiley
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #43 - 01/04/08 at 11:47:13
 
By accident I discovered a nice animation about the Trojans orbiting Jupiter .  
Hereunder is a link to the picture.  
http://chemistry.unina.it/~alvitagl/solex/hiltro.gif
Jupiter must be the body on top of the picture , I guess in rotating frame .
The picture was generated with the Solex program .  
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