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Strange Orbits - Chens work - Revisited (Read 8593 times)
frankuitaalst
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Strange Orbits - Chens work - Revisited
08/18/09 at 13:04:20
 
A while ago I've posted some strange orbits under the Topic "Chasing Suns" , beginning with the "Figure 8".  
Some orbits deserve a better visualisation , therefore I'll post some newer animations .  
I've found the initial values of the systems in the works of Dr. Kuo Chang Chen here :  
http://www.math.nthu.edu.tw/~kchen/papers/3BD.pdf
Hereunder is an animation of the famous "CrissCross " , in which the three planets have equal masses .  
I gave each planet Earth Mass and multiplied the values for postion with 1AU .
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Chen_CrissCross_Anim.gif
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frankuitaalst
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Strange Orbits - Figure 8
Reply #1 - 08/20/09 at 14:55:42
 
In the discussion of "chasing suns " Tony posted the Figure 8 gsim file . Its fun to play with the initial parameters , changing slightly the velocities aso .
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frankuitaalst
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Strange Orbits - Figure 8
Reply #2 - 08/20/09 at 14:57:20
 
An animation of the above file looks like this .
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Figure_8__XY_view_Animation.gif
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Strange Orbits - Figure 8
Reply #3 - 08/20/09 at 15:13:30
 
..whereas applying a small Z-component to each of the 3 bodies gives the following result :  
( I applied here a Z-component of 1% of the velocity of body 1 to two bodies  in + direction and one time 2% in - direction to the last body ) .  
In this way the system starts to rotate around the Z-axis , keeping however it's eight figure .
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Figure8_delta_vz_Anim.gif
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frankuitaalst
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Strange Orbits - Chens work - Revisited
Reply #4 - 08/31/09 at 14:38:22
 
Another example of Chens work is shown here :  
4 Earth sized planets with equal mass are orbiting in a trefoil like orbit .  
At the end of the animation the orbits are shown over half and later over a full period .  
Running the sil for longer time then 12 periods gives a degradation of the orbits , which will be restored , but broken up again , and so on . Seems the orbits are only dynamically stable .  
For those who want to play with a GravSim file I can provide one ...
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chen41111_Animation.gif
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frankuitaalst
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Strange Orbits - Chens work - Revisited
Reply #5 - 09/08/09 at 16:04:31
 
Here's another example of  a strange orbit . The initial values were also taken from the work of Chen.
Three planets with masses 1,5,10 orbit around each other , without central sun.  
The blue point in the middle is only there to indicate the center of gravity .  
 
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Chen_3pl_1510pi_Anim.gif
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Re: Strange Orbits - Chens work - Revisited
Reply #6 - 09/08/09 at 18:17:32
 
Thanks for sharing these remarkable orbits!
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frankuitaalst
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Strange Orbits - Chens work - Revisited
Reply #7 - 10/05/09 at 12:22:49
 
Applying a small velocity in the z-direction to the inner planets of the CrissCross figure ( see first post above ) gives the following result :  
The animation covers 1/4 of the period of rotation of the bodies .  
Again there's no central body .
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CrissCross_PlusVz_Anim.gif
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frankuitaalst
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Strange Orbits - Earth in a figure 8
Reply #8 - 11/02/10 at 09:35:56
 
Suppose we have 3 stars , each having the Suns mass orbiting in a figure 8 pattern .  
We then add an Earth planet at 1AU .  
 
What kind of orbit do we get then and is it stable ?  
Hereunder is a representation of such an orbit .  
Earths orbit is stable in this configuration if the separation of the stars is big enough  
I this example the screen width is 25 AU .  
If we squeeze the system ( fi a screen width of 20AU ) Earth orbit might get instable .  
 
In this system there's no difference between prograde and retrograde orbit .
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Figure8_with_Earth_at_1AU.gif
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Strange Orbits - Figure 8 with Earth
Reply #9 - 11/03/10 at 11:50:24
 
A variation on the above simulation gives the following funny result :  
I gave  the system a cycle of 16 years , whereas the Earth (in green) has a period of 1 year . So we should get a global cycle of 16 years .  
But I induced a small error in Earths period . The result is that we get an oscillating orbit for Earth , having a period of about 320 years.  
Seems as if the orbit is fixed with invisible springs .  
I cannot interprete what's going on here exactly , but it seems the system oscillates around its equilibrium point .  
 
The initial conditions of the system in x,y,z,vx,vy,vz (km) are the following
"E1",918976866.7,-230299806.8,0,5.515325,5.115012,0
"E2", -918976866.7,230299806.8,0,5.515325,5.115012,0
"Sun",0,0,0,-11.0306,-10.23,0
"Earth",-149500000,0,0,-11.0306,-40.20,0
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Figure8_with_Earth_16y_.gif
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