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 Strange Orbits - Chens work - Revisited (Read 9798 times)
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 . Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 . Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Strange Orbits - Figure 8 Reply #2 - 08/20/09 at 14:57:20   An animation of the above file looks like this . Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 . Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 ... Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 . Back to top IP Logged
 Tony YaBB Administrator Posts: 1057 Gender: Re: Strange Orbits - Chens work - Revisited Reply #6 - 09/08/09 at 18:17:32   Thanks for sharing these remarkable orbits! Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 . Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 . Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: 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 Back to top IP Logged
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