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Resonance Introduction Question (Read 2943 times)
JDoolin
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Resonance Introduction Question
12/29/12 at 19:23:24
 
Hi,
 
I was surprised to see these animations of resonance; the way they look like little spirograph diagrams...  But I'm a little bit confuddled.  
 
I also found this video:  http://star.arm.ac.uk/neos/JupiterResonance/indexflash.html
 
It appears to do the three-lobe loop that shows up in your 3-2-3-s.gsim file that comes pre-loaded in the gravity simulator.  
 
After slowing down this simulation and viewing it from a stationary (nonrotating) frame, I could see that the outer heavy object goes around twice in a circular orbit as the inner, lighter object goes around three times in an elliptical orbit.  
 
Every third pass, the two objects are very near each other.  Now what I'm wondering is what exactly happens here?  I mean, yes, it's clear that this is where there is an interaction between the large planet and the asteroid, but is the large planet speeding the asteroid up, or slowing it down.  In the 3-2-3-s.gsim file it looks like the large planet is behind the asteroid, so it must be slowing it down.  But it comes in behind every time, so it seems like it should be slowing it down every time...  Is there some other time that I'm missing, where the large planet is speeding the asteroid up?      
 
Thanks,
Jonathan
 
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frankuitaalst
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Re: Resonance Introduction Question
Reply #1 - 12/30/12 at 02:14:25
 
Quote from JDoolin on 12/29/12 at 19:23:24:
Hi,

I was surprised to see these animations of resonance; the way they look like little spirograph diagrams...  But I'm a little bit confuddled.  


Every third pass, the two objects are very near each other.  Now what I'm wondering is what exactly happens here?  I mean, yes, it's clear that this is where there is an interaction between the large planet and the asteroid, but is the large planet speeding the asteroid up, or slowing it down.  In the 3-2-3-s.gsim file it looks like the large planet is behind the asteroid, so it must be slowing it down.  But it comes in behind every time, so it seems like it should be slowing it down every time...  Is there some other time that I'm missing, where the large planet is speeding the asteroid up?

Thanks,
Jonathan


 
I think Tony made this sims to show the geometry of resonances in the first place , not to show interactions .The sim doesn't include interactions between secondaries. Both the planet and the asteroid have zero mass in this sim . If you "edit" tou can see both masses are set to zero .  
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JDoolin
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Re: Resonance Introduction Question
Reply #2 - 12/30/12 at 03:37:09
 
Quote from frankuitaalst on 12/30/12 at 02:14:25:


I think Tony made this sims to show the geometry of resonances in the first place , not to show interactions .The sim doesn't include interactions between secondaries. Both the planet and the asteroid have zero mass in this sim . If you "edit" tou can see both masses are set to zero .
Welcome to have you on board !

 
Thanks frankuitaalst
 
Ah, I did not realize that these resonance simulations were massless.  I had a fundamental misunderstanding--I suspected that the resonances were caused because the large planet would give the smaller object some kind of regular "pull" to stabilize it.  But to the contrary, any pull would destabilize the orbit.  
 
Now I realize this is a resonance of NON-interaction; not a resonance of interaction.  
 
So these resonances represent elliptical orbits that never get close enough to the big planet to be substantially accelerated by it.
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Tony
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Re: Resonance Introduction Question
Reply #3 - 12/30/12 at 13:27:06
 
Both orbiting objects can not be massless.  One must have mass.  The central star or planet must also have mass.  The object tracing out the crazy path can be massless, but it doesn't have to be.
 
In a resonance, the more massive object pulls the less massive object.  Or in the case of similar masses, they pull each other.  If an object approaches from behind, it is pulled into a higher and slower orbit, where it then retreats, until it meets again on the other side, where again it is pulled, but this time into a smaller, faster orbit, causing it to once again retreat.  Repeat indefinitly.
 
Look for more explanition on these pages.  Run these simulations.  Turn off the rotating frame (menu View > Rotating Frame) and it might be easier to visualize what is going on.
 
 
http://www.orbitsimulator.com/gravity/articles/pluto.html
http://www.orbitsimulator.com/gravity/articles/spitzer.html
http://www.orbitsimulator.com/gravity/articles/horseshoe.html
http://www.orbitsimulator.com/gravity/articles/janus.html
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frankuitaalst
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Re: Resonance Introduction Question
Reply #4 - 12/30/12 at 14:42:45
 

I thought both objects were set to zero mass Tony in the original 3 2 3s sim , that's what I seem to see when I edit them .  
Can you check out ? I added the sim hereby .
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Tony
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Re: Resonance Introduction Question
Reply #5 - 12/30/12 at 16:33:47
 
Those sims were to simply demonstrate the geometry as described on page 325 of "Solar System Dynamics."  If either of the objects got perturbed, the resonance would fail.  If one of the objects has mass, then the resonance can become a "mean-motion-resonance", and small perturbations will not destroy it.
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JDoolin
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Re: Resonance Introduction Question
Reply #6 - 12/30/12 at 17:26:16
 
Quote from frankuitaalst on 12/30/12 at 14:42:45:

I thought both objects were set to zero mass Tony in the original 3 2 3s sim , that's what I seem to see when I edit them .
Can you check out ? I added the sim hereby .

 
Mine definitely says zero for the two orbiting objects.  But try changing the mass of the exterior to 1, 5, and 500.  The orbit still appears stable with 1 earth mass or 5 earth masses, but with 500 earth masses the inner elliptical orbit becomes unstable.
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zero-mass-exterior.PNG
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