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Message started by frankuitaalst on 07/13/07 at 12:15:39

Title: Resonance and migration
Post by frankuitaalst on 07/13/07 at 12:15:39

Some time ago I read a theory stating that in a long past Jupiter may have forced Saturn in larger and larger orbits , which in his turn moved Neptune in even more larger and more eccentric orbits .
Neptune may have this way attracted bodies out of the Kuiper belt - and even Pluto -
Parts of them can have build part of the asteroid belt ...
The main force doing this job is called resonance resulting in migration .
Googling for resonance gives a lot of information .
The attracted asteroids may have caused the big lunar bombardment some 800 miljon years ago .
In order to find out some trends I simulated the solar system back in time for about 800.000 years , using the Picard integrator .
The result is shown herunder in the picture .
The results for the SMA were omitted ( they show a lot of "noise" ) but interesting is the strong resonance between Jupiter and Saturn . Their eccentricities and inclination are inversely bound . When Jupiter is far or high ,Saturn is short or low and vice versa.
Some resonances can also be seen for Uranus and Neptune , both influenced by a combination of Saturns and Jupiters movements .
In this short time scale it is not clear that Neptune may evolve to large eccentricities ...

Title: Re: Resonance and migration
Post by frankuitaalst on 07/13/07 at 14:17:44

Easy to simulate , but always surprising, are planet orbits around a central sun .
Herunder the result of two Earths . The first is our own earth , but with eccentricity 0 . The second Earth is placed at a circular orbit with period 14:13 years . So they are close initially and come close again after about 13..14 years .
Its nice to see how both planets give or steal their orbital energy to or from each other as they increase or decrease their mutual SMA .
The eccentricity however has a more parallel feature .
Although the general picture seems to be a little unpredictable , but planets resume several times their original circular orbit .
The picture can change dramatically if other ratios 3:2 ; 5:7 ,...are used .  


Title: Re: Resonance and migration
Post by Tony on 07/13/07 at 17:13:56

This might be of interest to you.  Last year I gave a presentation to my Astronomy class about the Resonant Capture Theory.  Here is my powerpoint presentation:
http://orbitsimulator.com/astro490/final.ppt

You can planetary migration in the beta version of Gravity Simulator using the Autopilot's "Continuous Orientation" and "Thrust" commands.

If you start Pluto in a circular orbit beyond Neptune, then make Neptune migrate outward, as its 3:2 resonance (or any strong resonance) sweeps past Pluto, it gets caught in the resonance and migrates out with Neptune.  The further it migrates, the more elliptical its orbit becomes.

Title: Re: Resonance and migration
Post by frankuitaalst on 08/08/07 at 11:32:18

This item has nothing to do with migration , but it shows the resonance of the planet Neptune and Pluto .
The sim was run for about 9000 years , showing the outer planets .
Screen scale is 100AU .
Neptune was taken as the rotating frame reference and shows itself as the green line at the left .
The frame was taken "edge on" , so the solar system is seen from aside .
I kew the orbit of Pluto is odd , but this is hardly to understand .... :-/.
Vieuwed from a point 90 rotated to this shows an even funnier picture .

Title: Re: Resonance and migration
Post by frankuitaalst on 08/08/07 at 12:47:27

Heres the same simulation as above , run for 9000 years , viewed edge-on, but at on angle of 90 from the previous one . Screen scale is also 100 AU . Neptune is shown here at the right .

Title: Re: Resonance and migration
Post by frankuitaalst on 08/08/07 at 13:16:42

Finally the most familiar view of the same sim :
Plutos orbit seen from above in a rotating frame of Neptune .
Screen scale is 130AU . Simulation was run for 25000 years . Neptune is the green "dot" at 5 'o clock .
Remarkable is the movement of the curl in the orbit of Pluto .
Seems to have an amplitude of about 90 .

Title: Re: Resonance and migration
Post by Tony on 08/08/07 at 14:55:53

Your last animation is similar to one on the "Simulations" page of this web site:
http://www.orbitsimulator.com/gravity/articles/pluto.html

Title: Re: Resonance and migration
Post by frankuitaalst on 08/08/07 at 15:00:02

yes indeed !
There also seems to be some resonance between Uranus and Neptune ( and thus also to Pluto)

Title: Re: Resonance and migration
Post by Tony on 08/08/07 at 16:11:21

There is no resonance with Uranus.  You're seeing the elliptical shape of its orbit in the rotating frame, but unlike Pluto, it marches forward indefinately in the same direction, rather than slowing to a stop and reversing periodically.  Hence, no resonance.

Title: Re: Resonance and migration
Post by frankuitaalst on 08/09/07 at 08:37:09

Simulating the last one , but in a rotating frame to Pluto instead of Neptune gives the following (amazing ) result :
Neptune seems to retrograde in a part of its orbit ....
Pluto is the green line at the bottom .

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