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Neptune - Uranus Switch (Read 10538 times)
frankuitaalst
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Neptune - Uranus Switch
12/27/07 at 10:54:33
 
Quote : http://www.lpi.usra.edu/meetings/LEA/whitepapers/Bottke_Levison_LHB_2007.pdf
I think this new post of Mal deserves a seperate topic .  
The picture in this article is really amazing as it seems the  team has simulated the outer planets back up to ....almost 1000 million years . That's a hughe amount of time !  
Remarkable are the  jumps at 880 Mio years but also at about 80 Million years in the semi-major axes of Neptune and Uranus . The jumps seem to come "suddenly" without apparent warning .  
I felt interested if the behaviour of the outer planets in the past shows some indication of instability and ran the outerplanetsystem for more than 2 million years ( this took 6 hours of CPU ) .  
Hereunder is an animated gif showing the outers from Jupiter to Pluto back in time .  
Unfortunately the screen was not calibrated at the origin , so the picture wobbles .  embarrassed
The only strong instability is in the orbit of Pluto which shows a precession with a period > 2 Mio years.  
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Re: Neptune - Uranus Switch
Reply #1 - 12/27/07 at 19:38:44
 
I thought that might get people interested Wink. In retrospect I guess I should have posted it on its own rather than in the News/Town Crier thread...
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frankuitaalst
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Re: Neptune - Uranus Switch
Reply #2 - 12/28/07 at 13:20:41
 
I found another interesting article about this topic  
http://www.psrd.hawaii.edu/Aug06/cataclysmDynamics.html.  
The article has a nice animation showing the switch and the resulting bombardment of asteroids .  
In annex is a animated gif showing the outer planets , going back in time . Simulation covers 10E+6 years and took more than a day of CPU .  
Except for the precession of the perihelium of all the planets there is not  yet after 10 million years a strong indication of instability .
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Re: Neptune - Uranus Switch
Reply #3 - 12/28/07 at 13:39:31
 
( trying to find a clue of instability in the "recent" past using GravSim  lips sealed) .  
After integrating for almost 10 Mio years the data obtained look as following :  
Semi major axis of all planets vary , as well as their eccentricity , in a periodic , somehow "chaotic" way as can be seen from the picture below .  
( data were referenced to 1 : present value ) .  
Applying a trend line to the obtained data gives a small trend towards smaller sma in the past .  
The slope  however is small ... and still gives (not yet ) no indication for a cataclism in the past ...
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Re: Neptune - Uranus Switch
Reply #4 - 12/29/07 at 01:44:56
 
What about this title  ? :
 Pluto may be an Earth like body which originated in the Earths region .   Shocked.
Some explanation :  
Running the outersystemplanets in order to find out some clues about the Neptune-Uranus switch , I ran a separate program with the Uranus-Neptune-Pluto system , in order to gain speed .  
The sim is running for many million years now but Neptune and Uranus are still on their location .  
Pluto however in this period of time ( > 100 million years) has seen all the edges of the solar system ..
It decided to leave his normal orbit after about 20 million years and is exploring the solar system , beeing now (150 Mio years ) within the Mars orbit .  
I wonder if this simulation is "realistic" as I omitted Jupiter and Saturn .  
I'll post some pictures
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Re: Neptune - Uranus Switch
Reply #5 - 12/29/07 at 09:08:10
 
As promised above : the picture of the Pluto/Uranus/Neptune simulation back in time .  
Simulation covers -180 Million years . ( timeframes are not taken at equal intervals )  
Pluto goes out of orbit after about 20 Mio years.  
Uranus and Neptune however stay in their usual orbits .  
Anybody here has an external reference for such simulation ?  
 
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Re: Neptune - Uranus Switch
Reply #6 - 12/29/07 at 12:59:55
 
Pluto likely was always external to Neptune.  As Neptune migrated outward, it captured Pluto into its 3:2 resonance.  As Neptune continued its outward migration, Pluto, trapped in the 3:2 resonance had no choice but to migrate as well, its orbit becoming more eccentric the further it migrated.
 
It's theorized that Jupiter and Saturn reached a 2:1 resonance which caused the gravitational instability that caused Neptune and Uranus to switch places.  But when I simulate this, I can not get Jupiter and Saturn to stay put in a 2:1 resonance.  They immediately perturb themselves out of this resonance.  Although its possible that their orbits were eccentric enough for the resonance to lock.
 
Another oddity about migrating planets:  They should gain mass as they migrate.  I tried this in Gravity Simulator, placing a Jupiter-sized planet at 1 AU, and a belt of 50 0.0001 Jupiter-mass particles just exterior to Jupiter.  I wanted to see if Jupiter would migrate as a result of ejecting some of these particles.  I suspected it would migrate in as it ejected particles.
 
In 500 years, it never did eject any particles, but many were placed on orbits with high aphelions.  And Jupiter did migrate as a result, 100,000 km sunward.  But it also collided with particles, absorbing 22 of the original particles, increasing its mass by 0.22%.  Extrapolating this, Jupiter needs to gain 2.2% of its mass to migrate 1 million km.
 
So in these migration scenerios, the migrating planets are also growing.
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Re: Neptune - Uranus Switch
Reply #7 - 12/30/07 at 02:26:48
 
Thanks for the information . I do have some questions :
* Pluto should be trapped into resonance with Neptune , both moving outward . What about Jupiter and Saturn ? They seem to avoid a 1:2 resonance . What I mean is that in the first case the resonance is a trap , in the second an instability ??? I don't get the picture .  
*I'm not familiar with accretion of mass and I don't get intuitively why a planet should migrate outwards if it gets more mass ( while I'm typing this : ok : conservation of momentum ), but the absorbed bodies had momentum too , so I might think the net picture is staying at its orbit ??
* the link posted by mal refers to the NICE model . I interpreted falsely  the picture as going back in time from now . This is incorrect . The NICE model seems to start with a circular model of the planets ( in which Uranus is the outermost ) which evolves in time to the present .I still wonder if it's possible to calculate back in time from now on.
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Re: Neptune - Uranus Switch
Reply #8 - 12/30/07 at 05:20:01
 
Heres a screenshot I would like to share : simulation of the outer planets for about 3.7 Mio years back in time .  
1 shot corresponds with 500.000 years . Interesting is the precession of the perihelium of Pluto which has a period of  about 3.7 million years
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Re: Neptune - Uranus Switch
Reply #9 - 12/30/07 at 18:58:01
 
Quote from frankuitaalst on 12/30/07 at 02:26:48:
Thanks for the information . I do have some questions :
* Pluto should be trapped into resonance with Neptune , both moving outward . What about Jupiter and Saturn ? They seem to avoid a 1:2 resonance . What I mean is that in the first case the resonance is a trap , in the second an instability ??? I don't get the picture .
*I'm not familiar with accretion of mass and I don't get intuitively why a planet should migrate outwards if it gets more mass ( while I'm typing this : ok : conservation of momentum ), but the absorbed bodies had momentum too , so I might think the net picture is staying at its orbit ??
* the link posted by mal refers to the NICE model . I interpreted falsely  the picture as going back in time from now . This is incorrect . The NICE model seems to start with a circular model of the planets ( in which Uranus is the outermost ) which evolves in time to the present .I still wonder if it's possible to calculate back in time from now on.    

 
I'm just guessing, but since Jupiter and Saturn are closer to the Sun than Neptune and Pluto, they are much closer to each other when near the 2:1 resonance.  Additionally, they're both more massive than Neptune and Uranus, so they heavily perturb each other.  As Neptune migrates outward, its 3:2 resonance gently approaches Pluto, allowing for a capture.
 
You can try this yourself in Gravity Simulator.  Create a Neptune at 20 AU, and 50 test particles at 30 AU +/- 30%.  Use Autopilot > Continuous Orientation > Prograde on Neptune, and Autopilot > Thrust 0.0000000001 m/s/s to set Neptune slowly migrating outward.  Create a data file which outputs all objects' periods, open it in Excel and create new columns that are Neptune's Period divided by test particles' periods.  You should see the ratio grow until it reaches either 3:2, or 2:1, at which point it locks.  The slower you migrate (you can play around with the 0.0000000001 number), the more objects you trap into resonance.
 
---------
 
It's not the acretion of mass that causes the planet to migrate.  It's the close encounters.  When 2007 WD5 passes Mars next month, Mars will boost its semi-major by 6 million kilometers if it follows the trajectory in the simulation I posted.  In response, Mars' semi-major axis will decrease.  But since Mars is significantly more massive than the asteroid, the decrease in its semi-major axis will not be noticable.  But if it did this billions of times, that would cause Mars to migrate in a noticable amount if there was a bias towards Mars boosing the asteroids outward or sunward.  Since Mars doesn't have enough gravity to boost something to solar escape velocity, any object it boosts will ultimately return to Mars to be boosted again, either inward or outward.  Over long periods of time, there may not be a bias, and Mars will not migrate, as it boosts equal amounts of asteroids inward or outward.
 
Jupiter, however, can boost objects to escape velocity.  In response, this will decrease Jupiter's semi-major axis.  Since an ejected object can not return to receive an inward boost from Jupiter, the net bias will be for Jupiter to migrate towards the Sun.
 
Neptune and Uranus, with their lower masses are less likely to boost an object to solar escape velocity.  But they may boost objects inwards that then get boosted to solar escape velocity from Jupiter.  These objects can not return to Neptune and Uranus for an outward boost, so the net bias is for Neptune and Uranus to migrate outward.
 
But if an object can approach one of these planets close enough to get a gravitational boost, it can also collide.  That's the case next month with 2007 WD5.  It will either receive an inward boost from Mars, or an outward boost from Mars, or it will collide with Mars.  So the point I was trying to make is that any planet that is migrating will also collide with a certain percentage of the objects that are causing it to migrate.  And based on my simple simulation, its a very significant percentage of these objects.  Therefore, a migrating object should also be a growing object.
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Re: Neptune - Uranus Switch
Reply #10 - 12/31/07 at 01:25:18
 
Thanks Tony for the explanation . I get the picture now  Smiley.  
So planetesimals are the clue for migration of the planets , given the mass of the planetesimals or disk is big enough related to the planets involved .  
I started a GravSim wich s running now with Jupiter en Saturn , together with 400    0.01Jup masses.  
Some of them are ejected , some are absorbed by Jupiter , while Jupiters SMA decreases indeed .  
 I'll see if I can post some info .
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Re: Neptune - Uranus Switch
Reply #11 - 12/31/07 at 01:34:25
 
Huh, so the close encounters actually what's causing Jupiter and Saturn to migrate? So on the one hand we can have gas drag pulling jovians towards the star, and then later on we can have interactions with planetesimals that can expand their orbits? Hm. I wonder what's happened in the extrasolar systems where the jovians have spiralled in then... what's happened to the planetesimals there - would they all still be in the outer system or would they have been scattered?  
 
I also note that the PSRD link says that Jupiter moved inward while Saturn moved outward, and then Saturn moved into the 2:1 - is that what you guys are simulating, or are you moving them both outward?
 
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Re: Neptune - Uranus Switch
Reply #12 - 12/31/07 at 02:03:16
 
There's 2 different simulations I'm referring to.  One in which I cause Neptune to migrate outward and capture particles in its exterior resonances.  In this simulation I force Neptune to migrate by applying a prograde acceleration.
 
Then there's the Jupiter simulation where I supply 50 test particles for Jupiter to interact with.  I'm re-running this simulation right now.  Jupiter starts at 5.00 AU, and the test particles are all at 5.10 AU, but in different locations along the orbit (random MA).  At first, Jupiter migrated lightly outward, but soon the inward trend dominated.  After 40 thousand years, Jupiter migrated 500,000 km inward.  It ejected 2 particles.  It drove 3 particles into the Oort Cloud, and it collided with 31 particles.  
 
I'm not sure how much gas drag effects the giant planets.  I would imagine by the time they became fully formed that solar radiation would have cleared the solar system of gas.  But that's just my guess.  I'm not that familiar with the accepted theory.  In systems where the Jovians have spiraled in, it might be possible that there was a thicker belt of material for them to interact with.  It's also possible that tidal forces caused them to spiral in once they pass the point where their orbital period is synchronous with the star's rotation.
 
In the Jupiter / Saturn simulation, I just simply created a Jupiter-mass planet and a Saturn-mass planet in a 2:1 resonance, both being in circular orbits.  This resonance did not last for even 1 orbit before they perturbed each other's SMAs, ruining the resonance.  Additional attempts at this simulation should include them migrating to the resonance to see if eccentricity develops, and if this eccentricity preserves the resonance.
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Re: Neptune - Uranus Switch
Reply #13 - 12/31/07 at 03:38:55
 
Post #8 above continued : the simulation of the outer planets back in time ( running now for 11 million years ) stays remarkebly stable .  
Screenshots are made every 250.000 years.  
Pluto's orbit seems to "roll" over neptunes orbit . Remarkable is also the "pulsation" of Uranus' orbit .
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Plutoprecession.gif (attachment deleted)  
 
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Re: Neptune - Uranus Switch
Reply #14 - 01/03/08 at 07:30:46
 
The simulation with the 5 outer planets back in time is remarkable stable ...
I stopped the sim after -39 Mio years as nothing spectacular happened ( Pluto was not ejected as in the sim where Jupiter and Saturn didn't take part ) .  
Pluto continues its precession as before .
Semi-major axes varied iwithin a certain field as before , but there is no tendency in any direction . This applies for all of those planets.  
Herunder are a couple of screenshots of this run (this runtook a couple of days  ) .  
The most interesting part of the analysis may be this : the evolution of the inclination and eccentricity of each planet is somehow periodic.  
The periodicity comes as two groups : it seems that Jupiter and Saturn perturb each other , and also Neptune and Uranus perturb each other .  
The perturbation of Pluto seems to be driven by Neptune in first case.
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Re: Neptune - Uranus Switch
Reply #15 - 01/03/08 at 12:35:41
 
39 million years :0 must have a good computer. whats your timestep for that 32,000?
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Re: Neptune - Uranus Switch
Reply #16 - 01/03/08 at 12:53:17
 
For this I used a seperate program which runs very fast for a little number of planets.  
It's called the Picard intregrator and adapts the timestep in order to maintain its accurancy . For this configuration of planets the "timestep" was about 13000 hours .
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Re: Neptune - Uranus Switch
Reply #17 - 01/03/08 at 15:31:37
 
wow thats a steep one, were do i download this? i am relativly new to gravity simulator and new to the forum so i would be thankfull to know what programs you guys use besides gravity simulator.
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Re: Neptune - Uranus Switch
Reply #18 - 01/04/08 at 06:47:51
 
Quote from ssc4k on 01/03/08 at 15:31:37:
wow thats a steep one, were do i download this? i am relativly new to gravity simulator and new to the forum so i would be thankfull to know what programs you guys use besides gravity simulator.

We normally use the software provided in this Forum . That's Gravity Simulator . The modarator Tony also takes care for upgrades , which are announced in this forum and can be downloaded .  
Personally i also use a private integrator which has some advantages as accurancy but it is far off as userfriendly as the Gravity Simulator . It's rather complicated to use it as it needs much input . Maybe the integrator will one day be "integrated" in the software of Gravity Simulator .  
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