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Outer solar system (Read 19138 times)
frankuitaalst
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Outer solar system
04/19/07 at 13:36:36
 
The post of Tony  in the topic "2002VE68" refers to an article of dr Wiegert . He simulated, using a sympletic integrator ,the outer solar system for about 20 million years !  As expected he found that a.o the orbit of Pluto is "chaotic" .  
I also simulated the outer solar system , omitting Mercury, Venus , Earth and Mars for about 450.000 years ...  
The result is shown hereunder ...
The result seems to be in accordance with the findings of dr Wiegert...
It seems that not only the orbit of Pluto is chaotic , but also the orbits of neptune and Uranus...
Furthermore there seems to be some regularity in the orbit of Saturn and Jupiter , with a period of about 50.000 years . The sim took about 3 hours to run .  
The units of i have to be diveded by 10.000 , those of eccentricity by 1000.  
Not shown above , but very observable during the run was a significant progression in the aphelion of the outer planets Saturn...Pluto ...
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frankuitaalst
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Re: Outer solar system
Reply #1 - 04/20/07 at 09:28:02
 
Running the simulation of the outer system backwards in time gives the following picture :  
Pluto seems to process around . The inner planets ( Jupiter and Saturn in green ) stay relatively stable .  
Saturn made a whole tour quite soon after the start of the simulation .
The sim was run for about 2.88 mio years .  
The picture was cut off on top and at the bottom
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Re: Outer solar system
Reply #2 - 04/20/07 at 14:32:11
 
The sim is now running at -4.44 Miliion years . Pluto seems to have completed it's orbit . The rest is stable  
.. I'll post the evolution tomorrow if the sim has reached about -8 mio years .
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Re: Outer solar system
Reply #3 - 04/20/07 at 15:02:52
 
It seems to me that all the planets are precessing.  That is why you have full circular bands that stretch from their perihelions to aphelions, rather than ellipses.  Pluto, being the most elliptical only exaggerates this on the graph.  Pluto's precession rate should be locked to Neptune's precession rate as they are locked into a 3:2 resonance.
 
In fact, if you look closely, you can see that Neptune is not finished yet either.  The lower part of its path is thicker than the upper part.  When it fully precesses, that will be filled in, and it should happen at the same time Pluto finishes.
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Re: Outer solar system
Reply #4 - 04/21/07 at 05:25:14
 
Indeed , some planets needs more time to precess. ...  
The sim was stopped after 7 Mio years .  
Herunder the evolution of the inclination of all the outer planets .  
It seems that Jupiter , Saturn and Uranus are "bound" as they have more or less the same general frequency . Jupiter may be the one who "leads".
Pluto and Uranus on the other hand have their own cycle too and seem to be bound also .  
The cycle time of these is enormous .  
Furthermore one can observe that the variation of Pluto is almost a perfect sine , whereas Neptune is disturbed.  
Please note the incl of pluto is on a different scale . I didn't manage in excel to put the scale on the axis ....
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frankuitaalst
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Re: Outer solar system
Reply #5 - 04/21/07 at 05:33:01
 
The evolution of the Eccentricity (*10000) shows more or less the same dependencies...
Pluto however has its own cycle , whereas Neptune tends to join the other planets ..
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Re: Outer solar system
Reply #6 - 04/21/07 at 12:06:10
 
Additionally , and perhaps most interesting the evolution of de Smei Major axises were calculated . To obtain a meaningfull graph the maps were separated into Jupiter + Saturn and the rest .  
Beacuse the SMA vary a lot I reduced each to the present SMA and calculated the ratio SMA/SMApresent. So each SMA starts at 1.  
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frankuitaalst
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Re: Outer solar system
Reply #7 - 04/21/07 at 12:19:46
 
The SMA show a lot of "chaos" . Interesting is that the variation of Jupiter is very low (due to Mass and distance to the sun ?) .Saturn and Pluto show a lot of variation . It also seems that the SMA of Pluto shows the most "chaos" .  
Both graphs used 11000 data points over the 7Mio simulated years .  
Is there a tendency ? Do the planets approach sun or do they drift away ? It doesn't seem to be .  
The dark black line represents the linear interpolation . The  slope of this function is small ( E-6 Mio Years) .  
This seems to indicate the system is overall stable.  
Interesting also is that Pluto seems to be part of the solar system for more than 7 Mio years.  
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Re: Outer solar system
Reply #8 - 04/21/07 at 13:53:11
 
Could you add a extrapolation to your trend line for Pluto's SMA for say 1/2 of the data period, 5500 periods, also do the same for Reverse.
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Re: Outer solar system
Reply #9 - 04/21/07 at 14:20:11
 
seems linear
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Re: Outer solar system
Reply #10 - 04/21/07 at 15:55:43
 
Pluto's sma should rise and fall with Neptune's.
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Re: Outer solar system
Reply #11 - 04/22/07 at 00:00:51
 
you're right . I'll make a plot for both of them
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Re: Outer solar system
Reply #12 - 04/22/07 at 01:11:38
 
easiest way to represent is the SMA Pluto asf SMA Neptune .  
The plot herunder shows no linear feature , so the orbit of Pluto is not bound to this of Neptune only in the long term . The resonance seems relatively small ( factor 0.008..) . SMA of Pluto seems to increase as SMA of Neptune decreases and vice versa.
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Re: Outer solar system
Reply #13 - 04/22/07 at 03:11:27
 
The same SMA of Pluto and Neptune ( both scaled to their present value ) gives the following graph .  
The black line gives the moving average of Plutos SMA (25 values ) .  
I tried different values of moving average from 2....200 , but couldn't detect any regular pattern .  
I'm afraid that Plutos motion is too much under influence of other planets, although it has now a 3:2 resonace to Neptune ...
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« Last Edit: 04/22/07 at 05:17:19 by frankuitaalst »  

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Re: Outer solar system
Reply #14 - 04/22/07 at 05:22:41
 
I think the chaos of Pluto must be generated by the influence of other planets .  
To find out I ran the same solar system but ONLY with the planets Neptune and Pluto (+sun) .  
The SMA changes of Neptune are very small (1/1000 ) about . These of Pluto are a lot larger .  
The last graph shows the evolution of SMA Pluto as a functioin of the SMA Neptune . Here there is a strong linearity !
It also seems the Pluto's SMA is small if the SMA of Neptune is large .
This corresponds somehow with the trend in the previous graphs .
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Re: Outer solar system
Reply #15 - 12/20/08 at 03:40:03
 
Cleaning up some files I discovered this animation of the evolution of the outer solar system , which I find worth to share :  
shown are the outer planets from Jupiter to Pluto for a period of 500.000 years from now in timesteps of 5000 years .  
Two things are amazing imo : first the strong precession of Pluto's orbit , second the big variation of Saturns orbit . If one looks close also Jupiters orbit varies a lot .  
The orbits of Neptune and Uranus look very stable , but in a longer run (not shown here )  Uranus also seems to get in some resonance
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Re: Outer solar system
Reply #16 - 12/20/08 at 09:14:01
 
Aren't Jupiter and Saturn in a 5:2 resonance?
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frankuitaalst
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Re: Outer solar system
Reply #17 - 12/20/08 at 09:18:13
 
Yes , nearly , the resonance is somewhat smaller than 5:2 . I'll post an evolution graph .
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Re: Outer solar system
Reply #18 - 12/20/08 at 11:32:33
 
Here's the promised graph showing the ratio of orbital periods .  
The two best known resonances ( Jup-Sat) and Nept-Pluto are depicted .  
Saturn and Jupiter will evolve to a 5:2 resonance in about 1000 years but will keep avoiding the exact resonance .
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Re: Outer solar system
Reply #19 - 12/20/08 at 20:15:52
 
cool
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Re: Outer solar system
Reply #20 - 12/26/08 at 02:36:05
 
Running the outer solarsystem for 5mio years from now gives the following animation .  
It  consists out of 50 individual frames , each covering 100.000 years .  
In this animation Pluto makes more than 1 precession .  
It's curious to see how Neptune has "quitr" periods succeeded by more "violent " periods .  
The file herunder is hughe (600 kB ) . So it may be better viewed having clicked on the icon .
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« Last Edit: 12/26/08 at 15:31:06 by frankuitaalst »  

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Re: Outer solar system
Reply #21 - 12/26/08 at 22:34:53
 
I think you meant "Uranus" that has violent and quiet periods.  That is interesting.
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Re: Outer solar system
Reply #22 - 12/26/08 at 22:48:09
 
Yes of course , hard days around christmas  Smiley
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Re: Outer solar system
Reply #23 - 12/27/08 at 05:41:03
 
The picture herunder may explain why Uranus has quiet and violent periods ...
Its eccentricity goes down to zero every 900 thousand years .  
( numbers are scaled with 100.000 and 10.000)
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Outer solar system
Reply #24 - 04/08/09 at 12:38:46
 
On demand of Kevin I made this graph showing the inclination and eccentricty evolution of our biggest gas giants in years from year 0. Simulation was run with Earth +Moon to Mercury omitted . ( adding them would not result in observable deviations I think ) .  
Saturn and Jupiter seem to be in counterphase in inclination , but also in eccentricity .  
However there is a varying phase lag between inclination and eccentricity for both bodies .  
At around 175.000 y inclination and eccentricity will be in counterphase for both bodies .  
Fi : A maximum inclination of Jupiter will then correspond with a maximum eccentricity of Jupiter . Same for Saturn .  
 
Additional graphs can be made for Uranus and Neptune . These orbital elements vary slower .
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JupSat Dance
Reply #25 - 04/08/09 at 16:01:35
 
My methods are cruder than Franks, since I don't generate plots.  But some checking with Solex (using all the planets+Earths moon) seems to suggest an exchange (dance) between Jupiter and Saturn where they swap inclination for eccentricity.
 
I assume Franks 0 point is 2007-02-01.  I used Solex "V!FG mode" (adaptive stepsize, 18-bit, full precision).  Around the year 142,000 AD Jupiter has a local maximum inclination of 0.4791 degrees to the INVARIABLE plane of the solar sytem while Saturn is inclined only 0.78 degrees to the invariable plane.  But when Jupiter comes down to an inclination of 0.238 in the year 168000, Saturn kicks up to an inclination of 1.01 to the invariable plane.
 
Uranus frequently has an inclination of more than 1 degree to the invariable plane.  This could explain why it likes to dance around so much...
Invariable plane 2009: http://home.comcast.net/~kpheider/MeanPlane.gif
 
Body, Year, INVInc, Eccent
Jup  142000, 0.479, 0.0379
Sat  142000, 0.789, 0.0747
Jup  168000, 0.238, 0.0560
Sat  168000, 1.010, 0.0372
 
-- Kevin
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Re: JupSat Dance
Reply #26 - 04/08/09 at 16:04:27
 
The year 168k...
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Outer solar system
Reply #27 - 04/09/09 at 08:49:29
 
Question for Tony I guess : there's a difference between the inclination data I obtain and Solex values .  
Kevin refers to the Invariable Plane for the Solex Sim.  
I think GravSim calculates the inclination with reference to the sun . I took for this sim the JPL J2000 Ephemeris, with Sun at center (0.0.0.0.0.0) coordinates .  
What can be the reason for this different values ?  
If we take zeroinitial  coordinates for the sun , the sun will move in absolute coordinates of course . Can this have some influence ?  
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Invariable plane
Reply #28 - 04/09/09 at 12:05:16
 
Quote from frankuitaalst on 04/09/09 at 08:49:29:
Kevin refers to the Invariable Plane for the Solex Sim.

 
Hi Frank;
 
http://en.wikipedia.org/wiki/Invariable_plane
The Invariable plane is the plane passing through its barycenter (center of mass) which is perpendicular to its angular momentum vector. In the Solar system, about 98% of this effect is contributed by the orbital angular momenta of the four jovian planets (Jupiter, Saturn, Uranus, and Neptune).  Jupiter seems to never get more than 0.5 degrees from this plane since Jupiter and Saturn control the barycenter point.
 
GravSim is using the traditional Ecliptic inclination.  Solex can use that "reference inclination" also.  But as a non-gas giant, AND being closer to the Sun with a quicker orbit, Earth's inclination will change far more rapidly than further out and far more massive Jupiter.
http://en.wikipedia.org/wiki/Ecliptic
 
Another good reference inclination (IMHO) is the Sun's equator.  Notice how Mercury (not surprisingly, since it is the closest planet to the Sun) stays close to the Suns equator (3.3 degrees) even though the bigger planets are pulling on it.
http://en.wikipedia.org/wiki/Ecliptic#Ecliptic_and_planets
 
Here are Solex's Ecliptic numbers for the year 145631 (when Mercury makes its closest passages to the Earth).  Notice how it says "ECLIPTIC Osculating Elements" in the upper left instead of "MEANPLANE Osculating Elements".  The eccentricity is the same using either reference inclination.
 
-- Kevin
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Outer solar system
Reply #29 - 04/09/09 at 12:20:27
 
Kevin , thanks for the clarification !  
My first tought was that the invariable plane was the fixed plane referenced to the zero point of Aries . Obviously I was wrong assuming this .  
This explains a lot .  
Thanks also for the Solex output. Seems both programs give the same result .   Smiley
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Deep Solex "V!FG mode" year 750k
Reply #30 - 04/09/09 at 13:06:57
 
Quote from frankuitaalst on 04/09/09 at 12:20:27:
Thanks also for the Solex output. Seems both programs give the same result .   Smiley

 
Hi Frank;
 
Here are my "Ecliptic" Deep Solex results that I ran over the weekend while experimenting.  I used Deep Solex "V!FG mode" (adaptive stepsize, 18-bit, full precision) all the way out to the year 750k.  How do these results line-up with your simulation without the inner planets? (Uranus is inclined more than his 3 more massive brothers; invariable inclination of Uranus=1.06 at year 750k.)
-- Kevin
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Outer solar system
Reply #31 - 04/09/09 at 13:16:42
 
Here's my plot for the outer gas giants . 0 time corresponds here with y 2007.
Sim was run with  Mars.....up to Pluto
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Re: Outer solar system
Reply #32 - 04/09/09 at 13:23:00
 
For comparison : the plot for Jupiter and Saturn over the same time-period .
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Uranus out of alignment with Jupiter and Saturn
Reply #33 - 04/09/09 at 13:43:45
 
At the year 500,000 Uranus has an ecliptic inclination of 0.72, but an "invariable plane" inclination of 1.02.  It is Uranus that is out of alignment with Jupiter and Saturn (not Neptune). Smiley
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If there was no Mercury through Earth, Mars would
Reply #34 - 04/10/09 at 08:37:59
 
Quote from frankuitaalst on 04/08/09 at 12:38:46:
Simulation was run with Earth +Moon to Mercury omitted.

 
Hi Frank;
 
I know you didn't use Mercury through the Earth for your calculations, but I would be curious to see what Mars eccentricity looks like on you simplified plots vs what Mars should look like over 1 to 2 million years.  See Solex chart (Aldo Vitagliano's work) for a 5.5 million year plot at http://main.chemistry.unina.it/~alvitagl/solex/marsecc.gif
It might make an interesting comparison to see how much of an influence the Earth does (or does not) have on Mars. Smiley
 
Your plots are really great for spotting trend lines.
-- Kevin
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Re: If there was no Mercury through Earth, Mars wo
Reply #35 - 04/10/09 at 09:25:56
 
Quote from kheider on 04/10/09 at 08:37:59:
Quote from frankuitaalst on 04/08/09 at 12:38:46:
Simulation was run with Earth +Moon to Mercury omitted.

Hi Frank;
I know you didn't use Mercury through the Earth for your calculations, but I would be curious to see what Mars eccentricity looks like on you simplified plots vs what Mars should look like over 1 to 2 million years.  See Solex chart (Aldo Vitagliano's work) for a 5.5 million year plot at http://main.chemistry.unina.it/~alvitagl/solex/marsecc.gif
It might make an interesting comparison to see how much of an influence the Earth does (or does not) have on Mars. Smiley
Your plots are really great for spotting trend lines.
-- Kevin

So am I . I'm running now the full system , but it may take some time. I expect to have some differences as I'm not taking into account relativity nor the oblateness of the sun . Keep you informed ... Smiley
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Re: If there was no Mercury through Earth, Mars wo
Reply #36 - 04/10/09 at 10:42:22
 
For Mars, I believe that the large (2.2 million year) cycle is controlled by Jupiter and that the mini-inner-cycle (96,000 years) is controlled by the Earth.
http://www.ips-planetarium.org/planetarian/articles/whenMarsClose/whenwasmarsthi sclose.pdf
 
In the year 208k Mars does hit an eccentricity of 0.123 (q=1.335AU) with a somewhat aggressive inclination of 4.81 degrees to the Invariable plane.
 
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Solex at -2 million years
Reply #37 - 04/12/09 at 22:29:22
 
Quote from frankuitaalst on 04/21/07 at 05:25:14:
Indeed , some planets needs more time to precess. ...
The sim was stopped after 7 Mio years.

 
Here is a screen capture from Solex at -2 million years. I used DE421, just the planets (EMB=Earth-Moon Barycenter; !FG options for "18-bit, full precision").
 
Like Franks plot shows Uranus is near a eccentricity minimum while Saturn is the most eccentric of the 4 gas giants.  Uranus is inclined 1.1 degrees to the invariable plane (so higher inclination at lower eccentricity).
 
http://www.orbitsimulator.com/yabbfiles/Attachments/OuterPlEccentricity.gif
 
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Re: Outer solar system
Reply #38 - 04/12/09 at 23:03:49
 
Nice to have a fit with Solex !  Smiley
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Outer solar system-Mars
Reply #39 - 04/18/09 at 04:47:16
 
As told in the "Mercury" thread I've run the solar system fror 250.000 years.  
The plots of the inner planets can be found on the Mercury thread .  
As the outer planets exhibit some  interesting features I share some plots .  
 
Mars inclination has surprisingly a period corresponding with 70.000 years ( same as Earth and Venus ) .  
This period is different from the period Jupiter and Saturn have ( about 50.000 years ) .  
Mars seems to be in an increasing eccentricity period .  
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Outer solar system- Jupiter
Reply #40 - 04/18/09 at 04:50:01
 
Jupiter seems to be stable . It's inclination period of 50.000 years is smaller than the inner planets period .
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Outer solar system- Saturn
Reply #41 - 04/18/09 at 04:51:59
 
Saturn seems to be in counterphase with Jupiter in inclination and eccentricity .
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