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Suppose that .... (Read 20576 times)
Tony
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Re: Suppose that ....
Reply #30 - 08/11/07 at 17:06:53
 
Quote from frankuitaalst on 08/11/07 at 03:15:10:
I'll post the .gsim file . This may explain a lot .

If you do that, I'll take a look.
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frankuitaalst
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Re: Suppose that ....
Reply #31 - 08/11/07 at 17:54:02
 
Sorry , but for some reason I get the "6 overflow" message . I use the Beta22april2007 version .
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Re: Suppose that ....
Reply #32 - 08/12/07 at 03:00:00
 
Heres the clue to the mystery above :  
The sim herunder shows this system edge on .  
What I didn't tell was that the planet was positioned originally high above the ecliptic of the sun orbits , right in the middle  embarrassed
One can see the suns react on a still unvisible planet . As the planet crosses the plane the suns "jump".  
The planet gets an overshoot , returns ...and so on .  
Seems to act as a "cosmic spring".  
I didn't succeed in putting this system in GravSim as the system is referenced in global coordinates.
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2SunsplusplanetEdge.gif
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Re: Suppose that ....
Reply #33 - 08/18/07 at 07:55:40
 
On the stability of a Lagrange orbit ...
Suppose our Earth had a sister-planet in its Lagrange point L4 or L5 .
What happens ?  
Not much , but ...
In the frames herunder the movement of both Earths is shown in a rotating frame of our Earth .  
Earth is at 3 'o clock , the sister planet is at 1 'o clock .  
The simulation starts with 1 Earth , showing also Mercury and Venus .  
The next frame shows the same simulation but with 2 Earths .  
Then the massas of the Earths are increased by 10, 100 ,1000 , 2000 , 4000, 8000...
Each picture shows the system after 250 years.  
The system gets unstable between as the sum of both masses  is somewhere in between 1.2% and 2.4% of the solar Mass.  
Running the application it seems that Venus plays a big role in the unstability of the system .  
At a given moment she really can't decide which Earth to visit first . Smiley
The last picture shows the last frame for above where Mercury , Venus and 1 Earth are ejected .  
Remarkable is the amazing orbit of Mercury in the 2*4000 Earth Mass simulation.
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LagrangeEarthMass.gif
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Re: Suppose that ....
Reply #34 - 08/18/07 at 12:27:57
 
It's about 4%, the mass ratio between the Sun and the combined masses of the double Earths.  Here's a link from the BAUT forum where we discussed this:
http://www.bautforum.com/astronomy/58590-orbit-earth-changes.html
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Re: Suppose that ....
Reply #35 - 08/19/07 at 12:07:12
 
Nice work in the above link in the BAUT-forum !  
The abstract of Chambers and Laughlin stipulates for the linear stability : 2mpl/(2mpl+Msun)< 0.03812 .  
http://adsabs.harvard.edu/cgi-bin/np...2L&db_key=AST&
 
This number of about 4% (0.03812) is AWFULLY correct as can be seen in the frames hereunder .  
4 sims were run with increasing mass of Earth so that the ratio becomes : 0.03792; 0.03811 ; 0.03820 and 0.03825 ( compare to 0.03812 ) for more than 1000 years .  
The first two are stable ( ratio = ok ) , Earths hardly move relatively .  
The third run is just above the ratio , here there is a dynamically stability , not a linear one .  
In the last run the ratio is exceeded by 0.00013 and the stabiltity is completely gone .
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Lagrange2Earths3.gif
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Re: Suppose that ....
Reply #36 - 08/20/07 at 11:30:49
 
Lagrangian points :  
Is a system which has a sister planet in its Lagrangian point L4 or L5 ( also at 60° behind or ahead ) capable to have also other bodies moving in an horseshoe orbit ?  
IT IS !  
Consider an Earth-Sun system , add a second Earth at 60° and add two minor bodies , starting at the opposite site of the sun , vieuwed from Earth . Give them a position of resp. 1.01 Au and 0.99 AU .  
So they start close to each other , but one is nearing the Earth , the other goes away from Earth .  
Here' s what happening in a rotating frame .....
 
Both planets orbit in a horseshoe , but whats even more : they interchange orbits after each close approach .  
The both Earths are the little dots at 1 and 3 'o clock .  
The system is sensitive to the starting conditions : bodies with more initial distance (> 1.02 AU /0.98 AU fi) tend to behave in a normal orbit .  
 
One can imagine what other civilizations living in such a system would see : a big body , as bright as Venus always staying at the same  distance from the sun , and then one smaller body which approaches and then goes away again ; then another similar  body approaches , which goes away again ...
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2EarthsLagrangeplushorseshoe.gif
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Re: Suppose that ....
Reply #37 - 08/21/07 at 10:13:00
 
Here' the GravSim .gsim file of the above system .  
The system should be unpaused and the view set to rotating frame around Earth1.  
For some reason I can't get the rotating frame synchronised with Earth1. Can Tony take a look at it ?  
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Re: Suppose that ....
Reply #38 - 08/21/07 at 11:02:17
 
Your 2 Earths do not start out 60 degrees away from each other.  They're spaced only about 52 degrees, which is not enough for a Lagrangian lock.  So when they pass each other, they affect each other's semi-major axis, and hence, each other's periods.  That's why you can't get a lock on the rotating frame period.
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Re: Suppose that ....
Reply #39 - 08/21/07 at 11:18:08
 
Try this:  http://orbitsimulator.com/gravity/simulations/trojanEarths.gsim
You get 2 Earths spaced 60 degrees, 2 trojan asteroids, one orbiting L4, and the other L5, a horseshoe asteroid, an an asteroid caught between the 2 Earths.
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Re: Suppose that ....
Reply #40 - 08/21/07 at 11:22:23
 
Thanks , I changed the initial conditions , put again the Earth2 at 60° and ran the application .  
I can now stabilise the Earth1 , but the Earth2 moves away ...(???) . It seems to form a 9 corner polygon .
I don't understand .  
Here"s the sim :
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Re: Suppose that ....
Reply #41 - 08/21/07 at 11:27:11
 
Quote from Tony on 08/21/07 at 11:18:08:
Try this:  orbitsimulator.com/gravity/simulations/trojanEarths.gsim
You get 2 Earths spaced 60 degrees, 2 trojan asteroids, one orbiting L4, and the other L5, a horseshoe asteroid, an an asteroid caught between the 2 Earths.

This works ! was it an existing simulation ?  
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Re: Suppose that ....
Reply #42 - 08/21/07 at 11:59:47
 
No, I just made this now:
 
File> New
Objects > Edit Object, rename Object 1 to Sun, change color to yellow
 
Objects> Create Objects
Mass: 1 Earth mass
SMA: 1 AU
Change all the 100% in the +- boxes to 0%
Mean Anomoly: 180
Choose Color
 
Repeat, except Mean Anomoly: 120
 
Objects> Create Objects
Number of objects: 50
SMA: 1 AU
Mean Anomoly: 180 +- 100%
 
Save the sim.
 
You now have 50 asteroids sharing an orbit with 2 Earths.  Choose one asteroid from each catagory and delete the rest.
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Re: Suppose that ....
Reply #43 - 08/21/07 at 12:07:24
 
Quote from frankuitaalst on 08/21/07 at 11:22:23:
Thanks , I changed the initial conditions , put again the Earth2 at 60° and ran the application .
I can now stabilise the Earth1 , but the Earth2 moves away ...(???) . It seems to form a 9 corner polygon .
I don't understand .
Here"s the sim :  

In this sim, Earth 2 doesn't have the same semi-major axis as Earth 1.  It is 10 million km closer to the Sun, so they'll never lock into a 1:1 resonance.
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Re: Suppose that ....
Reply #44 - 08/21/07 at 12:20:30
 
Some input error I think , inputting the X,Y coordinates . Your approach with the automatic generation is a lot quicker and gives accurate results . Smiley
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