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Stable Cross Binary orbit (Read 3813 times)
abyssoft
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Stable Cross Binary orbit
10/09/15 at 13:18:47
 
I think I stumbled across a phenomenon that is not supposed to be able to occur.
 
I have a planet that is successfully and apparently stably orbiting both members of a binary star system transferring between each member.
It is quite interesting to behold.
My sim has so far been successful 5 kyr. I'm using RK4 variable as the integrator.
 
Any feedback on this would be appreciated.
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Tony
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Re: Stable Cross Binary orbit
Reply #1 - 10/09/15 at 19:04:33
 
I had trouble opening your attachment, so I used your numbers to create a new one:  
 
http://orbitsimulator.com/gravity/simulations/scb.gsim
 
It seems to stay stable indefinitely.  This is a very cool orbit.  I didn't know this could exist either.
 
It seems to be very sensitive to the mass ratio between the stars.  If they're not equal, the planet gets ejected from the system after just a few orbits.
 
Frank posted some simulations a few years back about figure-8 orbits in the thread titled "Chasing Suns": http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1181200864/0
and "Chen's work revisited": http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1250625868/0#0
But I don't think any of Dr. Kuo Chang Chen's orbits behaved like yours, where the orbiting object keeps getting traded between 2 suns.  Sci-Fi writers have been known to ask if such orbits can exist.
 
Here's 3 different versions of your sim in the browser version, so you can share it with Mac and Linux users as well.  The third one sets it in a rotating frame, and demonstrates just how stable this configuration is.
 
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1444440707009_scb.ht ml      Locks Sun to middle of screen
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1444440707009_scb2.h tml    2 Suns orbit their barycenter
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1444440707009_scb3.h tml    rotating frame
 
In the browser version, press A on your keyboard for more options.  Then you can turn barycenter on or off.
Under the Preferences menu, you can choose RK4 variable time step and Do Events.
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abyssoft
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Re: Stable Cross Binary orbit
Reply #2 - 10/09/15 at 19:27:54
 
It would be interesting if this could scale up so that the planet stays near the habitable zone.
 
The maximum habitable area occurs at ~ 3.3 au sep. http://astro.twam.info/hz/#
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Tony
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Re: Stable Cross Binary orbit
Reply #3 - 10/09/15 at 20:22:29
 
How did you stumble upon the starting conditions for your simulation?
 
Here's another view showing how the apparent sizes of the 2 stars change as the planet orbits them.
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1444446416493_scb4.h tml
 
Press B to give you options for the right side of the screen.
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abyssoft
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Re: Stable Cross Binary orbit
Reply #4 - 10/09/15 at 20:46:37
 
I was starting to explore the work of Holman & Wiegert and stability in Binary systems.
I started my first evaluation using the following params and let v3.0c decide the rest.
 
I was going to walk through iterations of mu, e, i, and a standardized body 1me, 1re, e=0, i=0, around barycenter with semi-major axis being one of the variable params (c).
 
initial mu=0.5 (both bodies as 1 sun), e=0, i=0. semi-major of (c) distance was 256.116E-03 au
 
 
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Tony
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Re: Stable Cross Binary orbit
Reply #5 - 10/09/15 at 21:32:38
 
What is v3.0c?
 
In my experience, Wiegert is very approachable.  He enjoys it when people take an interest in his work.  Send him an email.  Show him your sim and ask him what he thinks.  My GUESS is that you've stumbled across some starting conditions which are unlikely to ever occur in nature.  If I make the masses of the stars differ by even 1%, the planet gets ejected within a few orbits.  I hope I'm wrong.  Imagine how strange habitable conditions would be upon such a world!
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abyssoft
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Re: Stable Cross Binary orbit
Reply #6 - 10/09/15 at 21:56:42
 
V3.0c, The desktop version of Gravity simulator I'm using, it was the 2011 august alpha release.
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Tony
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Re: Stable Cross Binary orbit
Reply #7 - 10/09/15 at 22:02:48
 
sorry,  I guess I should know my own acronyms  Shocked
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abyssoft
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Re: Stable Cross Binary orbit
Reply #8 - 10/09/15 at 22:04:49
 
lol well that was over 4 years ago
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frankuitaalst
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Re: Stable Cross Binary orbit
Reply #9 - 10/11/15 at 10:05:45
 
Quote from Tony on 10/09/15 at 21:32:38:
What is v3.0c?

In my experience, Wiegert is very approachable.  He enjoys it when people take an interest in his work.  Send him an email.  Show him your sim and ask him what he thinks.  My GUESS is that you've stumbled across some starting conditions which are unlikely to ever occur in nature.  If I make the masses of the stars differ by even 1%, the planet gets ejected within a few orbits.  I hope I'm wrong.  Imagine how strange habitable conditions would be upon such a world!

 
Definitevely weird ! Nice work aby !
A while ago I've done some simulations , Tony mentions above , for which I took the starting conditions from Chen's work : here  
http://www.math.nthu.edu.tw/~kchen/papers/COX.pdf
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