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Lagrange points in a binary system? (Read 4524 times)
EDG
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Lagrange points in a binary system?
03/16/10 at 19:21:18
 
Does anyone know (or have a way of finding out) where the Lagrange Points would be in a binary star system? I know where they'd be in a system with a small mass orbiting a big mass (e.g sun-jupiter, or earth-moon systems) but I'm not sure where they'd be if you had two large bodies with equal mass (e.g. two stars), orbiting their centre of mass.  
 
In the case of zero eccentricity, the two stars would be the same distance from eachother all the time. But for non-zero eccentricity the distance between them would be changing and I'd imagine that would complicate the problem somewhat.  
 
I figure that the L1 point must be where the two roche lobes of the stars intersect, right? And maybe L2 and L3 would be on opposite sides of the stars relative to the L1 point, but where would the L4 and L5 points be? Or would they just not exist in this sort of situation?
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Tony
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Re: Lagrange points in a binary system?
Reply #1 - 03/16/10 at 22:35:11
 
For circular orbits, try here:
http://orbitsimulator.com/formulas/LagrangePointFinder.html
 
For elliptical orbits, the L1 point is constantly on the move.  It's always the point where the centrifugal acceleration of a massless object balances the combined gravitational pulls of the two massive bodies.
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EDG
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Re: Lagrange points in a binary system?
Reply #2 - 03/17/10 at 01:29:20
 
So L1 (and maybe L2 and L3) might be present (but variable), but I guess if the mass ratio is less than 25 then L4 and L5 aren't present?
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Re: Lagrange points in a binary system?
Reply #3 - 03/18/10 at 11:25:51
 
Quote from Mal on 03/17/10 at 01:29:20:
So L1 (and maybe L2 and L3) might be present (but variable), but I guess if the mass ratio is less than 25 then L4 and L5 aren't present?

I think that if 2R is the separation of the binaries there is a L4/L5 point right in the middle , but at 2R distance "upwards" .  
Have to check this with a simulation.
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Re: Lagrange points in a binary system?
Reply #4 - 03/19/10 at 12:52:47
 
Quote from frankuitaalst on 03/18/10 at 11:25:51:
Quote from Mal on 03/17/10 at 01:29:20:
So L1 (and maybe L2 and L3) might be present (but variable), but I guess if the mass ratio is less than 25 then L4 and L5 aren't present?

I think that if 2R is the separation of the binaries there is a L4/L5 point right in the middle , but at 2R distance "upwards" .
Have to check this with a simulation.

Nope .  
There's a point right in the middle but at a hight of sqrt(3)*separation where a body is in equilibrium . So we have an equilateral triangle between all bodies . Alltough the 3rd body remains at its place for some orbits the position is not stable .
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Re: Lagrange points in a binary system?
Reply #5 - 03/25/10 at 00:46:09
 
Apparently there are L2 and L3 points in a binary - mass can be lost from them if the stars overflow their roche lobes (i.e. become bigger than the distance to L1). I suppose they must be on opposite sides of each star relative to the L1 point, while the L4/L5 wouldn't be stable in the system because the mass ratio isn't high enough.
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