Is there for example some L1 like libration point where the Hill spheres of the Sun and of the Alpha+Beta Centauri meet? And are Lagrange points between stars inside of a binary system, like Alpha and Beta Centauri, more or less stable because they are much more massive than planets?
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$\begingroup$ I dont think it's possible between different stars becuse it's too far away, and the stars aren't even orbiting each other $\endgroup$– MadBenderAug 21, 2015 at 8:12
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$\begingroup$ @MadBender True, probably not too much gravity action going on 2 ly from the Sun. Remains close binary star. $\endgroup$– LocalFluffAug 21, 2015 at 8:52
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2 Answers
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Lagrange points do exist between stars. In case of single stars, they are too far away from the stars to have any practical effect.
However, in case of the binary stars, the Roche Lobe has its apex located at L1.
"RochePotential color" by SamuelHon - Own work. Licensed under CC BY-SA 4.0 via Commons.
In case a star's surface extends beyond the Roche Lobe, it will lose the material outside the Roche Lobe to its companion star through the first Lagrangian point.
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$\begingroup$ Great illustration. If Earth had one Solar mass, would Sun-Earth L1 be more or less stable to orbit around? I imagine that there would be much steeper gravitational gradients to be pulled away by. On the other hand, low mass objects don't have useful Lagrange points. $\endgroup$ Aug 21, 2015 at 10:56
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$\begingroup$ Your answer and Wiki link has suddenly much helped my non-mathematical intuitive understanding of this stuff. $\endgroup$ Aug 21, 2015 at 11:32
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Yes, there are Lagrange points between starts, however, most are not stable enough to orbit around them because they are too far away from the stars.