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if a spacecraft is set into orbit around a binary star system such that it is collinear with the two stars. if the distance of the spacecraft from each of the stars is $R$ and $r$ then what will be the ratio of the masses of the stars? is this a stable one?

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In general this situation expressed in the title is true of arrangements with a light body in the first, second or third Lagrange point associated with a pair of orbiting massive bodies.

Such arrangements are, however, unstable and won't persist in real life without some kind of station-keeping.

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  • $\begingroup$ My comment deleted, (and forgotten), but now Lagrange points won't be. Thanks $\endgroup$ – user178231 Dec 10 '17 at 18:33
  • $\begingroup$ So basically L1 and L2 . $\endgroup$ – marshal craft Jul 5 '18 at 15:33

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