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Lagrange points L4 and L5 are stable for a test particle. But what happens if instead the body at L4/5 (let's call it C) has a mass significant enough that its gravitational pull on the other two (let's call them A and B) is not negligible anymore? It is rather well know that a ternary system with similar masses is not stable, unless it is strongly hierarchical, i.e. two of the bodies form a close binary system, and the third one orbits much farther away. All observed ternary system are such. But what would be the mass threshold of C beyond which L4/5 would not be stable anymore?

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  • $\begingroup$ Note that even for the restricted 3-body problem, the stability of $L_4$ & $L_5$ depend on the mass-ratio of the two massive bodies, see e.g. this Phys.SE post. $\endgroup$ – Qmechanic Feb 13 '19 at 18:08
  • $\begingroup$ I think you know the Sundman stability equations for a three body system? $\endgroup$ – Eli Feb 13 '19 at 20:34

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