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The usual examples of Lagrange points one most commonly encounters, Sun-Earth and Earth-Moon Lagrange points, are examples of 3-body problems where $M_1\gg M_2\gg M_3$. The Pluto-Charon system, however, are much closer in their relative masses, so much so that their barycenter is outside Pluto's surface. From Wikipedia:

Pluto and Charon are sometimes considered a binary system because the barycenter of their orbits does not lie within either body. The IAU has not formalized a definition for binary dwarf planets, and Charon is officially classified as a moon of Pluto.

How does this affect the orbital stability of the five Pluto-Charon Lagrange points?

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  • $\begingroup$ More important to the stability of their L-points should be that Charons orbit is very circular, has very low eccentricity. (But me and orbital mechanics don't understand each other, I don't dear make in an answer.) $\endgroup$
    – LocalFluff
    Dec 9, 2014 at 6:03
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    $\begingroup$ L1, L2 and L3 are never stable for objects in space, so I'm a little confused by your question, unless you want to compare different ranges of instability. They can still be useful places to park a spacecraft as the adjustments the spacecraft needs to make are significantly reduced. $\endgroup$
    – userLTK
    Nov 16, 2016 at 9:50
  • $\begingroup$ In Rocheworld, Robert L.Forward explains that with two equal sized bodies, the equivalent points are at 90°. The points move from 60 to 90 as the mass of the secondary increases. $\endgroup$
    – JDługosz
    Nov 20, 2016 at 20:20

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The L1, L2, and L3 points are unstable in any orbital system. (source)

The L4 and L5 points of a pair of bodies are only stable if the larger of the bodies is at least 25 times as massive than the smaller (source). The ratio of the Pluto/Charon system is only 8.7. Because of this, none of the Lagrange points are stable, and an object orbiting at any of them will require active station-keeping to compensate for perturbations in the orbit.

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    $\begingroup$ What about the three colinear points? $\endgroup$
    – Jerard Puckett
    Dec 10, 2014 at 11:58
  • $\begingroup$ Also, am I blind? I cannot seem to find a discussion of body 1 / body 2 mass & L4-L5 in your source. The wiki puts the ratio as $\ (25 + \sqrt{621})/2$, just not seeing it in the source. $\endgroup$
    – Jerard Puckett
    Dec 10, 2014 at 12:21
  • $\begingroup$ The closest I see is formula #25, which resolves to approximately 25, but I don't see where those numbers come from. $\endgroup$
    – RonJohn
    Mar 17, 2018 at 6:15
  • $\begingroup$ Does this imply that there is an L6, where the center of mass of the two binary planets is? $\endgroup$
    – gciriani
    Dec 24, 2021 at 11:54
  • $\begingroup$ @gciriani, the barycenter isn't a balance point the way L1 is. An object placed at the Pluto-Charon barycenter would either fall onto Pluto or be ejected from the system. (An object orbiting the Pluto-Charon barycenter at a sufficient distance, such as Pluto's other four moons, would be stable.) $\endgroup$
    – Mark
    Dec 25, 2021 at 0:26

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