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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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  • 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.) – LocalFluff Dec 09 '14 at 06:03
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    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. – userLTK Nov 16 '16 at 09:50
  • 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. – JDługosz Nov 20 '16 at 20:20

1 Answers1

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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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    What about the three colinear points? – Jerard Puckett Dec 10 '14 at 11:58
  • 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. – Jerard Puckett Dec 10 '14 at 12:21
  • The closest I see is formula #25, which resolves to approximately 25, but I don't see where those numbers come from. – RonJohn Mar 17 '18 at 06:15
  • Does this imply that there is an L6, where the center of mass of the two binary planets is? – gciriani Dec 24 '21 at 11:54
  • @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.) – Mark Dec 25 '21 at 00:26
  • What is the difference between the unstable equilibrium at L1 (or L2 and L3 for that matter) and the unstable equilibrium at the barycenter? It seems to me that an object at the barycenter and one at L1 would both fall toward Pluto if nudged toward it, and would both fall toward Charon if nudged toward it. So if there's a difference could please explain it? – gciriani Dec 25 '21 at 10:04
  • @gciriani, there's no equilibrium at the barycenter: the net gravitational force is towards Pluto. An object at the barycenter would accelerate towards Pluto at about 0.2 m/s. (An object in an orbit passing through the barycenter would be out of phase with Charon; I'm fairly sure the resulting three-body interaction would slow it down until it crashes into Pluto.) – Mark Dec 25 '21 at 21:41