# Do Pluto and Charon have unusual Lagrange points?

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?

• 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.) Commented Dec 9, 2014 at 6:03
• 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. Commented Nov 16, 2016 at 9:50
• 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. Commented Nov 20, 2016 at 20:20
• @JDługosz: How large must the mass of the secondary be for a noticeable deviation from 60°? Commented Jun 12 at 22:39

• 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. Commented Dec 10, 2014 at 12:21