<p>The L1, L2, and L3 points are unstable in any orbital system. (<a href="http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node126.html" rel="nofollow noreferrer">source</a>)</p>

<p>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 (<a href="http://wmap.gsfc.nasa.gov/media/ContentMedia/lagrange.pdf" rel="nofollow noreferrer">source</a>).  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.</p>

CC BY-SA 3.0
2018-03-17T06:15:44.713Z
The closest I see is formula #25, which resolves to approximately 25, but I don't see where those numbers come from.
RonJohn
CC BY-SA 4.0
2021-12-24T11:54:56.973Z
Does this imply that there is an L6, where the center of mass of the two binary planets is?
gciriani
CC BY-SA 4.0
2021-12-25T00:26:28.307Z
@gciriani, the [barycenter](https://en.wikipedia.org/wiki/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
CC BY-SA 4.0
2021-12-25T10:04:52.767Z
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
CC BY-SA 4.0
2021-12-25T21:41:32.327Z
@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
CC BY-SA 3.0
2014-12-10T11:58:38.350Z
What about the three colinear points?
Jerard Puckett
CC BY-SA 3.0
2014-12-10T12:21:39.037Z
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
CC BY-SA 4.0
2014-12-10T01:19:30.747Z
2018-05-21T20:54:11.060Z
2018-05-21T20:54:11.060Z
Mark
<p>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 <a href="https://en.wikipedia.org/wiki/Pluto" rel="noreferrer">Wikipedia</a>:</p>

<blockquote>
  <p>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.</p>
</blockquote>

<p>How does this affect the orbital stability of the five Pluto-Charon Lagrange points?</p>

CC BY-SA 3.0
2014-12-09T06:03:11.590Z
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
CC BY-SA 3.0
2016-11-16T09:50:21.467Z
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
CC BY-SA 3.0
2016-11-20T20:20:18.440Z
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
CC BY-SA 4.0
2024-06-12T22:39:47.267Z
@JDługosz: How large must the mass of the secondary be for a noticeable deviation from 60°?
Outis Nemo
<pluto><lagrange-point><charon>
Do Pluto and Charon have unusual Lagrange points?
Jerard Puckett
# Do Pluto and Charon have unusual Lagrange points?

(Asked by: username_0 on 2014-12-09)

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](https://en.wikipedia.org/wiki/Pluto):

> 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?

**Tags:** pluto, lagrange-point, charon
> **Comments:**
> **username_1**: 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.)  
> **username_2**: 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.  
> **username_3**: 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.  
> **username_4**: @JDługosz: How large must the mass of the secondary be for a noticeable deviation from 60°?  

---

## 1 answers

### Answer by username_5 on 2014-12-10. Score: 12

The L1, L2, and L3 points are unstable in any orbital system. ([source](http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node126.html))

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](http://wmap.gsfc.nasa.gov/media/ContentMedia/lagrange.pdf)). 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.

> **Comments:**
> **username_0**: What about the three colinear points?  
> **username_0**: 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.  
> **username_6**: The closest I see is formula #25, which resolves to approximately 25, but I don't see where those numbers come from.  
> **username_7**: Does this imply that there is an L6, where the center of mass of the two binary planets is?  
> **username_5**: @gciriani, the [barycenter](https://en.wikipedia.org/wiki/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.)  
> **username_7**: 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?  
> **username_5**: @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.)  

---

