<p>The figure 8 orbit is the <a href="https://www.maths.ed.ac.uk/%7Eateckent/vacation_reports/Report_Faustino.pdf" rel="nofollow noreferrer">only known stable orbital configuration for 3 bodies of equal mass</a>. Are there islands of stability, analogous to Lagrange points for 2 orbiting bodies, that trace their way around the figure 8?</p>

CC BY-SA 4.0
2024-04-19T21:20:31.513Z
There are other stable orbits for three bodies, such as a central body and two planets, or a central body, a planet and a moon.
James K
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2024-04-20T02:34:35.940Z
@JamesK edited, thanks
user121330
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2024-04-20T15:44:47.627Z
@ScienceSnake it's a good point. I can hear the joke now [CARSON: the figure-eight orbit is so stable... AUDIENCE: (in unison) How stable is it?"](https://movies.stackexchange.com/q/110906/45856) I think that in orbital there are several different flavors of stability; for example see the first paragraph of Wikipedia's [Lyapunov stability](https://en.wikipedia.org/wiki/Lyapunov_stability)
uhoh
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2024-04-20T18:47:52.163Z
I would somewhat hesitantly say "no"... Because "analogous" isn't really possible.  In the 2 body system, you can choose a rotating frame in which the planet is at rest.  In this rotating frame, you can consider the pseudo-potential, and find there are the five lagrange points.  But what is the analogy with a figure of 8 orbit? There isn't a way to get a rotating frame and find a pseudopotential... so there isn't an analogy to the Lagrange points.  I'm hesitant because someone might think of another way to form the analogy.
James K
CC BY-SA 4.0
2024-04-21T14:54:25.377Z
@ScienceSnake a quick question posted in Math SE just might bring an authoritative and comprehensive answer.
uhoh
<celestial-mechanics><lagrange-point>
Lagrange points for figure eight orbit
user121330
# Lagrange points for figure eight orbit

(Asked by: username_0 on 2024-04-19)

The figure 8 orbit is the [only known stable orbital configuration for 3 bodies of equal mass](https://www.maths.ed.ac.uk/%7Eateckent/vacation_reports/Report_Faustino.pdf). Are there islands of stability, analogous to Lagrange points for 2 orbiting bodies, that trace their way around the figure 8?

**Tags:** celestial-mechanics, lagrange-point

> **Comments:**
> **username_1**: There are other stable orbits for three bodies, such as a central body and two planets, or a central body, a planet and a moon.  
> **username_0**: @JamesK edited, thanks  
> **username_2**: @ScienceSnake it's a good point. I can hear the joke now [CARSON: the figure-eight orbit is so stable... AUDIENCE: (in unison) How stable is it?"](https://movies.stackexchange.com/q/110906/45856) I think that in orbital there are several different flavors of stability; for example see the first paragraph of Wikipedia's [Lyapunov stability](https://en.wikipedia.org/wiki/Lyapunov_stability)  
> **username_1**: I would somewhat hesitantly say "no"... Because "analogous" isn't really possible.  In the 2 body system, you can choose a rotating frame in which the planet is at rest.  In this rotating frame, you can consider the pseudo-potential, and find there are the five lagrange points.  But what is the analogy with a figure of 8 orbit? There isn't a way to get a rotating frame and find a pseudopotential... so there isn't an analogy to the Lagrange points.  I'm hesitant because someone might think of another way to form the analogy.  
> **username_2**: @ScienceSnake a quick question posted in Math SE just might bring an authoritative and comprehensive answer.  

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