<p>I have been reading about Lagrange points and Lagrange regions and how we can apply Laplace's equation for these regions however which are the boundary conditions of the Laplace equation at these points/regions?</p>

CC BY-SA 4.0
2023-05-18T22:10:07.490Z
*Welcome to Astronomy SE!* Could you add to your question ***where*** you've been reading about "how we can apply Laplace's equation for these regions"? If it's in a book, title, author, edition, chapter/page, if published scientific papers then just add links. Also, by Laplace's equation do you mean $\nabla^2 \phi=0$, or perhaps some other equation related to dynamical system behavior in a rotating frame? Laplace was pretty active and probably has a lot of equations out there! The more information you add to your question, the better. *Thanks!*
uhoh
CC BY-SA 4.0
2023-05-18T22:14:38.117Z
See for example [Laplace–Runge–Lenz vector](https://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector)
uhoh
CC BY-SA 4.0
2023-05-19T11:00:43.767Z
The vagueness of the question makes it a bit hard to determine what you are asking about. Have you read about the Jacobi integral, which is a constant of motion in the three body problem?
David Hammen
CC BY-SA 4.0
2023-05-21T04:09:17.223Z
I think that unless you respond to comments and clarify your question significantly, there's a good chance that close votes for "needs details or clarity" will begin to appear.
uhoh
CC BY-SA 4.0
2023-05-21T04:59:22.800Z
@DavidHammen Quanta Magazine's May 16, 2023 [New Proof Finds the ‘Ultimate Instability’ in a Solar System Model](https://www.quantamagazine.org/new-math-shows-when-solar-systems-become-unstable-20230516/) links to three new papers, the third being [A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes](https://arxiv.org/abs/2303.05979) which makes for some interesting reading (not that the others don't)
uhoh
<gravity><newtonian-gravity><lagrange-point>
Lagrange points and Laplace equation boundary condition
Volpina
# Lagrange points and Laplace equation boundary condition

(Asked by: username_0 on 2023-05-18)

I have been reading about Lagrange points and Lagrange regions and how we can apply Laplace's equation for these regions however which are the boundary conditions of the Laplace equation at these points/regions?

**Tags:** gravity, newtonian-gravity, lagrange-point

> **Comments:**
> **username_1**: *Welcome to Astronomy SE!* Could you add to your question ***where*** you've been reading about "how we can apply Laplace's equation for these regions"? If it's in a book, title, author, edition, chapter/page, if published scientific papers then just add links. Also, by Laplace's equation do you mean $\nabla^2 \phi=0$, or perhaps some other equation related to dynamical system behavior in a rotating frame? Laplace was pretty active and probably has a lot of equations out there! The more information you add to your question, the better. *Thanks!*  
> **username_1**: See for example [Laplace–Runge–Lenz vector](https://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector)  
> **username_2**: The vagueness of the question makes it a bit hard to determine what you are asking about. Have you read about the Jacobi integral, which is a constant of motion in the three body problem?  
> **username_1**: I think that unless you respond to comments and clarify your question significantly, there's a good chance that close votes for "needs details or clarity" will begin to appear.  
> **username_1**: @DavidHammen Quanta Magazine's May 16, 2023 [New Proof Finds the ‘Ultimate Instability’ in a Solar System Model](https://www.quantamagazine.org/new-math-shows-when-solar-systems-become-unstable-20230516/) links to three new papers, the third being [A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes](https://arxiv.org/abs/2303.05979) which makes for some interesting reading (not that the others don't)  

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## 0 answers

