Working model to demonstrate Lagrange points L4 & L5 -- possible?

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    Lagrange points
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Discussion Overview

The discussion revolves around the feasibility of creating a working model to demonstrate the Lagrange points L4 and L5 using a rotating surface. Participants explore both theoretical and practical aspects of this concept, including potential challenges and implications.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes fabricating a surface that rotates around a vertical axis to allow a bead to roll in an orbit around L4 or L5, questioning its feasibility in principle and the practical challenges involved.
  • Another participant references existing models based on Newtonian mechanics, suggesting that there are already effective demonstrations of similar concepts.
  • A participant expresses difficulty accessing a referenced site, indicating a potential barrier to further exploration of the topic.
  • One participant believes that while the concept could work in principle, practical challenges such as high friction, vibration from the turntable, and the precision required in manufacturing the gravity well shape could hinder success.
  • Another participant shares a video of a similar concept that appears to work well but notes that the complexity of the L4-L5 problem introduces additional challenges. They also mention the potential impact of gyroscopic effects on the behavior of the rolling bead, suggesting it could either complicate or enhance the model's functionality.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the feasibility of the model; while some believe it could work in principle, others highlight significant practical challenges that may prevent successful implementation.

Contextual Notes

Participants mention various practical limitations, such as the need for precise manufacturing of the surface and control over the turntable speed, which remain unresolved in the discussion.

Swamp Thing
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If we fabricate a surface like this...

1694162616033.png


(source:www.youtube.com/watch?v=7PHvDj4TDfM)

... and rotate it around the appropriate vertical axis at the appropriate speed, would it be possible to get a bead to roll in an "orbit" around L4 or L5.

(a) Possible at all in principle?

(b) Practical challenges?
 
Last edited:
Astronomy news on Phys.org
At the moment I am not able to access that site -- "network error". (All other usual sites are accessible)
I will try later.
 
I see no reason it couldn’t work in principle, but I think it may be too difficult in practical terms.

Even for large museum quality rigid gravity demonstrations friction is pretty high and the orbits decay quickly. You’d have to make it as smooth as possible.

Spinning it on a turntable will introduce vibration that will also decay the orbits. You’d need good bearings.

Another issue would be getting the shape of the gravity wells just right. I don’t know how you would precisely manufacture the double well surface.

You’d have to experiment with the turntable speed, but you should be able to calculate a speed that gives the best Lagrange points. The turntable speed would need to have precise controls
 
I just found this video that is a bit similar in concept, and it seems to work pretty robustly...



That said, the L4 - L5 problem is much more complex since it involves more things that you have to get just right.

And I found this video which leads to believe that gyroscopic effects in the rolling ball would probably change the behavior in a drastic way and break everything.



Or maybe if one is lucky, the gyroscopic effect may actually make it work better than it would otherwise.
 

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