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

In summary, the article discusses the feasibility of creating a working model to demonstrate the Lagrange points L4 and L5, which are stable points in a two-body system where a small object can maintain a stable position relative to the two larger bodies. It explores the principles behind these points, potential methods for demonstrating their characteristics, and the implications for understanding celestial mechanics and space exploration.
  • #1
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:
Physics news on Phys.org
  • #3
At the moment I am not able to access that site -- "network error". (All other usual sites are accessible)
I will try later.
 
  • #4
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
 
  • #5
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.
 

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

What are Lagrange points L4 and L5?

Lagrange points L4 and L5 are positions in space where the gravitational forces of two large bodies, such as the Earth and the Moon, and the centrifugal force of a smaller object, such as a satellite, balance each other. These points form an equilateral triangle with the two large bodies and are stable, meaning objects placed there tend to stay put.

Is it possible to create a working model to demonstrate Lagrange points L4 and L5?

Yes, it is possible to create a working model to demonstrate Lagrange points L4 and L5. Such a model can be physical or computational. A physical model would typically involve a rotating system to simulate the gravitational forces and centrifugal effects, while a computational model would use numerical simulations to visualize the dynamics of objects at these points.

What materials and tools are needed to build a physical model of Lagrange points L4 and L5?

To build a physical model of Lagrange points L4 and L5, you would need materials such as a rotating platform, weights to represent the large bodies, a small object to represent the satellite, and possibly springs or elastic bands to simulate gravitational forces. Tools might include a motor for rotation, a stand or base for stability, and measurement devices to ensure accuracy.

How can a computational model be used to demonstrate Lagrange points L4 and L5?

A computational model can be created using software that allows for the simulation of gravitational forces and motion, such as MATLAB, Python with libraries like NumPy and SciPy, or specialized astronomical simulation software. By inputting the masses of the two large bodies and the initial conditions of the smaller object, the software can calculate and visualize the stable points L4 and L5.

What are the educational benefits of demonstrating Lagrange points L4 and L5 with a model?

Demonstrating Lagrange points L4 and L5 with a model provides several educational benefits. It helps students and observers visualize complex gravitational interactions, enhances understanding of orbital mechanics, and illustrates the concept of equilibrium points in a dynamic system. Additionally, it can inspire interest in astrophysics and engineering by providing a tangible example of theoretical concepts.

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