What is the width of the Lagrange points?

In summary, the Lagrange points, particularly L4 and L5, can be used as stable placeholders for objects when building in space. The width of the points, which are circular in shape, can vary depending on the body's starting motion, but for L1, L2, and L3, quasi-periodic Lissajous orbits with radii of up to 200,000 km are used. More information can be found on their stability in the provided Wikipedia link.
  • #1
CowedbyWisdom
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Hello everyone! I just finishexd reading Death By Black Hole and I was interested in the Lagrange points. Neil talks about how if you placed objects inside of them you could use the points as place holders for objects while building in space. I couldn't seem to find anything about the width of the points. I understand they are circular in shape but does anyone have any idea about how wide these rings are? Thanks in advance.

-Jack
 
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  • #2
Welcome to PF!

Hello Jack! Welcome to PF! :smile:

L4 and L5 are stable, so a body placed near either should oscillate around it

i haven't done the maths, but i suspect that "near" means anywhere, so long as the body starts stationary (or nearly so) relative to the Lagrange point

(ie, obviously if it has a substantial sideways motion, it'll orbit one of the parent bodies instead, in exactly the same way as it would if it was moving too fast at the the Lagrange point)

L1 L2 and L3 are unstable, but they do have quasi-periodic Lissajous orbits which are used (with radii of up to 200,000 km), see http://en.wikipedia.org/wiki/Lagrange_points#Stability for details :wink:
 

1. What is the width of Lagrange points?

The width of Lagrange points refers to the distance between the two Lagrange points associated with a binary system, such as a planet and its moon or two stars. It is essentially the separation between the two equilibrium points where the gravitational forces of the two bodies are balanced.

2. How is the width of Lagrange points calculated?

The width of Lagrange points is calculated using a mathematical formula known as the Lagrange point equation. This equation takes into account the masses and distances of the two bodies in the binary system, as well as the gravitational constant. The result is the distance between the two Lagrange points, or the width.

3. Why is the width of Lagrange points important?

The width of Lagrange points is important because it determines the stability of a binary system. The wider the distance between the Lagrange points, the more stable the system is. This is because a wider separation means there is more room for smaller objects, such as planets or asteroids, to orbit around the Lagrange points without being affected by the gravitational forces of the larger bodies.

4. Can the width of Lagrange points change?

Yes, the width of Lagrange points can change over time. This is because the masses and distances of the two bodies in a binary system can change due to factors such as the movement of the bodies or the addition of new bodies to the system. As a result, the gravitational forces and equilibrium points can also shift, affecting the width of the Lagrange points.

5. How is the width of Lagrange points used in space exploration?

The width of Lagrange points is used in space exploration to identify potential locations for spacecrafts and satellites to orbit. These points provide a stable position for objects to remain in a relatively fixed location in relation to the two bodies in the binary system. This makes it easier for spacecrafts to study and gather data on the bodies without being affected by their gravitational forces.

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