Linked Questions

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Proving the Stability of the Stable Lagrange Points

I'm working on a problem in Kibble's Classical Mechanics (Chapter 11, Problem 12) and came upon a method for exploring the stability of an equilibrium point that I wasn't familiar with. The question ...
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How wide is the $L_4$ and $L_5$ Moon-Earth Lagrangian point?

How far would an object need to be displaced from the $L_4$ and $L_5$ Lagrangian points so that it can escape returning to those points?
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Physical importance of centrifugal force and Coriolis force in the context of the restricted 3-body problem

In the textbook Galactic Dynamics (Binney and Tremaine), the restricted three-body problem to find the trajectory of a test mass that orbits in the combined gravitational field of two masses $M$ and $...
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5 Lagrangian points: why isn't there a line of stability between $L_1$ and $L_4$ and $L_1$ and $L_5$ respectively? [duplicate]

Given the 5 Lagrangian points of two large orbiting bodies: (from wikipedia), why isn't there a line of stability between L1 and L4 and L1 and L5 respectively (as depicted in red in the modified ...
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35 views

Large mass body on Lagrange point L4/5

Lagrange points L4 and L5 are stable for a test particle. But what happens if instead the body at L4/5 (let's call it C) has a mass significant enough that its gravitational pull on the other two (let'...
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1answer
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How to understand $L_4$ and $L_5$ Lagrange points gravity balance? [duplicate]

It's relative easy to understand gravity balance of Lagrange points $L_1$, $L_2$ and $L_3$. But I am having a hard time to understand how a body would be "kind of" balanced out on Lagrange points $L_4$...
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2answers
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How are the Lagrange points determined?

According to Hyper Physics, there are 5 equilibrium, or Lagrange points of the Earth-Moon system and only 2 of them are said to represent stable equilibrium points. This made me think if there is an ...
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3answers
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Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable?

Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable? I am doing a physics presentation in front of my class and I am just confirming this is correct, and if it isn't, could somebody ...
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2answers
349 views

Why are L4 and L5 Lagrange points stable as points and not part of a circle? [duplicate]

I read this Phys.SE thread which is similar Why are L4 and L5 lagrangian points stable? but I did not want to necro that thread. It seems that most discussions of a three body problem are presented ...
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1answer
72 views

Coexistence at Lagrange points

I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these ...
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2answers
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Gravitational potential outside Lagrangian points or Lagrange points

The diagram in Why are L4 and L5 lagrangian points stable? shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly: If I ...
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2answers
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Definitions of Lagrange points: $L_4$ and $L_5$ [duplicate]

We have the the five Lagrange points (let consider Earth and Sun): $L_1$ - lie between Sun and Earth; $L_2$ - beyond the Earth; $L_3$ - beyond the Sun; And what's the difference between $L_4$ and $...