Lagrange Points — Top-Down Orbital View (2D)

Mass Ratio

μ = M₂/(M₁+M₂) 0.03

Time

Speed 1.0×

Launch Test Particle

Live Readouts

L4/L5 stability (μ < 0.0385)

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Particle at

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State

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How this 2D companion works

The 3D version renders the effective-potential landscape as terrain seen from an orbiting camera. This 2D companion drops that landscape and instead shows the same circular restricted three-body problem from directly above, in the synodic frame that co-rotates with the two masses — so both bodies and all five Lagrange points sit still while a launched test particle's motion reveals the local dynamics directly, integrated with the same nonlinear equations of motion (RK4).

L1-L3 sit on the line joining the masses and are saddle points of the effective potential: always unstable, regardless of mass ratio. L4 and L5 form equilateral triangles with the two masses; they are stable only when μ is below the Routh criterion, μ < 0.0385209 — above that even the "stable" points shed a nearby particle.

primary mass secondary mass L1 / L2 / L3 (unstable) L4 / L5 test particle