Lagrange Points — Stable vs Unstable Station-Keeping

Focus Point

L1/L2 sit on the Sun-Earth line and are unstable saddle points. L4/L5 sit 60° ahead/behind Earth in its orbit and are genuinely stable.

Station-Keeping (L1 & L2)

OFF — no correction burns fire. Watch the halo loop grow until the spacecraft is lost.

Simulation Speed

Time acceleration 3.0 wk/s

Selected Spacecraft

Mission time

0.0 wk

Loop radius

–

Status

Active

Est. time until lost

–

Cumulative station-keeping fuel

0.00 m/s

All 4 Scenarios — Live Comparison

Pt	Status	Weeks	Fuel m/s

How it works

A spacecraft parked exactly at L1 or L2 sits on a gravitational saddle: nudge it and the perturbation grows exponentially, like a ball balanced on a hilltop. Real missions there (JWST, SOHO) fly a small halo loop and fire correction thrusters roughly every 2-3 weeks to cancel that growth before it escapes.

L4 and L5 sit in a gravity well shaped by the Coriolis force in the rotating frame — like a ball in a bowl. A spacecraft nudged near L4/L5 naturally curves back and librates in a bounded loop forever, with no burns required.

This simulation integrates the real restricted three-body equations of motion (Runge-Kutta 4) for the Sun-Earth system (μ = 3.003×10⁻⁶) in the co-rotating frame — the instability and the weeks-scale timeline are not scripted, they fall directly out of the physics. L-point offsets and loop sizes are exaggerated for visibility; the underlying dynamics and timescale are real.

🛰️ SPACECRAFT LOST — drifted out of range

L1

Status Active

Fuel used 0.00 m/s

Sun

Earth

L1 / L2 (unstable)

L4 / L5 (stable)

Spacecraft

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Cumulative station-keeping fuel used, all 4 scenarios (m/s)

L1 L2 L4 L5