How to Use the Lagrange Point Stability (L1-L5) 3D Explorer - Step by Step
Open the Lagrange Point Stability 3D Explorer, drag the mass-ratio slider or press a real-system preset, then press "Perturb all 5 points" and watch a real RK4 integration decide which of the five Lagrange points hold a nudged object and which let it drift away.
Pick a mass ratio
Drag the #t3dLpsMuSlider (log-scaled, from about 3e-7 to about 0.5) to any value, or press one of the four real-system preset buttons - #t3dLpsPreset_sunearth, #t3dLpsPreset_sunjupiter, #t3dLpsPreset_earthmoon, or #t3dLpsPreset_plutocharon. Your choice is saved to localStorage so it is still there next visit.
Watch the five points recompute live
Every time the mass ratio changes, the two body spheres and all five Lagrange-point markers move to their real positions - L1, L2, L3 by root-finding along the line joining the two bodies, L4 and L5 by the exact equilateral-triangle formula, 60 degrees ahead of and behind the smaller body.
Press "Perturb all 5 points"
Press #t3dLpsPerturbBtn to spawn a small test object at each of the five resolved points and integrate the real rotating-frame equations of motion every frame. Watch the trails: the three markers at L1, L2, and L3 always escape, while L4 and L5 stay bounded only when the current mass ratio is below Routh's critical ratio, about 0.0385.
Read the color and the facts panel
The L4/L5 markers turn green when the current ratio is below Routh's critical ratio and red when it is above, matching the trails you just watched. The facts panel updates live with the current mu, the closest named real system, and (for small mu) the Sun-Earth-scaled L1 distance in kilometers.
Clear and try another system
Press #t3dLpsResetBtn to clear the test particles, then pick a different preset or slider value to compare - for example Sun-Jupiter (stable, thousands of real Trojan asteroids) against Pluto-Charon (above the critical ratio, unstable).
Drag to orbit and use fullscreen
Drag to orbit the camera, scroll or pinch to zoom, and use the Fullscreen button to expand the whole wrapper for a clearer view of all five points and their trails at once.
Next: see when to use this explorer or how it compares to the Lagrange Points 3D Explorer.
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