Home▸Space & Astronomy▸2D Lagrange Points — Effective Potential & Test-Particle Orbits

2D Lagrange Points — Effective Potential & Test-Particle Orbits

2D top-down restricted three-body simulator in the rotating reference frame: the five Lagrange points L1-L5 are solved numerically from the real mass ratio, the effective (Jacobi) potential is rendered as a live contour heatmap, and a launched test particle is integrated with real gravity, centrifugal and Coriolis forces — showing genuine stability at L4/L5 and instability at L1-L3.

Space & Astronomy2DModerate60 FPS📱 Mobile-adapted🌍 Earth ⇄ 3D version

Details

CategorySpace & Astronomy

RenderingCanvas 2D

DifficultyModerate

Target FPS60

ControlsSystem selector (Sun-Earth/Sun-Jupiter/Earth-Moon/Equal), mass-ratio slider, L-point launch selector, perturbation slider, potential/labels/trail toggles, speed slider, Start/Pause, Clear, Reset; click or tap the canvas to launch a test particle at that position

Canvas 2DRestricted Three-Body ProblemLagrange PointsEffective PotentialRotating FrameCoriolis ForceRK4Celestial Mechanics

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This 2D companion to the 3D Lagrange Points laboratory solves the real restricted three-body problem in the co-rotating frame: the five Lagrange points are found numerically from the actual mass ratio of the chosen two-body system, the effective (Jacobi) potential is rendered as a genuine contour heatmap, and a launched test particle is integrated with real gravitational, centrifugal and Coriolis forces — so stability at L4/L5 and instability at L1-L3 emerge from the physics, not from a scripted animation.

⚙ Under the hood

2D top-down restricted three-body simulator in the rotating reference frame: the five Lagrange points L1-L5 are solved numerically from the real mass ratio of the chosen two-body system, the effective (Jacobi) potential is rendered as a live contour heatmap, and a launched test particle is integrated with real gravitational, centrifugal and Coriolis forces — showing genuine stability at L4/L5 and instability at L1-L3.

Canvas 2DRestricted Three-Body ProblemLagrange PointsEffective PotentialRotating FrameCoriolis ForceRK4Celestial Mechanics

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install