Home▸Small Solar System Bodies▸Trojan Asteroids & Lagrange Points

🛰️ Trojan Asteroids & Lagrange Points

Interactive 3D simulation of Trojan asteroids librating around the L4 and L5 Lagrange points of a Sun-planet system, with real restricted three-body physics.

Small Solar System Bodies2DModerate60 FPS

Trojan asteroids share a planet's orbit around the Sun, trapped in a 1:1 resonance 60° ahead (L4) or 60° behind (L5). This simulation numerically integrates the real restricted three-body problem in the co-rotating frame to show why these two points trap thousands of asteroids while the other three Lagrange points do not.

🔬 What It Demonstrates

In the frame rotating with the planet, gravity plus the centrifugal and Coriolis pseudo-forces balance exactly at five points. L4 and L5 are stable for any planet/star mass ratio below about 0.0385 (Routh's criterion), so asteroids nudged away from them curve back instead of drifting off — producing bounded tadpole or horseshoe orbits instead of escape.

🎮 How to Use

Drag to orbit the camera and scroll to zoom. Adjust the mass-ratio slider (or use the planet presets) to see the Trojan cloud shrink or destabilize, click any asteroid to select it, then use the radial/tangential nudge sliders to test whether it stays trapped or escapes.

💡 Did You Know?

Jupiter hosts over 13,000 known Trojans split into a "Greek camp" at L4 and a "Trojan camp" at L5, but Earth, Mars and Neptune have confirmed Trojans too — Earth's first, 2010 TK7, wasn't found until 2010.

⚙ Under the hood

Interactive 3D simulation of Trojan asteroids librating around the L4 and L5 Lagrange points of a Sun-planet system, driven by real restricted three-body physics.

trojan-asteroidslagrange-pointsthree-body-problemorbital-resonancecelestial-mechanics

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