🛰️ Lagrange Points — Stability & Halo Orbits

L1 lies between the two bodies (Sun-Earth L1 is ~1.5 million km from Earth), L2 lies behind the smaller body on the far side from the larger (Sun-Earth L2 is ~1.5 million km beyond Earth), L3 lies behind the larger body on the opposite side. L4 and L5 lie 60° ahead of and behind the smaller body in its orbit, forming equilateral triangles with both bodies.

The Sun-Earth L2 point keeps the Sun, Earth, and Moon all in the same direction behind the spacecraft, allowing a single sunshield to protect instruments from solar and terrestrial radiation and thermal emission. Spacecraft at L2 can maintain a thermally stable, very cold environment and observe the sky continuously — ideal for infrared and cosmic microwave background observatories.

A spacecraft at an unstable Lagrange point (L1, L2, L3) displaced slightly will experience a net force pushing it further away, requiring active station-keeping. At L4 and L5 (when the mass ratio exceeds ~25:1), the Coriolis force in the rotating frame acts as a restoring force, causing displaced objects to orbit around the Lagrange point in a stable configuration called a tadpole orbit.

Trojan asteroids are small bodies that orbit the Sun at a planet's L4 or L5 Lagrange points, sharing the planet's orbit while remaining stably 60° ahead (L4, the Greeks) or behind (L5, the Trojans). Jupiter has over 10,000 known Trojans. Mars, Neptune, Uranus, and Earth (one confirmed) also have Trojan asteroids. The NASA Lucy mission is currently visiting Jupiter's Trojans.

Lagrange points are connected by invariant manifolds — gravitational superhighways — that allow spacecraft to travel between them using very little propellant. The Interplanetary Transport Network (ITN) exploits these manifolds to plan trajectories through the solar system by surfing between Lagrange points of different planet-Sun systems. The Genesis and ISEE-3 missions used L1 halo orbits; the JWST uses a halo orbit around Sun-Earth L2.