Five special points where a small object can ride along with two orbiting bodies. JWST parks at Sun-Earth L2; Jupiter's Trojans swarm L4 and L5.
Lagrange PointsLive
restricted three-body problem
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In a two-body system, five points let a small object stay fixed in the rotating frame. L1-L3 sit on the line through the two masses (unstable); L4 and L5 lead and trail the secondary by 60° and are stable for μ below 0.0385 — where Jupiter's Trojan asteroids live. JWST orbits the Sun-Earth L2.
Reading this result: At μ=0.150 the masses are too comparable: even L4 and L5 turn unstable, so every Lagrange point here needs active station-keeping to hold a spacecraft in place.
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How it works
In the restricted three-body problem, the combined gravity and rotation create an effective potential with five equilibrium points. L1-L3 lie on the line joining the two masses and are unstable; the triangular points L4 and L5 are stable when the mass ratio is below 0.0385. Toggle the potential to see the contours that define them.
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