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Lagrange points
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Five positions where a small body co-moves with two large bodies.
Five points where a small body can stay fixed relative to two large masses. L1, L2, L3 are unstable on a line; L4 and L5 are stable if M₁/M₂ > 24.96. The James Webb telescope orbits Sun–Earth L2.
Trojan asteroids at Jupiter's L4/L5.
Unstable points need station-keeping.
In more detail
Lagrange points are five positions where a small object can stay in a fixed relation to two large bodies. They arise from the balance of gravity and orbital motion.
Real-world uses
- The James Webb Space Telescope orbits the Sun-Earth L2 point.
- Solar observatories are placed at L1 for continuous sunlight views.
- The James Webb Space Telescope sits near a Lagrange point where its orbit stays fixed relative to Earth and the Sun.
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Frequently asked questions
Why are they useful?
Objects there need little fuel to stay in position relative to the two bodies.
How many are there?
Five in the restricted three-body problem: L1 to L5.
Do Lagrange points give a stable orbit?
Some do. L4 and L5 are stable for a sufficiently large mass ratio, while L1, L2 and L3 are unstable and need corrections.
Related topics in Gravitation & Orbits
Tides · Tidal locking · Roche limit · Two-body problem · Effective potential · Binary stars