In any two-body gravitational system (Sun-Earth, Earth-Moon), there are exactly five special points where a small object can maintain a stable position relative to both bodies. These are the Lagrange points, discovered by Euler (L1-L3, 1767) and Lagrange (L4-L5, 1772).

The five points

L1 — Between the two bodies. The gravity of each partially cancels, and the orbital period matches. Sun-Earth L1 is ~1.5 million km sunward. SOHO and DSCOVR live here, watching the Sun.

L2 — Beyond the smaller body (away from the larger). The combined gravity plus orbital dynamics give the right period. Sun-Earth L2 is ~1.5 million km anti-sunward. The James Webb Space Telescope orbits here — shielded from the Sun by the Earth, with an unobstructed view of deep space.

L3 — On the opposite side of the larger body from the smaller one. Sun-Earth L3 is on the far side of the Sun. Scientifically uninteresting (no missions), but beloved of science fiction as the home of “Counter-Earth.”

L4 and L5 — 60° ahead of and behind the smaller body in its orbit, forming equilateral triangles with the two main bodies.

Stability

L1, L2, and L3 are unstable — like balancing a ball on a hilltop. A small push sends you drifting away. Spacecraft at L1 and L2 use small station-keeping burns to stay in halo orbits around the point (JWST uses about 1 m/s of delta-v per year).

L4 and L5 are stable — like a ball in a bowl. Objects naturally oscillate around these points. This is why Jupiter’s L4 and L5 points are populated by thousands of Trojan asteroids (the target of NASA’s Lucy mission). Earth, Mars, and Neptune have Trojans too.

Why L2 is the prime real estate of astronomy

Sun-Earth L2 is arguably the most valuable location in the solar system for space telescopes: - Thermally stable (Sun, Earth, and Moon are all in roughly the same direction → one sunshield protects from all three) - Minimal radio interference from Earth - Continuous communication with Earth (never behind the Sun) - Low station-keeping cost

After JWST: the planned Nancy Grace Roman Space Telescope and LISA gravitational wave detector will also orbit L2.