The Five Spots Where Gravity Sits Still

In 1772, Joseph-Louis Lagrange wrote a paper on the three-body problem and found a quiet result. For any pair of large bodies — Sun and Earth, Earth and Moon — there are exactly five points in space where a small third body can sit and orbit with them as if it were locked to a turntable. Centrifugal force and the combined gravitational pull of the two big bodies cancel out. He called them L1 through L5.

Three of the five (L1, L2, L3) sit on the line through the two big bodies. They are technically unstable — like a marble on top of a hill — but the slope is gentle enough that a spacecraft can hold position with small periodic thrusts costing only a few meters per second of fuel each year. The James Webb Space Telescope sits at Sun-Earth L2, about 1.5 million km behind Earth, where one sunshade can block the Sun, Earth, and Moon at the same time. SOHO, which watches the Sun, lives at L1.

The other two (L4 and L5) sit at the points of equilateral triangles with the two big bodies. These are genuinely stable. Anything that wanders into the basin of L4 or L5 tends to stay. Sun-Jupiter L4 and L5 are full of trapped asteroids — the Trojans, more than 13,000 known — that have been parked there for billions of years. Earth has its own small Trojan, 2010 TK7, found in 2010, leading us in our orbit by sixty degrees.

Lagrange did the math without ever expecting humans to use it. Two and a half centuries later we are using it to park telescopes.