Planets · 6 of 6

The Lagrange Points

Where can a spacecraft keep pace with the Earth around the Sun?

The five places where a spacecraft can keep pace with the Earth around the Sun, seen from outside the orbit, and where each one sits in your sky.

You’ll be able to point to where the Lagrange points sit in your sky.

9 steps · about 7 min

Before this: Spotting the Planets (6 min), Racing and Crawling (4 min)

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The ring is Earth's orbit, and the five marks are the Lagrange points, where a small body goes round once a year in step with us. The puzzle: nearer the Sun means faster, as Racing and Crawling showed, yet L1 is inside our orbit.

Run half a year. All five keep their places: L3 always behind the Sun, science fiction's hidden Counter-Earth; L4 60° ahead, L5 60° behind. They are fixed to the Earth's orbit, not to the stars.

The answer. At L1 Earth's pull cancels a little of the Sun's, so a craft there can go round as slowly as we do. At L2 Earth adds to the Sun's pull, so a craft farther out keeps up. Both are drawn close; really they are four Moon-distances out.

L1 to L3 are saddles: a craft there rolls off, like a ball on a saddle, unless it steers. L4 and L5, the far corners of the two triangles, are stable: what drifts in stays. Earth's L4 holds two small asteroids; Jupiter's L4 and L5 hold thousands.

Back on the ground, at midnight in December: L2 is the point straight away from the Sun, high in the sky. The Webb telescope works out there, too faint to see, on the ecliptic in Gemini's feet. In June the same point sits behind the Sun.

Webb is not parked on the point. L2 is a saddle, and a craft left there drifts off within weeks, so Webb circles it on a loop hundreds of thousands of km wide, about the size of the ring, firing its thrusters every few weeks to stay on it.

L4 is 60° west of the Sun along the ecliptic, so it is up before dawn, here beside Spica. The Sun, still below the horizon, has L1 in front of it and L3 behind; SOHO has watched the Sun from L1 since 1996.

And L5, 60° east of the Sun, follows it down at dusk. So, in your sky: L1 and L3 on the Sun, L4 at dawn, L5 at dusk, and L2, Webb's home, at midnight. All five ride the ecliptic, carried round with the Sun once a year.

Five places to park, carried round with the Earth yearly.

L1 and L2, four Moon-distances either side
Stable L4 and L5, 60° ahead and behind
L2 is up at your midnight

The Lagrange Points

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