Balance points: where gravity holds things still

Things in space do not usually stay put. But there are a few special places where they nearly can.

Think of the Sun and the Earth. In five spots near them, the pull of the Sun and the pull of the Earth work together in just the right way. A spacecraft put in one of those spots goes round the Sun in exactly one year, in step with the Earth, and so keeps its place beside us.

These spots are called Lagrange points, after the mathematician who worked them out.

They are very useful. The James Webb Space Telescope sits at one of them, 1.5 million km from the Earth, about four times as far as the Moon.

Nature uses them too. Thousands of asteroids are gathered at two of Jupiter’s balance points, travelling round the Sun ahead of the planet and behind it.

The puzzle they solve. Kepler’s third law says that the closer something is to the Sun, the faster it goes round. A spacecraft a little nearer the Sun than the Earth should pull ahead of us, and one a little further out should fall behind. So how can anything keep station?

The answer is that the Earth’s own pull joins in. At the right spot, it adds to or takes away from the Sun’s pull by just enough to make the spacecraft’s year the same length as ours. Joseph-Louis Lagrange found the complete set of five such points in 1772. Every pair of orbiting bodies has them: Sun and Earth, Earth and Moon, Sun and Jupiter.

The five points, for the Sun and Earth.

Point	Where	Steady?	What is there
L1	1.5 million km from the Earth, towards the Sun	No	Sun-watching spacecraft such as SOHO, with an unbroken view
L2	1.5 million km from the Earth, away from the Sun	No	Telescopes: Webb, and Euclid
L3	On the far side of the Sun, opposite the Earth	No	Nothing
L4	On the Earth’s orbit, a sixth of a lap ahead	Yes	Two small asteroids found so far
L5	On the Earth’s orbit, a sixth of a lap behind	Yes	None found yet

Why L2 suits telescopes. From L2 the Sun, Earth and Moon are all in the same part of the sky. A telescope there can hide from the heat and glare of all three behind one sunshade and look out at the rest of the universe in the cold and dark. Webb’s mirror has to stay below about −220 °C to see faint infrared light, and that would be impossible near the Earth.

Not steady, but cheap. The first three points are like the top of a hill: a ball placed exactly on top stays, but the slightest nudge sends it rolling away. Spacecraft do not sit on them. They trace wide, slow loops around them, and fire small thrusters every few weeks to stay close. Webb uses only a little fuel a year this way and should last well over twenty years.

Steady: the Trojans. L4 and L5 are different. An object nudged away from either of them is steered back, and ends up circling the point slowly. Things that wander in can stay for billions of years. Jupiter has gathered many thousands of asteroids at its two, called Trojans. NASA’s Lucy spacecraft is on its way to see them at close range and reaches the first group in 2027. Mars and Neptune have Trojans of their own, and so does the Earth, though only two small ones are known.

Some moons share an orbit in the same way. Saturn’s moon Tethys has two tiny companions, Telesto and Calypso, one a sixth of a lap ahead and one behind.

The limit of a planet’s hold. L1 and L2 also mark roughly how far a planet’s gravity wins over the Sun’s. Inside that distance something can stay in orbit round the planet. Outside, the Sun takes it away. For the Earth this reach is about 1.5 million km, and the Moon, at 384,400 km, is safely inside. Every planet’s moons lie within its own such region, which is called its Hill sphere.