LibratrixLagrange Points / Three-Body EquilibriumSticker

Libratrix slings her hammock where the pulls balance, and she knows how thin that balance is.

In 1772 Joseph-Louis Lagrange found that, for two large bodies circling each other, there are five places where a small third body can keep pace with them: three on the line through the pair and two at the corners of equilateral triangles. In the frame turning with the pair, gravity and the outward pull of the rotation cancel there.

Her favourite is L2 of the Sun and Earth, about 1.5 million km beyond Earth, directly away from the Sun, the first two lines on this page. Telescopes love it: the Sun, Earth and Moon all stay on one side, so one shield can block them all. The James Webb Space Telescope works there. Strictly, it does not sit at L2; it follows a large halo orbit around it.

The catch is that L2 is a saddle, not a bowl. Drift a little and the drift grows. So Webb fires small thrusters to stay on track, with station-keeping burns scheduled on average every 42 days; 21 days is only the minimum spacing. Libratrix gives a small nudge every six weeks or so.

Her cousins at L4 and L5 have it easier. Those points sit on hilltops of the effective potential, yet the Coriolis effect holds a body there in a stable loop, provided the larger mass outweighs the smaller by more than about 24.96 times, the last line. Edward Routh published that condition in 1874–75; Gascheau had found it in 1843. Sun and Jupiter qualify, and Jupiter’s Trojan asteroids gather there. In 2011 the first Earth Trojan was identified.

Balanced. Barely. Nudge me often.