Lagrange

Around 1750, Leonhard Euler figured out something really cool.

Who? If you’ve taken calculus, you might remember that his name is pronounced like “Oiler.” That’s how I remembered who he was a few years back.

Anyway, our boy Euler was working on solving a puzzle gravity presented. It was called the “three-body problem”, and it sought to predict the motions of three objects interacting via gravity.

Euler, known for his intellect and love of mathematical challenges, was naturally attracted to this difficult problem. Like Newton, he was deeply interested in discovering how the universe worked at a fundamental level. Besides, being able to predict where celestial bodies would be in the sky could help tremendously with navigators at sea.

Euler realized that there was a place out there in space where an object felt a perfect balance of gravitational forces between the two other (bigger) objects. This point was a bit like the eye of a hurricane, in the sense that powerful forces swirled all around this point.

Euler found three points where this little tug-of-war ends in a stalemate, where an object can feel no force. Can you feel this in your mind’s eye?

Joseph-Louis Lagrange built on Euler’s work two decades later, adding two more points for a total of five. Lagrange found something incredibly curious: the two new points formed equilateral triangles with the two large masses. This shocking discovery opened up as many new questions as it answered, but it also implied a hidden order to the universe.

Equally importantly, these two new Lagrange points weren’t in between the two large bodies at all. Instead, there were two more points outside of this plane where the force was balanced, so to speak.

Lagrange proved this with math, but seeing is believing. At the turn of the 20th century, astronomers found clusters of asteroids locked in these points of stability around Jupiter and the Sun. It was a stunning confirmation of his work.

Today, L4 and L5 are not just filled with asteroids; they are potential locations for future space habitats, offering unique advantages for both stability and observation.

Today, we use Lagrange points for scientific observation and communication. At L1 (between the Sun and the Earth), satellites study the Sun and how it affects the Earth, and to give a small advance warning of impending solar storms. The James Webb Space Telescope (JWST) is positioned at L2—on the other side of the Earth from the Sun—to help us uncover clues about the early universe, and to take a peek at exoplanets.

Tomorrow, we might use the inherent stability of Lagrange points to build space colonies or outposts. There's also the future possibility of mining the very stable asteroids in the region.

All of this makes Lagrange points fertile material for science fiction. Thanks to Lagrange, who was able to stand on the shoulders of Euler, and thanks to an unbroken path of scientific curiosity and innovation since then, we’re much better positioned to explore our universe … and maybe to travel further out into it one day.