The Three-Body Problem and Nicole-Reine Lepaute, an Astronomer Who Tackled It

This post is about a mathematical puzzle and a French astronomer-mathematician who tried to solve it: the Three-Body Problem, and Nicole-Reine Lepaute, an aristocratic woman working in Enlightenment-Era France. (See images one and two.)

Practically as soon as Isaac Newton developed his ideas about gravity, he also realized that, while he could predict the orbits of two celestial bodies interacting with each other, he couldn’t figure out how to calculate the effects of gravity upon three bodies over time. And in fact, mathematicians still haven’t solved this — there isn’t a formula to exactly know exactly what the orbits of the three bodies will be.

However, the French noblewoman Nicole-Reine Lepaute (d 1788) did make progress in this area with a particular application. Lepaute, who had shown enormous precociousness in learning as a child and had married a royal clockmaker, was in just the right social and economic position to break into the scientific and mathematical circles of her day.

Having made the acquaintance of astronomer Jérôme LaLande through her husband, Lepaute impressed LaLande with her mathematical abilities. She co-authored a work dealing with the mathematics of timekeeping before LaLande and Lepaute joined with another scientist named Alexis Clairaut to figure out the next passage of Halley’s Comet.

This was in fact a Three Body Problem of sorts, because the gravitational pull of Jupiter and Saturn on the comet needed to be considered along with the sun. While the dynamic trio worked for half a year on their calculations and did come within a month in predicting Halley’s arrival, this wasn’t the same thing as landing upon a formula that would make sense of it all: rather, they were working in a narrow range of time and place.

The Three-Body Problem embodies a chaotic system, a seemingly insurmountable task with which mathematicians still labor. The work of Nicole-Reine Lepaute fits into that history, in a way that parallels how intellectually curious women of her time had to struggle against barriers to education.