The comet calculator: Nicole-Reine Lepaute

On 5 January 1723, Nicole-Reine Étable de la Brière was born in the Luxembourg Palace in Paris, the ancient seat of the kings of France, but she wasn’t a princess. She was the daughter of a valet, and her parents lived on site.  

The child quickly showed her intelligence, passing her nights reading books. When she was still young, one of her sisters said to her, “I am the whitest,” to which she immediately replied, “And I, the wittiest!”

At the age of 25, Nicole married the royal clockmaker, Jean-Andre Lepaute. He was famous across Europe for technical achievements in his field. Many observatories depended on his pendulum models because a precise time determination is essential for astronomical observations.

Nicole soon became interested in her husband’s profession, and began to collaborate with him. Her first research dealt with the relationship between the length of a pendulum and the duration of its swing, a subject of keen interest at the time. The result, titled “Table des longueurs des pendules” in Traité d’horlogerie, was published in 1755.

Her talent was noticed by young astronomer Joseph Lalande. He reported that “Madame Lepaute … was too smart not to have the curiosity; she noted, she calculated, she described the work of her husband …”.

Some sources indicate that during this period Lalande was responsible for the observatory at the Luxembourg Palace, so he probably had a privileged and well-informed view of the situation.

From clocks, it is a short step to astronomy, especially if you have someone such as Lalande nearby, and you are a savant calculatrice, or ‘learned calculator’. In an era where computers did not exist and their mechanical ancestors were rare and quite limited, Nicole was recruited to the cause.

Calculations were essential to astronomical research. No scientist was spared this long and tedious activity, which required deep knowledge of physics and maths, not just the application of algorithms. Nicole was easily the equal of her colleagues. She started her first important work in astronomy in 1757, in collaboration with Lalande and the mathematician Alexis Clairaut.

The project was ambitious and complex. Lalande wanted to accurately determine the date of the return of Halley’s comet. To do this, it was necessary to calculate the effects of the gravitational pull of Jupiter and Saturn on the path of the comet, which required deriving approximate solutions for the mathematical poser known as the ‘three-body problem’ – specifying the movement of a trio of objects in line with their masses, positions and velocities.

Using Newton’s laws, this involved a huge amount of work computing the distances and forces of attraction exerted on the comet by each planet for periods of 100 and 50 years.

Nicole and the two scientists were consumed by this work for more than half a year. As Lalande recalled: “For six months we made calculations from dawn to dusk, sometimes even during the meals … The help given by Mme. Lepaute was such that without her I would not have been able to complete such a colossal enterprise.”

Today, it seems almost incredible that three people without computers could carry out this task. Eventually, they announced to the Academy of Science that the perturbed comet would reach perihelion, the point of closest approach to the sun, in mid-April 1759. This corrected the forecast made by Halley himself, who had placed the event in 1758.

Nicole’s mathematical and astronomical activity continued. In 1761 she published the calculations of all observations made during the transit of Venus across the sun, and the following year worked on the orbit of a new comet and calculated the duration and size of an annular solar eclipse set to be visible in Europe in 1764.

In 1774 she took on a new role at the Academy of Science, where she computed the positions of the planets, the sun and the moon. The last years of her life were spent nursing her sick husband. She died a few months before him on 6 December 1788.