Since comets orbit in such highly elliptical paths, their orbits can be much harder to calculate than those of planets and most asteroids. In the late 1700s, the French mathematician and scientist Pierre-Simon de Laplace (1749–1827) had laid down a set of equations to make these calculations, but they were cumbersome and difficult. In 1797 the German astronomer and physician Heinrich Wilhelm Matthaeus Olbers (1758–1840) published a new way to calculate cometary orbits that was more accurate and easier to use than Laplace’s technique. The method earned Olbers a reputation as one of the leading astronomers of his time.

Olbers, a highly respected physician who was praised for his vaccination campaigns and for heroically treating people during several epidemics of cholera, set up an observatory in the second floor of his house in 1781. He discovered his first comet in 1780, at the age of twenty-two. Over the course of his lifetime, he discovered five comets and calculated the orbits of eighteen others. He hypothesized, correctly, that the tail of a comet was created from matter leaving the comet’s nucleus and swept back by the flow of energy from the Sun. Olbers was also the discoverer of the second and third asteroids ever found, Pallas in March 1802 and Vesta in March 1807, respectively.