German mathematician and astronomer Friedrich Wilhelm Bessel (1784–1846) was twenty years old when he recalculated the orbit of Halley’s comet and mailed his findings to astronomer Heinrich Olbers (1758–1840), who was famous for the paradox named in his honor. When Bessel was twenty-six years old, he was appointed director of the Koenigsburg Observatory, a position he held until his death in 1846. During his career, Bessel cataloged the positions of more than fifty thousand stars. To study perturbations (small disturbances) of planetary motions in the solar system, he developed a series of mathematical equations that helped describe complex, overlapping motions and vibrations. Today these equations are called the Bessel functions in his honor, and are indispensable tools in the fields of applied mathematics, physics, and engineering. Using innovative techniques, he measured the apparent motions of a large number of stars more accurately than ever before.