Unlike many men of achievement, Friedrich Wilhelm Bessel did little to give an indication of his forthcoming accomplishments during his early and limited education. He stumbled upon his genius by way of accepting an apprenticeship as a bookkeeper with a merchant house when he was 15 years old. Then, because Bessel wished to further his career and enter the world of foreign trade, he studied navigation as well as geography and foreign languages. This study of navigation soon blossomed into the study of astronomyand became an avocation that eventually led to a life's work affecting not only mathematics, but profoundly changing the world of astronomy. In his own lifetime, Bessel's discoveries were applauded as "inaugurating a new era of practical astronomy" and hailed as the "beginning of modern astronomy."
Bessel was born in Minden, Germany, on July 22, 1784. Not much is recorded about his family, except that his father was a government employee whose salary barely kept the nine children fed, and his mother came from Rheme, where her father was a minister. In 1812, Bessel married Johanna Hagen. The couple had five children, two boys and three girls, and the marriage was said to be successful except for the loss of both sons when they were quite young. Bessel was fond of taking walks and, despite his small stature and less than robust health, enjoyed hunting. His only other form of relaxation was his correspondence with fellow astronomers and mathematicians.
Bessel's discoveries and achievements were not based on any sort of formal education; instead, he was almost self-taught. When Bessel was only 20 years old, he studied the 1607 observations of Thomas Harriot to calculate the orbit of Halley's Comet. After writing a paper on his calculations, Bessel sent it to astronomer Wilhelm Olbers, who was so impressed that he arranged for its publication in Monatliche Corresondenz. Olbers immediately recognized genius when he saw it and further prevailed on officials at the Lilienthal Observatory to make Bessel an assistant. During his four years at Lilienthal, Bessel attracted the attention of Friedrich Wilhelm III of Prussia, who was appointed him director of the Royal Observatory at Königsburg in 1810, where he spent the next 30 years.
While at the observatory, Bessel improved upon the work of past astronomers and paved the way for further discoveries for future cosmologists. Since the time of Isaac Newton, men of science had been attempting to calculate the distance of stars, and until Bessel they had failed. This failure can be attributed to two things--the lack of proper instruments and the lack of a proper method for going about the measurement. In 1829, telescope maker Joseph Fraunhofer of Austria designed the equipment and Bessel designed the method that would finally provide the answer.
Bessel reasoned that the easiest and most reliable way to measure the distance of a star was to measure its annual parallax. This parallax, or shift in the apparent position of an object resulting from the Earth's orbit around the sun, had to be painstakingly measured every night for a year in order for Bessel's conjectures to be taken seriously by his peers. Using the speculations of astronomer James Bradley and his own intuition, Bessel accomplished what Bradley and all who had come before him could not and became the first person to accurately determine the distance of a star from Earth. Bessel's calculations vastly expanded astronomers' abstractions of space, and turned the conception that the Earth was part of a solar system into the realization that it is actually part of a universe. Bessel astounded his fellow astronomers when he proved that one of the nearest stars to Earth, 61 Cygni, was more than 60 trillion miles away. Bessel was also the first to use the term "light years" as a way of vividly explaining this distance. Traveling at the speed of light, 186,000 miles per second, it would take 10.3 years to reach 61 Cygni. Using his newly found method of computation, Bessel further compiled a catalog of the position of 75,000 stars.
In a paper written in 1840, Bessel recounted that Uranus displayed certain small but noticeable "ir__regularities" in its orbit. The planet, it seems, alternately slowed down and then ran ahead of its expected positions. Bessel surmised that this could only be due to the influence of an as yet unknown planet laying somewhere beyond it. Although Bessel did not live to see his hypothesis confirmed, that planet later proved to be Neptune. In 1842, Bessel calculated the mass of Jupiter by studying the orbital period of each of its major moons and established that while it had 388 times the mass of Earth, its overall density was only 1.35 times the density of water, bringing to light that this mammoth planet was essentially very light for its size.
The same sort of "irregularities" bothered Bessel when he studied the luminous stars Sirius and Procyon. Bessel proposed that the slight but significant erratic behavior of the two stars must be caused by "invisible companions." After Bessel's death, more powerful telescopes provided the evidence to prove him correct, and we now know those "invisible companions" as Sirius B and Procyon B.
Most of Bessel's gifts to the realm of mathematics materialized as a result of his astronomical breakthroughs, but that does not lessen the importance of his legacy to mathematical functions still used extensively today in such fields as geology, physics, engineering, and of course applied mathematics. These Bessel functions, also known as cylinder functions, were first devised to unlock the mystery of "planetary perturbation." This deviation of a planet from its regular orbit, usually caused by the presence of one or more bodies acting upon it, could be accurately calculated and anticipated due to Bessel's functions and later were used as solutions for a differential equation--intrinsic in the investigation of numerous problems in mathematical physics.
In addition to his duties at the Royal Observatory, Bessel was required to spend a considerable amount of time surveying. Like everything else he did, this task brought him acclaim and notoriety. Using his own idea for an improved measuring device, he commissioned the construction of an instrument that would accurately gauge base lines. Then, by using the methods of Karl Friedrich Gauss, he developed a new system of triangulation. These two accomplishments enabled Bessel to paint a mathematically accurate and, at that time, an astounding picture of the form and magnitude of the Earth. Bessel's work on triangulationsalso resulted in the eventual establishment of the International Bureau of Weights and Measures.
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