Friedrich Bessel

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Friedrich Bessel
Friedrich Wilhelm Bessel (1839 painting).jpg
C. A. Jensen, Friedrich Wilhelm Bessel, 1839 (Ny Carlsberg Glyptotek)
Born (1784-07-22)22 July 1784
Minden, Minden-Ravensberg (present-day Germany)
Died 17 March 1846(1846-03-17) (aged 61)
Königsberg, Prussia (present-day Kaliningrad, Russia)
Residence Prussia
Nationality Prussian (German)
Fields Astronomy and mathematics
Institutions University of Königsberg
Doctoral students Friedrich Wilhelm Argelander
Known for Bessel functions
Stellar parallax
Bessel ellipsoid
Notable awards Lalande Prize (1811)
Gold Medal of the Royal Astronomical Society (1829 & 1841)

Friedrich Wilhelm Bessel (German: [ˈbɛsəl]; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician (systematizer of the Bessel functions, which were discovered by Daniel Bernoulli). He was the first astronomer to determine the distance from the sun to another star by the method of parallax.

Although he left school at the age of 14, he was appointed in January 1810 as director of the Königsberg Observatory by King Frederick William III of Prussia. On the recommendation of fellow mathematician and physicist Carl Gauss he was awarded an honorary doctor degree from the University of Göttingen in March 1811.

Bessel won the Gold Medal of the Royal Astronomical Society in 1829 and 1841. The asteroid 1552 Bessel was named in his honour.

Life and work[edit]

Bessel was born in Minden, administrative center of Minden-Ravensberg, as second son of a civil servant. At the age of 14 Bessel was apprenticed to the import-export concern Kulenkamp at Bremen. The business's reliance on cargo ships led him to turn his mathematical skills to problems in navigation. This in turn led to an interest in astronomy as a way of determining longitude.

Bessel came to the attention of a major figure of German astronomy at the time, Heinrich Wilhelm Olbers, by producing a refinement on the orbital calculations for Halley's Comet in 1804, using old observation data taken from Thomas Harriot and Nathaniel Torporley in 1607.[1]

Two years later Bessel left Kulenkamp and became Johann Hieronymus Schröter's assistant at Lilienthal Observatory near Bremen. There he worked on James Bradley's stellar observations to produce precise positions for some 3,222 stars.[1]

In January 1810, at the age of 25, Bessel was appointed director of the new founded Königsberg Observatory by King Frederick William III of Prussia. There he published tables of atmospheric refraction derived from Bradley's observations, which won him the Lalande Prize from the French Academy of Sciences in 1811. While the observatory was still in construction Bessel elaborated the Fundamenta Astronomiae based on Bradley's observations.

The Königsberg Observatory began operation in 1813. Starting in 1819, Bessel determined the position of over 50,000 stars using a meridian circle from Reichenbach, assisted by some of his qualified students. The most prominent of them was Friedrich Wilhelm Argelander.

With this work under his belt, Bessel was able to achieve the feat for which he is best remembered today: he is credited with being the first to use parallax in calculating the distance to a star. Astronomers had believed for some time that parallax would provide the first accurate measurement of interstellar distances—in fact, in the 1830s there was a fierce competition between astronomers to be the first to measure a stellar parallax accurately. In 1838 Bessel won the race, announcing that 61 Cygni had a parallax of 0.314 arcseconds; which, given the diameter of the Earth's orbit, indicated that the star is 10.3 ly away.[2][3][4] Given the current measurement of 11.4 ly, Bessel's figure had an error of 9.6%. Nearly at the same time Friedrich Georg Wilhelm Struve and Thomas Henderson measured the parallaxes of Vega and Alpha Centauri.

As well as helping determine the parallax of 61 Cygni, Bessel's precise measurements allowed him to notice deviations in the motions of Sirius and Procyon, which he deduced must be caused by the gravitational attraction of unseen companions.[5][6][7] His announcement of Sirius's "dark companion" in 1844 was the first correct claim of a previously unobserved companion by positional measurement, and eventually led to the discovery of Sirius B.

An additional responsibility of Bessel at Königsberg was geodesy.[8] Bessel published a method for solving the geodesic problem;[9] he was responsible for the survey of East Prussia which joined the Prussian and Russian trianguation networks;[10] and he obtained an estimate of increased accuracy for the figure of the Earth, nowadays referred to as the Bessel ellipsoid.[11][12]

Despite lacking a university education, Bessel was a major figure in astronomy during his lifetime. He was elected a fellow of the Royal Society, a foreign member of the Royal Swedish Academy of Sciences in 1823, and the largest crater in the Moon's Mare Serenitatis is named Bessel after him. Bessel's work in 1840 contributed in some degree to the discovery of Neptune. In 1832, he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences.[13] Bessel won the Gold Medal of the Royal Astronomical Society in 1829 and 1841.

In the second decade of the 19th century while studying the dynamics of 'many-body' gravitational systems, Bessel developed what are now known as Bessel functions. Critical for the solution of certain differential equations, these functions are used throughout both classical and quantum physics. Even in the absence of any work in astronomy, Bessel's role in developing the functions which now bear his name would have, by itself, placed him among the most significant and influential mathematicians of the 19th century.

Bessel is responsible for the correction to the formula for the sample variance estimator named in his honour. This is the use of the factor n-1 in the denominator of the formula, rather than just n. This occurs when the sample mean rather than the population mean is used to centre the data and since the sample mean is a linear combination of the data the residual to the sample mean overcounts the number of degrees of freedom by the number of constraint equations — in this case one.

In 1842 Bessel took part in the annual meeting of the British Association for the Advancement of Science in Manchester, accompanied by the geophysicist Georg Adolf Erman and the mathematician Carl Gustav Jacob Jacobi.

After several months of illness Bessel died in March 1846 at his observatory from retroperitoneal fibrosis.[14] This was several months short of the discovery of Neptune in the fall of that year, by his colleagues at Berlin Observatory.


Bessel married Joanna, the daughter of the chemist and pharmacist Karl Gottfried Hagen. He was the uncle of the physician and biologist Hermann August Hagen, and the hydraulic engineer Gotthilf Hagen who was also Bessel's student and assistant from 1816 to 1818.

Bessel had two sons and three daughters. His eldest daughter, Marie, married Georg Adolf Erman, member of the scholar family Erman. One of their sons was the renowned egyptologist Adolf Erman.


  • Fundamenta Astronomiæ (1818)
  • Tabulæ Regiomontanæ (1830)


  1. ^ a b Chisholm 1911.
  2. ^ Bessel, F. W. (1838). "Bestimmung der Entfernung des 61sten Sterns des Schwans" [Determination of the distance to 61 Cygni]. Astronomische Nachrichten (in German) 16 (365–366): 65–96. Bibcode:1838AN.....16...65B. doi:10.1002/asna.18390160502. 
  3. ^ Bessel, F. W. (1838b). "On the parallax of 61 Cygni". Monthly Notices of the Royal Astronomical Society 4 (17): 152–161. Bibcode:1838MNRAS...4..152B. doi:10.1093/mnras/4.17.152. 
  4. ^ "A brief history of light years". National Geographic. Retrieved 14 August 2013. 
  5. ^ Bessel, F. W. (1844a). "Ueber Veränderlichkeit der eigenen Bewegungen der Fixsterne" [Variations of the proper motions of the fixed stars]. Astronomische Nachrichten (in German) 22 (514): 145–160. Bibcode:1844AN.....22..145B. doi:10.1002/asna.18450221002. 
  6. ^ Bessel, F. W. (1844b). "Ueber Veränderlichkeit der eigenen Bewegungen der Fixsterne (Fortsetzung)" [Variations of the proper motions of the fixed stars (continued)]. Astronomische Nachrichten (in German) 22 (515): 169–184. Bibcode:1844AN.....22..169B. doi:10.1002/asna.18450221202. 
  7. ^ Bessel, F. W. (1844c). "On the variations of the proper motions of Procyon and Sirius". Monthly Notices of the Royal Astronomical Society 6 (11): 136–141. Bibcode:1844MNRAS...6R.136B. doi:10.1093/mnras/6.11.136a. 
  8. ^ Viik, T. (2006). "F.W. Bessel and Geodesy". Struve Geodetic Arc 2006 International Conference: The Struve Arc and Extensions in Space and Time. August 13–15, 2006. Haparanda and Pajala, Sweden: Lantmäteriet, Gävle, Sweden, 2006. pp. 53–63. 
  9. ^ Bessel, F. W. (2010) [1825]. . Translated by C. F. F. Karney & R. E. Deakin. "The calculation of longitude and latitude from geodesic measurements". Astronomische Nachrichten 331 (8): 852–861. arXiv:0908.1824. doi:10.1002/asna.201011352. English translation of Astron. Nachr. 4, 241–254 (1825). Errata. 
  10. ^ Bessel, F. W.; Baeyer, J. J. (1838). Gradmessung in Ostpreussen und ihre Verbindung mit Preussischen und Russischen Dreiecksketten [The East Prussian Survey and its connection with the Prussian and Russian networks] (in German). Berlin: Dümmler. 
  11. ^ Bessel, F. W. (1837). "Bestimmung der Axen des elliptischen Rotationssphäroids, welches den vorhandenen Messungen von Meridianbögen der Erde am meisten entspricht" [Estimation of the axes of the ellipsoid through measurements of the meridian arc]. Astronomische Nachrichten (in German) 14 (333): 333–346. Bibcode:1837AN.....14..333B. doi:10.1002/asna.18370142301. 
  12. ^ Bessel, F. W. (1841). "Ueber einen Fehler in der Berechnung der französischen Gradmessung und seinen Einfluß auf die Bestimmung der Figur der Erde" [Concerning an error in the calculation of the French survey and its influence on the determination of the figure of the Earth]. Astronomische Nachrichten (in German) 19 (438): 97–116. Bibcode:1841AN.....19...97B. doi:10.1002/asna.18420190702. 
  13. ^ "Book of Members, 1780–2010: Chapter B". American Academy of Arts and Sciences. Retrieved 24 June 2011. 
  14. ^ "Bessel's Tod" [Bessel's death]. Astronomische Nachrichten (in German) 24 (556): 49–52. 1846. Bibcode:1846AN.....24...49B. doi:10.1002/asna.18460240402. 


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