Burckhardt Four Page Handwritten Manuscript with Calculations on the Comet of 1770
ref. 13574Johann Karl Burckhardt 1773-1825 German-born astronomer and mathematician. Burckhardt carried out extensive studies on the orbits of comets and his study of a comet of 1770 now known as Lexell's Comet or D/1770 L1 cemented his professional reputation. This comet is known for passing closer to earth than any other comet in recorded history when it reached only 0.0146 AU from Earth on July 1 1770. Offered here is a 4 page handwritten manuscript of his calculations for that comet of 1770 dated December 1804. Written in French. Burckhardt completed his research in 1807 finding that the comet had an elliptical orbit with a period of 5.57 years. Burckhardt has titled the Manuscript in his hand "Pull of the Comet of 1770 by the Earth from the Formula of the Spatial Mechanics Volume 4." A small sampling of Burckhardt's extensive calculations and proofs in this manuscript includes the following: "1 I would take for a constant plane that of the eleptic and for the x axis the vertical radius of Earth. At the moment of the entry of the comet in the field of gravity F; so we will have A1 = 0; B1 = 0; C1 = 0. 2 We will take a day as the limit of t. We will see later on if we could use a smaller interval. 3 I will suppose the point of entry in the field of activity at 273567 this is based on an observation of Mr. Messier The duration of 8 days with the exit on the 5th of July 0.5567. 4 We will therefore have for the Earth Z1 always equal to zero. 6 One sees for the earth generally with great exactitude x=0.000142t2 y=. For the gravitational center of earth. 7 For the Comete one employs the.elements of observation made after the perihelic part of the passage. N.B. I have neglected to express the precession of the equinoxes.and that the observation requires the movement of a contoured lens." Burckhardt proceeds to provide detailed calculations of the comets approach and recession from June 27 to July 6 taking extra care to mark the day of its closest approach to earth--July 1. The comet of 1770 never reappeared and is today considered a "lost comet" but it presented a fascination to astronomers for years afterward. Lexell for whom the comet is named initially calculated the orbit at around 5 and a half years. But the fact that a comet with so short a period had never been previously recorded and that it did not reappear in 1776 threw doubt on Lexell's calculations and induced the Institute of France to establish a prize for whomever could determine its orbit. Burckhardt became the winner when he was able to show through his calculations that the comet's had come within the sphere of Jupiter's attraction in 1767 which swung it into its close 1770 orbit. It did not reappear in 1776 because it was directly in line with the sun rendering it invisible. And why had it never reappeared since Burckhardt determined that in 1779 it had come again within the orbit of Jupiter and from there had been flung off into distant space. He thereby confirmed Lexell's initial calculation and provided a scientific explanation for the comet's very strange activity. Journal of the Franklin Institute Thomas P. Jones M.D. ed. pg. 319-320. Thompson & Homans: Washington D.C. 1832. Burckhardt's tracing of the orbit of the comet of 1770 cemented his reputation in the scientific community. Today he is remembered in particular for his work in fundamental astronomy and for his lunar theory which was in widespread use for the construction of navigational ephemerides of the Moon for much of the first half of the nineteenth century and for his studies on the orbits of comets. In 1812 he published an improved lunar theory after that of Pierre-Simon Laplace. Burckhardt's lunar tables appear to have been the first to be based on a least squares adjustment of the coefficients to selected lunar observations of which about 4000 were used. They were officially used for computing the lunar ephemerides in the Nautical Almanac from 1821 to 1861. unknown books
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