GAUSS AND CERES
Ceres was observed only briefly in early 1801 and then disappeared in the glare of sunlight. Gauss took the observations (spanning only 9 degrees of sky angle, during the first 40 days of that year) and calculated from them where to look at a later time, around the end of the year, when it would be out of the glare. Here are excerpts from a nice student term paper about this (at a Rutgers History of Science website)
Thanks to Leorah Weiss and
http://www.math.rutgers.edu/~cherlin/History/Papers1999/weiss.html
===excerpts===
Then,on January 1, 1801, the Italian astronomer Joseph Piazzi discovered a planetoid, working from an observatory in Palermo, Italy. This object, which he christened
Ceres, was moving in the constellation Taurus. Astronomers were only able to observe the planetoid for 41 days, during which its orbit swept out an angle of only 9 degrees. Ceres was then lost to sight when its light vanished in the rays of the sun, and the astronomers could no longer find it. There was now a challenge of calculating Ceres' orbit using only the observations Piazzi made, so that astronomers would be able to sight Ceres when it reemerged. [1,5,6,8,10]
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The technical execution of Gauss's method is very involved, and required over 100 hours of calculation for him. His first tactic was to determine a rough approximation to the unknown orbit, and then refine it to a high degree of precision. Gauss initially used only 3 of Piazzi's 22 observations, those from January 1, January 21, and February 11. The observations showed an apparent retrograde motion from January 1 to January 11, around which time Ceres reversed to a forward motion. Gauss chose one of the unknown distances, the one corresponding to the intermediate position of the 3 observations, as the target of his efforts. After obtaining that important value, he determined the distances of the first and third observations, and from those the corresponding spatial positions of Ceres. From the spatial positions Gauss calculated a first approximation of the elements of the orbit. Using this approximate orbital calculation, he could then revise the initial calculation of the distances to obtain a more precise orbit, and so on, until all the values in the calculation became coherent with each other and with the three selected observations. Subsequent refinements in his calculation adjusted the initial parameters to fit all of Piazzi's observations more smoothly [11].
In September of 1801, Zach published several forecasts of the prospective orbit, his own and Gauss's among them; Gauss's prediction was quite different from the others and expanded the area of the sky to be searched [1]. Using Gauss's ephemeris for Ceres (astronomical almanac showing its predicted location at various times), astronomers found Ceres again between November 25 and December 31. Zach, on December 7, and then Olbers, on December 31, located Ceres very close to the positions predicted by Gauss. Between the discovery of Ceres in 1801 and the present day, over 1,500 planetoids have been identified, with Ceres remaining the largest [5,10]. While continually improving and simplifying his methods, Gauss calculated ephemerides for the new planetoids as they were discovered. When Olbers found Vesta in 1807, Gauss calculated the elements of its orbit in only 10 hours. His calculations of parabolic orbits were even faster, as is natural. He could calculate the orbit of a comet in a single hour, where it had taken Euler 3 days using the previous methods [5,6].
Gauss published his methods in
1809 as "Theoria motus corporum coelestium in sectionibus conicus solem ambientium," or, "Theory of the motion of heavenly bodies moving about the sun in conic sections." [1,2,3,5,6,11]. Gauss first wrote this work in German, but his well-known publisher, Perthes, requested he change it to Latin to make it more widely accessible (sic). In fact, the astronomical methods described in Theoria Motus Corporum Coelestium are still in use today, and only a few modifications have been necessary to adapt them for computers [11]. Gauss's determination of Ceres's orbit made him famous in academic circles worldwide, established his reputation in the scientific and mathematical communities, and won him a position as director at the Gottingen Observatory. [5,10]
==endquote==
Gauss was born in 1777, so in 1801 when Piazzi first observed Ceres and Gauss made the first successful calculation of its orbit, he was 24 years old....