CELESTIAL MECHANICS: LEUSCHNER 11 



(1) CERES. 



The first and largest of the minor planets was discovered 1801, 

 January 1, by Piazzi in Palermo. 1 



Piazzi assumed that the object was a comet, but several astronomers 

 succeeded in proving from the 22 meridian observations near the 

 stationary point over an heliocentric arc of 9 that it was a planet 

 moving in a nearly circular orbit; thus Burckhardt 2 computed 

 Elements A, Olbers 3 the circular Elements B, Piazzi* the circular 

 Elements C. Only the computation by Gauss, 5 Elements D, was 

 accurate enough, especially in the determination of perihelion and 

 eccentricity, to indicate where the planet might be found the following 

 year. 



Olbers found Ceres again 1802, January 1, % from the predicted 

 place, near the place where, three months later, he discovered the 

 second of the minor planets. The new observations naturally 

 increased the accuracy of the elements notably; thus Gauss 6 computed 

 Elements E, from observations in 1801, and January 1802; represen- 

 tation in February 1802, +7" in a, 20" in 8. Burckhardt 7 including 

 the perturbations larger than 30' found Elements F. 



For some years the orbit of Ceres was investigated by Oriani, 

 Burckhardt, and Gauss by taking the perturbations into account, but 

 the efforts of Gauss went farther than those of the others. Burck- 

 hardt 8 started with the computation of perturbations at intervals of two 

 days, and later computed tables founded upon them. Oriani 9 used 

 Laplace's method, with which also Gauss started. Gauss developed 

 the perturbations first in 1802, together with Elements VIII, G, and 

 formed tables of perturbations 10 and later in 1805 11 when he used 

 the same interpolatory development of the perturbative function as 

 Hansen later used in 1830. 



The orbit computation was taken up later by Heiligenstein. 12 He 

 derived Elements H from the oppositions 1818, 1820, 1821, 1822, 1825, 

 1826, 1827, with special perturbations of the elements by Jupiter, 

 (mass 1/1053.924). Representation of the normal places 10" to 

 +6" in mean longitude. Correction to the ephemeris for 1830 April, 

 May, 6" in a, 10" in 8. 



Heiligenstein's ephemeris deviates 15' from the ephemeris in B. J. 

 1830, which was based on the elements of Gauss (XIII, 1809), using 

 the tables of perturbations by Gauss and an empirical correction by 

 Encke of 14' to the mean longitude determined from the last 

 observations. 18 



