CELESTIAL MECHANICS: LEUSCHNER 23 



(4) VESTA 



Vesta was discovered by Olbers 1 at Bremen on March 29, 1807. 



Preliminary elements were computed by Gauss 2 and also by Burk- 

 hardt. 3 The third set of Elements A by Gauss is based on obser- 

 vations from March 29 to July 11. They were used to compute the 

 ephemeris for 1808-1809. 



The preliminary work of Gauss was continued by Gerling, 4 who 

 supplied the ephemeris for a number of years. His last set of Ele- 

 ments B, are based on the first six oppositions. 



Burkhardt's preliminary work was continued by Daussy 5 (refer- 

 ence not available here). In his work he took into consideration the 

 perturbations by Jupiter, Saturn, and Mars, and was able to represent 

 the first seven oppositions satisfactorily. On account of the small 

 eccentricity and inclination, the methods of La Place and Le Verrier 

 were sufficient. 



On account of increased error in the ephemeris for 1818 based 

 on Gerling's first elements, Encke computes a set of Elements C, 

 based on oppositions 1812, 1815, 1816, and 1818. 



In Astronomisches Jahrbuch 1829, pp. 156-158, Encke gives the 

 results of his work on Vesta based on fourteen oppositions by also 

 using Nieolai's value of Jupiter's mass (1/1054), for the perturbations 

 due to Jupiter. He also makes use of Daussy's tables for the per- 

 turbations of Saturn and Mars. His new set of Elements D repre- 

 sents the oppositions from 1807 to 1825 within 6". Elements D 

 are then brought up to the epoch of 1827. Astronomisches Jahr- 

 buch from 1830 to 1866, contains the elements and ephemerides com- 

 puted by Encke. (See Elements E.) The method of computation 7 

 was that of the variation of the elements by special perturbations of 

 Jupiter. In this work Encke was assisted by Bruhns and Schiaparelli. 

 In A. N. 332, Encke comments on the poor results obtained for planets 

 (1), (2) and (3), by using Laplace's value for the mass of Jupiter 

 and also publishes a new value of Jupiter's mass (1/1050), obtained 

 from the results of Vesta. 



The Berliner Jahrbuch for 1868 publishes mean Elements F by 

 Briinnow. 8 They are also published in Watson's Theoretical Astron- 

 omy. Briinnow completes the work of Wolfers and Galle 9 who de- 

 veloped expressions for the perturbations in longitude and radius 

 vector after Hansen's method. Bninnow's elements represent the 

 oppositions from 1810 to 1851 within 6" to +10". For Jupiter's 

 mass he used 1/1050. 



