CELESTIAL MECHANICS: LEUSCHNER 15 



(2) PALLAS 



Discovered by Gibers at Bremen 1802, March 28. 1 Gibers attempted 

 to compute a circular and a parabolic orbit for the new planet, both 

 of which failed. His computation showed the orbit had a large 

 inclination and considerable eccentricity. 



From observations extending from April 1 to July 8, Gauss 2 com- 

 puted Elements A (Gauss V). They are improvements on preliminary 

 sets. With these elements an ephemeris for 1803 was computed. 



From observations extending from April 4 to May 20, Burkhardt 3 

 computed Elements B. With these elements Burkhardt computed 

 the perturbations in longitude, latitude, and radius vector covering 

 the period April 4 to May 20. 



The planet was reobserved by Harding 1803, Feb. 21st. The com- 

 parison between Gauss' ephemeris and observations was as follows: 



1803 Aa AS 



Feb. 21 +2' 02" 34" 



Feb. 23 +2 35 57 



On the basis of these residuals, Gauss 4 improved Elements A 

 Gauss (V). These new Elements C (Gauss VI) represent the obser- 

 vations as follows: 



1803 Aa AS 



Feb. 21 - 20"0 + 15"8 



Feb. 23 + 7.8 7.7 



From a set of elements, based on oppositions 1804, 1805, 1807, 1808, 

 Gauss 5 derived an improved set of Elements D from a least squares 

 solution. This solution includes also the oppositions 1803 and 1809 

 and forms the basis for the computation of perturbations as outlined 

 below. 



Gauss 6 first attempted to construct tables of perturbations for the 

 four known minor planets, but the large eccentricity and inclination 

 forced him to formulate a theory for Pallas based on the variation 

 of the elements expressed analytically and integrated by mechanical 

 integration. From two successive calculations of the special pertur- 

 bations, due to Jupiter, Gauss derived the improved Elements E, 

 which represented the heliocentric longitudes for the first seven oppo- 

 sitions within 8". 



In 1811 Gauss 6 began his first computation of general perturbations 

 due to Jupiter. For this purpose he used Laplace's elements of Jupiter, 



