CELESTIAL MECHANICS: LEUSCHNER 51 



(447) VALENTINE (1899 ES). 



Discovered by Wolf and Schwassmann 1 at Heidelberg 1899, Octo- 

 ber 27. 



Preliminary elements were computed by Kreutz 2 based on observa- 

 tions 1899, October 29, November 11 and December 3. Elements A. 



Corrections to the ephemendes based on improved elements in 1902 3 

 Aa +16 S , AS 2'; in 190* January 13, Aa +36 S , AS 0'.3. 



A more complete investigation of the orbit was undertaken by Hans 

 Osten. 5 He received from Kreutz five sets of elements, B to F, which 

 refer to different epochs in order to show the effects of the perturba- 

 tions. Kreutz states that Elements B to E are comparable and are 

 to be preferred to Elements F. Elements B to E were determined from 

 five normal places (1899 to 1904). The residuals for the normal 

 places are 



la Ib II III IV V 



AacosS +5'1 -f-8'7 +i:2 -3'2 -0'7 +35^5 

 A5 +14 +8-1 -1.1 +4-0 -0-2 - 3.0 



For the purpose of investigating the general perturbations for this 

 planet, Osten makes use of Kreutz' Elements B, Leverrier's elements 

 for Jupiter and Saturn, except for the adoption ofTETilFs values of the 

 mean motion for each, for Jupiter's mass Newcomb's value and for 

 Saturn's mass Bessel's value. The perturbations of the first order of 

 the masses are determined according to Hansen's method. As a test 

 on his results, he compares observations with theory for seven normal 

 places (1894 to 1906) with the following results: 



Aa cos 6 A6 



1. 1894 -10!73* - 0;54* 



2. 1899a +5.07 + 1.41 



3. 1899b + 8.28 + 8.06 



4. 1901 + 0.32 1.01 



5. 1902 + 2.44 + 1.39 



6. 1904 +33.26 +16.12 



7. 1906 +32.06 2.52 



On the basis of these residuals the elements were corrected, which 

 resulted in Elements G. The comparison between observation and 

 computation for the normal places gives: 



* Weight 1/9. Observation uncertain. 



