60 CELESTIAL MECHANICS: LEUSCHNER 



(624) HECTOR, 1907 XM. 



Discovered by Kopff 1 at Heidelberg on February 10, 1907, >)/V W,63. 



A preliminary orbit, Elements A, was computed by Stromgren 2 based Afi 

 on observations from February 10 to April 16. These elements gave 

 the following residuals: 



1907 AA A 



Feb. 10 1".0 +2".2 



April 19 +2 .8 +8 .3 



He reports that Hector is another planet with mean motion nearly 

 equal to that of Jupiter. Since the perturbations of Jupiter are small 

 and the perturbations of the other planets will be ineffective for a 

 long time, this planet will remain in the neighbourhood of the libration 

 point for a long time. 



An observation by Palisa February 29, 1908, gives a correction to 

 f7, Jl3 the ephemeris 3 based on Elements A as follows: Aa= 37 s A8=+6'.3. 

 r 0,317 An ephemeris is published by Stromgren 4 for the opposition of 1909 

 based on Elements A. 



In preparation for the ephemeris of 1911, Stromgren, 5 assisted by 

 J. Fischer-Petersen, computes a new set of Elements B, based on nine 

 normal places (oppositions 1907, 1908, 1909), taking into account 

 the perturbations due to Jupiter and Saturn. These elements represent 

 the normal places, AacosS between +0'.30 and .17, and AS between 

 0'.04 and +OM6. 



The planet was next observed in July 1911. The comparison be- 

 tween observation and ephemeris (from Elements B) was unsatisfac- 

 tory. Stromgren, assisted by Ruben Andersen, 6 again investigated the 

 orbit based on observations from 1907 to 1911. For this purpose 

 Elements A were used to compute the residuals for five observations, 

 July 4 to 16, 1911. A tenth normal place was formed from these five 

 places with the following residuals Aacos8 = 52' 23" .9 AS = 11' 

 36". 6. A weight of five (number of observations) was given to this 

 normal place. Combining this normal place with the solution that 

 led to Elements B, a new set of elements was derived, Elements C. 

 With these elements the special perturbations, due to Jupiter and 

 Saturn, were computed by the method of Encke, for 1906 to 1912. 

 The observations for 1907 and 1908 were then computed without taking 

 into account the perturbations (reported as being small) and the obser- 

 vations of 1909 and 1911 were represented with perturbations. From 

 these representations ten new normal places were formed and new 

 Elements D were obtained from a least square solution. This set 



