Astronomy. — ''Theory of Jupiter s Satellites. I. The i)iterrnediary 

 orbit". By Piof. W. dk Sitter. 



(Communicated in the meeting of March 29, 1919). 



The follüvviiig pages contain the elaboration of the theory whieh 

 was outlined in my paj)erM of 1918 March 23. Only the resnits 

 will be given here: the conipntations will be pnblished in detail in 

 the Annals of the Observatory at Leiden. The present pa|)er gives 

 the determination of the intei-mediary orbit. As has been explained 

 in the "Cullines", the motion of the satellites is theieby represented 

 as a keplerian ellipse WMth the constant seini-axis a, and excentricity 

 e,-, the perijoves having the common retrograde motion — xr. 



Instead of the time we use the independent variable r, i.e. we 

 connt the time in nnits of 1.1221899034 mean solar days. The unit 

 of mass is the mass of Jupiter, and the niiit of length has been so 

 chosen that the Ganssian I'onstant /= 1. This unit of length is 

 a» = 0.0070854378 astronomical units, 

 The adopted masses of the satellites are'): 

 m, = 0.00003796 (1 -^ X,) 

 m, = 0.00002541 (1 ■ ;,J 

 m, = 0.00008201 (1 + ;.,) 

 m, = 0.00004523 (1 + ;. J. 

 The mass of the sun is J/= 1047.40 (1 -\- 2 m,), or 



il/= 1047.600 

 For the quantities / and K depending on the ellipticity, we take 



J = 0.021 86^(1 + /„) A" -^0.00259(1 ^ ).,). 



These occur exclusively in the combinations Jh^ and Kb* respectively, 

 of which the adopted values expressed in our units are 

 /o.</ .76' =5.99693 18 — 10 

 /o<7/ir6^ = 2.72766 — 10. 

 The mean distance of Jnpiter from the sun, expressed in our 

 unit, is 



lofl A = 2.865871. 



1) Outlines of a new theory of Jupiter's satellites, these Proceedings Vol XX, 

 p. 1289. 



*) See Annalen van de Sterrewacht te Leiden, Deel XII, Eerste Stuk, Appendix. 



