Astronomy. — ''Outlines of a new theory of Jupiter's satellites." 

 By Prof. W. de Sitter. 



(Communicated in the meeting of March 23, 1918). 



1. Fundmnental principles of the theory. 



The great difficulty in the theory of the four old satellites of 

 Jupiter arises frotn the mutual commensurability of the mean molions 

 of the three inner ones. The fourth satellite is not affected by this, 

 and, so far as periodic inequalities are concerned, its theory does not 

 give rise to particular difficulties, and is in many respects siuiilar 

 to the lunar theory, only much simpler, since the ratio of the month 

 ami the year, which for our moon is 7i8. '^ ^or the fourtii satellite 

 only about 7i8o- '^''^ secular perturbations of the equations of the 

 centre of the four satellites are however so intimately connected 

 with each other, that it is not possible to keep the fourth satellite 

 apart, but the theory of the four satellites must be treated as one 

 whole. 



I denote the satellites by the suffixes 1 to 4, and T put: 



ai the semi-axis major, 



Hi the mean motion, 



lüi the true orbit-longitude, 



Xi the mean longitude, 



li the mean anomaly, 



fi the true anomaly, 



?', the radius-vector, 



ei the excentricity, 



:rr, the longitude of the perijove. 



If now we put ^ 



(n, — n,) < = T , 

 then, if an appropriate zero of longitude and time is chosen, we 

 have 



;, = (4 - x) T, 



;i, = (2— x)T + 180°, 



;., = (1 - h) r, 



1) This T differs 180° from the angle which was called r in my previous work. 

 See these Proceedings Feb. and March 1908: "On the Masses and Elements of 

 Jupiter's satellites, and the mass of the system." (Vol. X, pp. 653 and 710). 



