﻿A NEW METHOD FOR CORRECTING A PLANET S ORBIT. 



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COS 6 D„ Z = - sin W D sin M' 

 A 



And, finally, 



(22) 



(23) 



The following are (Astr. Nachr. XXVIII. 11.5) Goetze's general expressions, by 

 means of which AV D, M', &c. may be computed : 



sin W D sin M = — sin {I — Ji') ; 

 sin "W D cos M =:z cos {I — SL') cos I ; 

 cos W D = — cos (? — />') sin I ; 

 M' = M + a)' + r; 



(24) 



sin W E sin N ^ — cos {I — SI') sin h ; 

 sin W E cos N = — sin {I — Ji') sin J cos I -|- cos S sin I ; 

 cos W E := sin {I — SI') sin 5 sin I -j- cos 5 cos I ; 



N' = N 4- w' + I- ; 



sin W F sin P = cos {I — PJ) cos 6 ; ") 



sin "W F cos P ^ sin (/ — PJ) cos i cos I -|- sin J sin I ; 

 cos W F = — sin {I — SI') cos 6 sin I -f- sin 5 cos I ; 



P' = P + to' + V. 



(25) 



(26) 



In these expressions, i2', o', I, denote respectively the distance of the planet's as- 

 cending node upon the plane II., counted from the same origin as I is, the distance (in 

 the direction of motion) from this ascending node to the perihelion, and the inclination 

 to the plane II. 



15. We will now let the approximate orbit-plane itself become the plane II. We 

 have first to devise means 'for referring observed geocentric places to it. We shall, 

 therefore, suppose that the planet's geocentric orbit-longitude, so to speak, is denoted 

 by 7^, it being counted from the ascending node upon the equator ; that 6 denotes, like- 

 wise, its geocentric orbit-latitude, referred in the same way to .the orbit. 



It must be observed that throughout this portion of the investigation we are speak- 

 ing of the approximate orbit as a. fixed plane of reference. 



Let J2,i,ci)i, ii 5 denote the approximate longitude of the ascending node upon the equator. 



