SECOND BOOK. 



INVESTIGATION OF THE ORBITS OF HEAVENLY BODIES FROM GEOCENTRIC 



OBSERVATIONS. 



FIRST SECTION. 



DETERMINATION OF AN ORBIT FROM THREE COMPLETE OBSERVATIONS. 



115. 



SEVEN elements are required for the complete determination of the motion 

 of a heavenly body in its orbit, the number of which, however, may be dimin 

 ished by one, if the mass of the heavenly body is either known or neglected ; 

 neglecting the mass can scarcely be avoided in the determination of an orbit 

 wholly unknown, where all the quantities of the order of the perturbations must 

 be omitted, until the masses on which they depend become otherwise known. 

 Wherefore, in the present inquiry, the mass of the body being neglected, we re 

 duce the number of the elements to six, and, therefore, it is evident, that as many 

 quantities depending on the elements, but independent of each other, are re 

 quired for the determination of the unknown orbit. These quantities are neces 

 sarily the places of the heavenly body observed from the earth ; since each one 

 of which furnishes two data, that is, the longitude and latitude, or the right ascen 

 sion and declination, it will certainly be the most simple to adopt three geocentric 

 places which will, in general, be sufficient for determining the six unknown ele 

 ments. This problem is to be regarded as the most important in this work, and, 

 for this reason, will be treated with the greatest care in this section. 



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