SECOND SECTION. 



RELATIONS PERTAINING SIMPLY TO POSITION IN SPACE. 



47. 



IN the first section, the motion of heavenly bodies in their orbits is treated 

 without regard to the position of these orbits in space. For determining this 

 position, by which the relation of the places of the heavenly body to any other 

 point of space can be assigned, there is manifestly required, not only the position 

 of the plane in which the orbit lies with reference to a certain known plane (as, 

 for example, the plane of the orbit of the earth, the ecliptic), but also the position 

 of the apsides in that plane. Since these things may be referred, most advanta 

 geously, to spherical trigonometry, we conceive a spherical surface described 

 with an arbitrary radius, about the sun as a centre, on which any plane passing 

 through the sun will mark a great circle, and any right line drawn from the 

 sun, a point. For planes and right lines not passing through the sun, we draw 

 through the sun parallel planes and right lines, and we conceive the great circles 

 and points in the surface of the sphere corresponding to the latter to represent 

 the former. The sphere may also be supposed to be described with a radius 

 infinitely great, in which parallel planes, and also parallel right lines, are repre 

 sented in the same manner. 



Except, therefore, the plane of the orbit coincide with the plane of the ecliptic, 

 the great circles corresponding to those planes (which we will simply call the orbit 

 and the ecliptic) cut each other in two points, which are called nodes ; in one of 

 these nodes, the body, seen from the sun, will pass from the southern, through the 

 ecliptic, to the northern hemisphere, in the other, it will return from the latter to 

 the former ; the former is called the ascending, the latter the descending node. We 

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