SECT. 2.] TO POSITION IN SPACE. 55 



fix the positions of the nodes in the ecliptic by means of their distance from the 

 mean vernal equinox (longitude) counted in the order of the signs. Let, in fig. 1, 

 Q, be the ascending node, A Q B part of the ecliptic, C Q D part of the&quot; orbit ; 

 let the motions of the earth and of the heavenly body be in the directions from A 

 towards B and from C towards D, it is evident that the spherical angle which Q, D 

 makes with Q B can increase from to 180, but not beyond, without Q ceasing 

 to be the ascending node : this angle we call the inclination of the orbit to the 

 ecliptic. The situation of the plane of the orbit being determined by the longi 

 tude of the node and the inclination of the orbit, nothing further is wanted 

 except the distance of the perihelion from the ascending node, which we reckon 

 in the direction of the motion, and therefore regard it as negative, or between 

 180&quot; and 360, whenever the perihelion is south of the ecliptic. The following 

 expressions are yet to be observed. The longitude of any point whatever in 

 the circle of the orbit is counted from that point which is distant just so far back 

 from the ascending node in the orbit as the vernal equinox is back from the same 

 point in the ecliptic : hence, the longitude of the perihelion will be the sum of the 

 longitude of the node and the distance of the perihelion from the node ; also, the 

 true longitude in orbit of the body will be the sum of the true anomaly and the 

 longitude of the perihelion. Lastly, the sum of the mean anomaly and longitude 

 of the perihelion is called the mean longitude : this last expression can evidently 

 only occur in elliptic orbits. 



48. 



In order, therefore, to be able to assign the place of a heavenly body in space 

 for any moment of time, the following things must be known. 



I. The mean longitude for any moment of time taken at will, which is called 

 the epoch : sometimes the longitude itself is designated by the same name. For 

 the most part, the beginning of some year is selected for the epoch, namely, noon 

 of January 1 in the bissextile year, or noon of December 31 preceding, in the 

 common year. 



II. The mean motion in a certain interval of time, for example, in one mean 

 solar day, or in 365, 365J, or 36525 days. 



