96 OUTLINES OF NATURAL PHILOSOPHY. 



99. The position and the species of the orbit, 

 being thus determined, the calculation of the 

 sun's place for any given time, is reduced to the 

 geometric problem, of drawing a line through 

 the focus of an ellipsis, so as to cut off a sector 

 between it and the transverse axis, having a gi- 

 ven ratio to the whole elliptic area. 



If AGPH (fig. 13.) be the orbit of the sun ; F the 

 focus in which the earth is placed ; and G the 

 place of the sun at a given time ; then ihe time of 

 the sun's describing the arch PG, or of the radius 

 vector describing the sector PFG, is given ; and 

 the time of an entire revolution, or of the radius 

 vector describing the whole elliptic area, being al- 

 so given, the ratio of the sector PFG, to the whole 

 ellipsis AGPH, is given. If, from this, the posi- 

 tion of the straight line FG can be determined, it 

 is evident, that the angle PFG, and the position 

 of G, are found. 



This is known by the name of KEPLER'S Problem ,- 

 . it can only be resolved by approximation. 



a. The angle PFG, which measures the angular dis- 

 tance of the sun from the Perigee, or lower apsis, 

 is called the true anomaly. 



b. If a circle be described from the centre F, with a 



radius = y a (a* . *)*' its radius will be equal to 



i that 



