10 ELEMENTS OF AN ORBIT. SECT. II. 



earth by a very simple computation. These two quantities, 

 however, will not give the place of a planet in space. Its dis- 

 tance from the sun (N. 56) must also be known ; and, for the 

 complete determination of its elliptical motion, the nature and 

 position of its orbit must be ascertained by observation. This 

 depends upon seven quantities, called the elements of the orbit 

 (N. 57). These are, the length of the major axis, and the ex- 

 centricity, which determine the form of the orbit ; the longitude 

 of the planet when at its least distance from the sun, called the 

 longitude of the perihelion ; the inclination of the orbit to the 

 plane of the ecliptic, and the longitude of its ascending node : 

 these give the position of the orbit in space ; but the periodic 

 time, and the longitude of the planet at a given instant, called 

 the longitude of the epoch, are necessary for finding the place of 

 the body in its orbit at all times. A perfect knowledge of these 

 seven elements is requisite for ascertaining all the circumstances 

 of undisturbed elliptical motion. By such means it is found 

 that the paths of the planets, when their mutual disturbances are 

 omitted, are ellipses nearly approaching to circles, whose planes, 

 slightly inclined to the ecliptic, cut it in straight lines, passing 

 through the centre of the sun (N. 58). The orbits of the 

 recently-discovered planets deviate more from the ecliptic than 

 those of the ancient planets : that of Pallas, for instance, has an 

 inclination of 34 42' 29'8" to it ; on which account it is more 

 difficult to determine their motions. 



Were the planets attracted by the sun only, they would always 

 move in ellipses, invariable in form and position ; and because 

 his action is proportional to his mass, which is much larger than 

 that of all the planets put together, the elliptical is the nearest 

 approximation to their true motions. The true motions of the 

 planets are extremely complicated, in consequence of their mutual 

 attraction, so that they do not move in any known or symme- 

 trical curve, but in paths now approaching to, now receding from, 

 the elliptical form ; and their radii vectores do not describe areas 

 or spaces exactly, proportional to the time, so that the areas be- 

 come a test of disturbing forces. 



To determine the motion of each body, when disturbed by all 

 the rest, is beyond the power of analysis. It is therefore neces- 

 sary to estimate the disturbing action of one planet at a time, 



