ABOUT COMETS. 791 



pouncling of the motion of the observer with the motion of the planet 

 observed rendered the problem very difficult. 



Copernicus furnished the key, by showing that the sun and not the 

 earth is the center of the solar system. Tycho Brahe soon followed, 

 and furnished an extensive series of accurate observations that afford- 

 ed Kepler the material upon which he based his studies that devel- 

 oped those immortal laws defining the forms of the orbits of the 

 planets, the character of their motions, and the relation between the 

 dimensions of their orbits and their periods of revolution. 



It remained for Newton to discover the existence of the law of 

 universal gravitation, of which Kepler's laws are an immediate se- 

 quence. 



Thus the secrets of the motions of the planets were explained. 

 But comets, those erratic visitants of our system, whose advent in 

 olden time filled the mind with universal awe, were still an unfathomed 

 mystery. Suddenly they would blaze out in the sky, and as suddenly 

 pass out of sight, and no astronomer could tell whence they came or 

 whither they went, or the laws which governed their motions. 



Kewton first showed that comets also were obedient to the attrac- 

 tion of gravitation. He demonstrated this fact by means of the comet 

 of 1680. The orbit of this comet he found not to differ perceptibly 

 from a parabola. 



After Newton, Edmund Halley, from a careful study of the comets 

 of 1531, 1607, and 1682, ventured the assertion that these were only 

 different appearances of one and the same body, whose period of revo- 

 lution was about seventy-five years. Halley, consequently, predicted 

 a reappearance of this comet in 1759. This comet was shown to move 

 in a very elongated ellipse. In accordance with prediction, reappear- 

 ances of this comet occurred in 1759 and 1835. 



Since the time of Newton all the comets which have come to view 

 have been submitted to a careful study. To determine the orbit of 

 any newly discovered member of our system, it is necessary that its 

 direction in space from the earth at three dates, as nearly equidistant 

 as may be, should be determined by observation. 



The data for the problem are, then, as follows : the positions of the 

 earth with reference to the sun at three different dates, and the posi- 

 tions of the heavenly body with reference to the earth at the same 

 dates. The unknown elements which describe the character of tbe 

 orbit and its position in space are as follows : 



I. The mean longitude of the body at any convenient epoch. 



II. The semi-major axis of the orbit. 



HI. The eccentricity of the orbit. 



IV. The longitude of the perihelion. 



V. The lono^itude of the ascendino; node. 



yi. The inclination between the orbit-plane and the plane of the 

 earth's orbit. 



