Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/844

us) produces no perceptible change in the appearance and rotation of the star-sphere. That the whole span of the earth s orbit was as a mere point compared with the dis tance of the stars, so that the earth on one side of the sun was, in effect, at the centre of the star-sphere, while it was equally at the centre when on the opposite side, or many millions of miles from its former position, was not

unreasonably regarded by Tycho Brahe as scarcely credible.

Chapter. VI.—Copernican System—Kepler's Laws—Gravitation—The Laws of the Solar System.

Leaving the rotation of the star-sphere out of consideration, the apparent motions of the sun, the moon, and the five planets known to the ancients, are most naturally explained by regarding the sun as the centre around which Mercury, Venus, the earth, Mars, Jupiter, and Saturn revolve in that order as to distance, while the moon revolves round the earth. For though there are thus two centres of motion, yet only a small body travelling in a relatively small orbit is set revolving round the earth, now presented as a subordinate orb in the system ; and the whole family, including the moon, are set revolving around the sun, for the moon accompanies the earth in her circuit. In the Tychonic system the sun, though presented as a subordinate orb, because travelling round the earth, was yet set as the centre round which all the planets revolved. Either system was, however, altogether more reasonable than the Ptolemaic, in which all the planets were supposed to move around imaginary centres. Copernicus well indicated the superiority of his system when he said, "We find in this arrangement what can be discerned in no other scheme, an admirable symmetry of the universe, an harmonious disposition of the orbits. For who could assign to the lamp of this beautiful temple a better position than the centre, whence alone it can illuminate all parts at once? Here the sun, as from a kingly throne, sways the family of orbs that circle around him."

It is hardly necessary to point out that the arrangement suggested by Copernicus explains the motions of the sun and moon as readily as the system which presents both these bodies as moving around the earth. Peculiarities in the motions of the earth and moon are indeed left unaccounted for by a simple theory of uniform circular motion around the sun and earth as centres; but so they were in the Ptolemaic system until eccentric and epicyclic movements were provided, and these were as admissible in the Copernican theory as in the Ptolemaic. It is easy to show also that the general motions of the planets their progressions, stations, retrogressions, &c. were explained by the Coper nican system. Thus, let S (fig. 20) be the sun, E^E , <kc., the earth s orbit, P^P.,, &c., part of the orbit of a superior planet ; and when the earth is at E 1 let the planet be at Pj, so that the planet is in opposition to the sun when at P r Starting from these positions, suppose that the earth and planet in the same interval of time pass over the arcs E,E 2 and P,?,, E^, being greater than P^. Then obviously E 2 P 2 is inclined to E^j ; and if these two lines are produced they will meet beyond P r Let them be pro duced beyond their point of intersection to K 1} K 2 respec tively ; then the observer on the earth sees the planet in direction EjKj when the earth is at E,, and in direction E 3 K a when the earth is at E.,. Hence the planet appears to have moved in direction KjK, or backwards, though it has really moved in direction PjP,. Carrying the earth on with her more rapid motion, it is obvious that we come to a part E 3 E 4 of the earth s orbit, where her motion is so inclined to the line of sight E 3 P 3 or E 4 P 4 to the planet, that the effect of the earth s more rapid motion is neutral ised, and these lines of sight are parallel. At this time, then, the planet neither seems to advance nor retrograde, but appears to be stationary. After this it is manifest that the planet will seem to advance, and with gradually increas ing rapidity, until when the earth is at E. and the planet at P s (the planet, however, being then in conjunction with the sun, and therefore invisible), the planet lies in direction E 3 P 6 far in advance of K u K 2 . At this time the unseen planet is advancing most rapidly, because the earth s motion, as from E 5 to E 6 , and the planet s motion, as from P 5 to P 6 , combine to cause the advance of the direction of the line E ri P 6 , the centre round which for the moment the direction-line to the planet is turning lying at between the earth and planet, instead of beyond the planet, as at O in the position first considered. Passing from conjunc tion to opposition, the planet goes through similar changes in a reverse order. Its progressive motion gradually diminishes, till it becomes stationary; thence the planet retrogrades through opposition t-o its next station ; and so on continually, the total result cf its motion in each synodical revolution being a progression from west to east. We see also that the planet is in opposition when in the middle of its retrograde arc, while it is in conjunction when in the middle of its larger arc of progression. All this corresponds precisely with the observed relations.

Fig. 20.—Diagram Illustrating Apparent Paths of Planets.

The same reasoning applies to the case of an inferior

planet. In fact, we may employ the same figure for this case as for that of a superior planet. Thus, suppose P^Pj (fig. 20) the earth s orbit, and E^.Ej, &c., that of an inferior planet, and let the motions be as in the former case, then the same lines represent the direction-lines, only the observer looks along these lines in the contrary direc tion. Now we see that the direction-lines P,E,, P 2 E 2 are carried backwards as viewed from P,, P n , until they reach the parallel positions P 3 Ej, P 4 E 4 , at which time the observer on P sees the planet E at a stationary point. After that the direction-lines are carried forward, until, when the earth is at P 5 and the interior planet at E 5 , this planet is seen in direction P 5 E J5 or far in advance of its former direction P^,. And at this time, as is seen by the posi tion of the lines P 5 E 5 and PgE^, the inferior planet is advancing most rapidly. In fact, all the motions of an inferior planet viewed from a superior one are precisely the same as those of the superior planet viewed from the inferior one, but are traced out on opposite parts of the heavens, a thesis which needs no other proof than the fact, that the line of sight from the inferior to the superior planet is also the line of sight from the superior to the inferior planet ; so that, whatever point the superior planet viewed from the inferior appears to occupy in the star- sphere at any moment, the point directly opposite is that

occupied by the inferior planet as viewed from the superior.