77. The discussion of the possibility that the earth may move, and may even have more than one motion, then follows, and is more satisfactory though by no means conclusive. Coppernicus has a firm grasp of the principle, which Aristotle had also enunciated, sometimes known as that of relative motion, which he states somewhat as follows:—
“For all change in position which is seen is due to a motion either of the observer or of the thing looked at, or to changes in the position of both, provided that these are different. For when things are moved equally relatively to the same things, no motion is perceived, as between the object seen and the observer.”[49]
Coppernicus gives no proof of this principle, regarding it probably as sufficiently obvious, when once stated, to the mathematicians and astronomers for whom he was writing. It is, however, so fundamental that it may be worth while to discuss it a little more fully.
Fig. 37.—Relative motion.
Let, for example, the observer be at A and an object at B, then whether the object move from B to B′, the observer remaining at rest, or the observer move an equal distance in the opposite direction, from A to A′, the object remaining at rest, the effect is to the eye exactly the same, since in either case the distance between the observer and object and the direction in which the object is seen, represented in the first case by A B′ and in the second by A′ B, are the same.
Thus if in the course of a year either the sun passes successively through the positions A, B, C, D (fig. 38), the earth remaining at rest at E, or if the sun is at rest and the earth passes successively through the positions a, b, c, d, at the corresponding times, the sun remaining at rest at S, exactly the same effect is produced on the eye, provided that the lines a S, b S, c S, d S are, as in the figure, equal in length and parallel in direction to E A, E B, E C, E D respectively. The same being true of intermediate points, exactly the same apparent effect is produced whether the sun describe the circle A B C D, or the earth describe at the same rate the equal circle a b c d. It will be noticed further that, although the corresponding motions in the two cases are at the same times in opposite directions (as at A and a), yet each circle as a whole is described, as indicated by the arrowheads, in the same direction (contrary to that of the motion of the hands of a clock, in the figures given). It follows in the same sort of way that an apparent motion (as of a planet) may be explained as due partially to the motion of the object, partially to that of the observer.
