Fig. 14.—The apparent motion of a planet.
27. A typical case of planetary motion.—The Copernican theory, enormously extended and developed through the Newtonian law of gravitation (see [Chapter IV]), has completely supplanted the older Ptolemaic doctrine, and an illustration of the simple manner in which it accounts for the apparently complicated motions of a planet among the stars is found in Figs. [14] and [15], the first of which represents the apparent motion of the planet Mars through the constellations Aries and Pisces during the latter part of the year 1894, while the second shows the true motions of Mars and the earth in their orbits about the sun during the same period. The straight line in [Fig. 14], with cross ruling upon it, is a part of the ecliptic, and the numbers placed opposite it represent the distance, in degrees, from the vernal equinox. In [Fig. 15] the straight line represents the direction from the sun toward the vernal equinox, and the angle which this line makes with the line joining earth and sun is called the earth's longitude. The imaginary line joining the earth and sun is called the earth's radius vector, and the pupil should note that the longitude and length of the radius vector taken together show the direction and distance of the earth from the sun—i. e., they fix the relative positions of the two bodies. The same is nearly true for Mars and would be wholly true if the orbit of Mars lay in the same plane with that of the earth. How does [Fig. 14] show that the orbit of Mars does not lie exactly in the same plane with the orbit of the earth?
Exercise 13.—Find from [Fig. 15] what ought to have been the apparent course of Mars among the stars during the period shown in the two figures, and compare what you find with [Fig. 14]. The apparent position of Mars among the stars is merely its direction from the earth, and this direction is represented in [Fig. 14] by the distance of the planet from the ecliptic and by its longitude.
Fig. 15.—The real motion of a planet.
The longitude of Mars for each date can be found from [Fig. 15] by measuring the angle between the straight line S V and the line drawn from the earth to Mars. Thus for October 12th we may find with the protractor that the angle between the line S V and the line joining the earth to Mars is a little more than 30°, and in [Fig. 14] the position of Mars for this date is shown nearly opposite the cross line corresponding to 30° on the ecliptic. Just how far below the ecliptic this position of Mars should fall can not be told from [Fig. 15], which from necessity is constructed as if the orbits of Mars and the earth lay in the same plane, and Mars in this case would always appear to stand exactly on the ecliptic and to oscillate back and forth as shown in [Fig. 14], but without the up-and-down motion there shown. In this way plot in [Fig. 14] the longitudes of Mars as seen from the earth for other dates and observe how the forward motion of the two planets in their orbits accounts for the apparently capricious motion of Mars to and fro among the stars.
