Page:Popular Science Monthly Volume 64.djvu/334

It is to be noted that either of these explanations will completely account for all the observed phenomena.

New moon occurs when the earth, moon and sun are in a straight line. At sunset the new moon is seen in the west. After 27 days the moon has made one circuit among the stars, moving from west to east. But in those 27 days the sun has likewise moved eastwardly, about 27 degrees. The moon, then, has to make one circuit and a little more in order to be again in the line joining the earth and sun, in order to be again 'new.' The time from one new moon to the next—the lunar month—is about 29¹⁄₂ days (more exactly 29^d 12^h 55^m 2^s.9) for this reason. Just as there is a difference between the moon's sidereal and synodic period, so there is a corresponding difference between the sidereal and tropical year, because the equinoctial points are in motion relatively to the stars.

The Superior Planets.—In the system of Ptolemy, Mars, Jupiter and Saturn were supposed to be further from the earth than the sun—to be above it—and they were, therefore, called superior planets; while Mercury and Venus were called inferior planets. The facts of observations for one of the superior planets, for Mars, for example, are as follows. If on any day Mars rises at the same time as Sirius, on the next day it will rise a little later, and so on. The planet, therefore, moves eastwardly among the stars. It continues its motion so that at the end of 687 days (1.88 years) the planet again rises at the same time as Sirius. It has therefore made a complete circuit of the sky (from one star back to the same star again) in a little less than two years. Its orbit was supposed by Ptolemy to be a circle (the deferent) about the earth like the sun's orbit. In like manner Jupiter makes a revolution in 4,333 days (11.86 years), and Saturn in 10,759 days (29.46 years). Such are the general motions of the three superior planets; but there are irregularities in their motions that must be accounted for.

For example, the actual motion of the planet Jupiter among the stars for the year 1897 is as follows: Beginning on October 28, 1897, the planet's motion is eastwards until January 22, 1898; here it turns and moves westwards until May 28; here, again, it turns and moves eastwards and its direct motion continues for the rest of its period of nearly twelve years. Ptolemy accounted for the irregularities of motion just described by supposing that Jupiter revolved in a small circular orbit—the epicycle—once in 365 days, while, at the same time, the center of the epicycle moved along the circumference of the deferent circle, making a complete revolution in about twelve years.

As time elapses the center of Jupiter's epicycle will move onwards on the deferent while Jupiter will move onwards in its epicycle. The combination of these two motions will produce a direct motion of the planet. After Jupiter has moved through a quarter of a circumference on its epicycle the planet will appear to the observer on the earth to move in a retrograde direction, because it will move to the right or left on its epicycle faster than the center of the