calculations of phenomena could be made, not a physical explanation based on mechanical laws.
The problems relating to the motions of the heavenly bodies are more complex and must be considered somewhat in detail. It is necessary to describe the observed phenomena for each body separately, and to adopt a system which will explain every phenomenon and appearance in turn.
The Moon.—The facts of observation, familiar to us all, are that the new moon sets in the west about sunset, and that on every succeeding night the moon sets at a later hour. It, therefore, moves to the east among the stars from night to night, which can readily be verified by observation. If the moon is near the stars of Orion on one night, it will be found many degrees to the east of them on the night following. It sets later and later every night throughout the month. If it is in the same longitude as the stars of Orion on any one day, it will be again in that longitude about a month (27 days) later (more exactly, 27d 7h 43m 11s.5). It has moved through the whole circuit of the heavens, 360°, in 27 days. Ptolemy explained the phenomena, as we explain them to-day, by asserting that the moon revolves in an orbit, about the earth as a center, making a complete revolution among the stars (from one star back to the same star again) in 27 days. Its motion among the stars is always forward—always from west to east.
The Sun.—The observed phenomena with regard to the sun are of the same nature. If the sun rises at the same time as the bright star Sirius on a particular day of the year, on the next day it will rise later than Sirius. It has, therefore, moved a certain distance (about one degree) eastwardly during that day. On the next following day it will have moved about two degrees east of Sirius and will rise correspondingly later; and so on for each succeeding day. After 180 days (six months) the sun will have moved about 180 degrees to the east of Sirius. Sirius will be visible on the meridian at midnight, (when the sun is 180° away from the meridian). At the end of 365 days (more exactly, 365.2564 days) the sun will have moved eastward through 360° and will again rise at the same moment as Sirius. The sun, then, appears to move eastwardly among the stars (from one star back to the same star again) once in 3651⁄4 days. At different times of the year it is among different groups of stars, and it is for this reason, therefore, that we see different groups of stars at different seasons of the year. Orion is visible in the winter skies, Scorpio in the summer, because Orion and Scorpio are 180 degrees apart in longitude. Ptolemy's explanation of all these phenomena is that the sun moves about the earth in a circular orbit at such a rate as to make a complete revolution in 3651⁄4 days. The explanation of Copernicus is that the earth revolves about the sun in the same period.
