astronomersrefused to look through Galileo’s telescope when it seemed to reveal things that contradicted Ptolemy, Ptolemy himself did not ignore “what can be seen up there” in favor of some mathematical fable. He would have looked through Galileo’s telescope. However, nothing about the appearance of the heavens, as Ptolemy and his predecessors were able to study them, forced them or him to reject the intellectualtradition that held that all heavenly movement occurred in perfect circles and spheres.
The “spheres” were not the planets themselves, but transparent glass spheres in which the planets traveled. Astronomers spoke of “crystalline” spheres, each having an inner and an outer wall, with space between the two walls for the planet to move. The spheres were nested one within the other, with eachsuccessive sphere just small enough to fit within the one outside it. They were tightly packed with no extra space left between them, but not so tightly as to prevent their moving, one against the other, with the outer surface of one sphere scraping against the inner surface of the next larger.
Sitting at the center of this system of nested crystalline spheres was Earth. The outermost spherein the arrangement was the sphere of the stars. The innermost sphere—nearest Earth—was the sphere in which the Moon moved. The others each contained a planet, except for the one that contained the Sun. Each body could move only between the outer and inner walls of its own sphere. Not all scholars agreed about the nature and mechanics of these spheres, but there was general agreement that a planetcouldn’t break through those walls and enter another planet’s sphere. In fact, in this system,
no
heavenly body could break through the walls of a sphere. That would shatter it. This last restriction became significant for Tycho Brahe and Johannes Kepler.
One of the most stubborn problems for ancient astronomers was how to explain a phenomenon known as the “retrograde” movement of the planets.A planet normally moves from west to east against the background of stars. However, during a period known as its “opposition,” when it is on the opposite side of Earth from the Sun, a planet appears for a while to move from east to west. Scholars were faced with the problem of explaining this in a model that required uniform movement and perfect circles and spheres. The solution, devised beforePtolemy, was ingenious.
Figure 1.1: Early astronomers thought of the planets and the Sun and Moon as each moving in its own “crystalline” sphere (a), with these spheres nested one within the other and Earth at the center (b).
A carousel is a helpful analogy for understanding the idea: On the simplest carousel, the horses are bolted directly to the floor, which is a large, rotating disk. They circle, as the diskrotates, but they have no other motion. If the amusement park is dark and there is a light attached to the head of one horse, an observer, positioned at the center of the carousel in such way as not to move with the rotating disk, sees the light circle steadily. It will have no “retrograde motion”—never seem to back up.
Suppose instead that the observer does occasionally see the light stop,back up for a while, and then resume its former motion. This isn’t a random occurrence, as it might be if the light were on the cap of the ticket taker as he moves among the riders, or if a large firefly happened to venture into the carousel. The backing up happens regularly and predictably. The observer decides that the horse with the light on its head must not be bolted directly to the rotatingdisk. Instead, each horse is part of a minicarousel perched near the edge of that disk. Hence, in addition to their motion with the disk, the horses are moving around in smaller circles, chasing their tails.
Figure 1.2: On this carousel the horses are attached to smaller rotating disks that ride on the perimeter of the large, rotating floor. As