The first had to do with the supposed crystalline spheres that both Ptolemy and Copernicus—and everyone else—had believed to carry the planets around their orbital center (for Ptolemy, the Earth; for Copernicus, the Sun). No one before Kepler had thought of the planets as bodies moving through empty, or nearly empty, space (in fact, Kepler could not conceive of empty space and so assumed the existence of an “ether” through which the planets moved). For, as they said, what would move them? Why would they not fall into the Earth, or Sun, as center? Only if they were supported on the great transparent spheres that in their turn revolved around the center would the planets be held in their places in the cosmos. The crystalline spheres were thus necessary in order to “save the appearances.”
But they do not do that! wrote Kepler. In the first place, if there were such spheres, they would refract the light from the Fixed Stars—but we observe no such refraction. In the second place, the crystalline spheres of certain planets would at certain times have to intersect the crystalline spheres of other heavenly bodies—but how could this be? Finally, the hypothesis of the crystalline spheres is unnecessary—and that is the worst thing about it!
The second disagreement had to do with the supposed regular circular motions of the heavenly bodies (or their spheres). This too is incorrect, said Kepler. Assuming that the Moon, say, or Venus always moves at the same speed in a perfect circle around its center of revolution will never save the appearances. Instead, the planets—as bodies in space—move in elliptical rather than circular orbits around the Sun, which remains fixed at one focus of the ellipse. Nor do the planets always move at the same speed; the farther away from the Sun they are, the slower they move, and the closer, the faster. This assumption about elliptical orbits much simplified the computations of astronomers everywhere.
These two disagreements would have been in vain without a third. To the question, why do the planets move around the Earth (the Sun)? Ptolemy and Copernicus had given the same answer: because the planets are on great crystalline spheres that revolve around their center, and it is the natural movement of a sphere so to move. Kepler had discarded the spheres and also the regular circular motion. He needed something to replace them. In seeking it he came very close indeed to being the greatest astronomer who ever lived. He just missed it—that honor belongs to Newton.
Kepler supposed that there must be some sort of invisible, but still physical or material, relationship between the Sun and the planets such that the Sun causes the motion of the planets around itself. Taking his clue from Gilbert’s On the Lodestone, he realized that this relationship must be allied to the force that causes things on the Earth to fall, but he did not discover the simple inverse-square law of gravitation that is Newton’s glory. Instead, Kepler thought of the Sun’s light as somehow reaching out and sweeping the planets around in their elliptical orbits. It was a noble effort and all the more astonishing when you consider that Kepler had probably never looked through a telescope when he died in 1630.
Kepler’s Epitome comprises five books. Only the last two need to be read; the first three are Kepler’s homage to the memory of Copernicus. The fourth book discusses the motions of the heavenly bodies, viewed in a new way. The fifth book deals in more detail with the orbits of the planets and shows how these may be much more easily understood on the new assumptions.
These two last parts of the Epitome are not hard to read—Kepler himself did not approve of “boring demonstrations”—and they are fascinating. Kepler went so far and came so close, but he was unable to take the next steps that led to Newton and Einstein.
GALILEO GALILEI
1564–1642
Two New Sciences
Galileo Galilei was born in Pisa in 1564, the son of a mathematician and musician who had had bitter experience of the impecunious nature of both those professions. He therefore determined to make of his son a doctor and sent him to the University of Pisa to study medicine. But Galileo, sitting in the chapel one day in 1581, began to notice a certain lamp that hung from the ceiling and was swinging in the wind. The wind blew harder and softer and the lamp swung through longer and through shorter arcs—but, Galileo observed, the time it took to swing through its arcs was always the same. At the age of seventeen he had discovered, without at the time naming it, the isochronicity of the pendulum (he later worked out its use in clocks) and, what is more, had become hooked on mathematical physics.
Indeed, he had discovered mathematical physics. Until his day, mathematics and nature were held to have no connection; mathematics was philosophical speculation and had no basis in reality. Galileo was the first man to put them together, to declare, as he did in one of his works, Saggiatore, that the “book of Nature is …written in mathematical characters.”
Galileo’s mathematical bent was confirmed, and his reputation made, soon after the episode of the lamp when he disproved Aristotle’s ancient dictum that heavy bodies fall faster than light ones. At twenty-five he managed to obtain a position that supported his scientific researches. He taught mathematics first at Pisa, then at Padua, from 1592 to 1610, where he was a popular lecturer.
In 1609 he learned of experiments being conducted by Dutch lens makers to construct a telescope, and he immediately sent for information. He combined the lenses as directed by them but was disappointed in the result. He soon saw what the trouble was, corrected it, and produced a telescope having ten times the magnifying power of any other. That very night he took it outdoors and pointed it at the Moon. The surface of the Moon, he discovered, was not smooth but rough and pitted; there were mountains and valleys just as on Earth. This was extraordinary. Everyone believed that the heavenly bodies were made out of a special stuff, the quintessence, which was immutable. But the surface of the Moon as seen through Galileo’s telescope showed clear signs of having changed, as the Earth’s surface changes. Aristotle, Galileo concluded, was wrong again.
The battle between Galileo and the Aristotelians continued throughout his life. His discoveries with the telescope confirmed Galileo in his belief that the Copernican hypothesis, that the Sun and not the Earth is the center of the solar system, was not just a hypothesis but was true, and in several works he defended this position. The Aristotelian teachers complained to the Inquisition, which recognized the danger in a man who did not care where truth led him. Galileo was tried, convicted, and forced to recant. The picture of the greatest living scientist being forced to declare in public that everything he knew to be true was false, and that he had been foolish to believe it, is terrifying. It is one of the worst things the Church of Rome ever did, and even a number of Galileo’s clerical friends believed his condemnation inexcusable.
Galileo’s completed Two New Sciences in 1634, only a few months after his trial and condemnation. He had been confined to his house, where he remained for the rest of his life, but he never stopped working and experimenting, and writing. Two New Sciences has the surprising form of a conversation among three persons, one of whom represents Galileo himself, a second the intelligent layman, and a third—Simplicio—the naive common man. The two sciences, on which Galileo had worked throughout his life, are statics and dynamics, and together they comprise what was known of mechanics in the early seventeenth century. The book presents many new and surprising theorems, and the dialogue form turns out to be an effective way of explicating them.