10.1.1—
Copernicus, Galileo, Newton

The emergence of the "new science" of the sixteenth and seventeenth centuries is sometimes referred to under the heading of the "Copernican revolution" in physics. And it is true that Copernicus played a crucial role in starting a conceptual revolution in astronomy that paved the way for the development of what was to become Newtonian mechanics. It is important to see, however, that Copernican astronomy in its own right is only the first step towards a mature physics.^[2] Copernicus's own concerns were still largely those of an astronomer . He was concerned with finding a description of planetary motion. His own model of that motion, however, was highly influenced by his Ptolemaic predecessors: a system of circular orbits and epicycles around a point close to the sun.^[3] (The sun was not at the center of Copernicus's system; it, like the planets, orbited another point in space. It is also worth noting that Copernicus's model contained more epicycles than Ptolemy's. The virtue of this model lay neither in its elegance nor in its predictive accuracy [see Kuhn 1957: 169-171].) Kepler, by contrast, was engaged in a project of finding a kind of mathematical description of planetary motion that would at once be elegant and exact. One important breakthrough—the one we probably imprinted upon when we learned about the progress of modern physics—was Kepler's discovery of the fact that planetary orbits are elliptical and that orbital speed can be determined on the basis of the area of the ellipse subtended by a portion of the orbit.^[4] But when we learned this, we probably overlooked what was really important about this discovery. The fact that orbits take the form of an ellipse rather than some other conic form is really irrelevant to the progress of physics. What is crucially important is that the motions of the planets can be described exactly by mathematical expressions, regardless of which ones, and that they can all be described by the same kinds of expressions.^[5] Physics would have done just as well if planetary orbits had been of a different, yet precisely describable shape. Celestial mechanics would have gotten nowhere so long as the only descriptions of planetary motion were in terms of a motley batch of epicycles having no discernible overarching pattern.

The further progress of modern physics was facilitated by the emergence of two other mathematical innovations: the development of algebraic geometry allowed for the possibility of performing algebraic cal-

culations upon the motions of the planets through time, and the calculus provided for the possibility of making calculations about acceleration. The culmination of these advances was Newtonian mechanics, which summarized the interactions of gravitational bodies in a set of extremely elegant mathematical equations that came to be known as "Newton's laws." Newtonian mechanics unified the fields of astronomy, celestial mechanics, and sublunary physics under one set of mathematical descriptions, and stood as the standard for scientific theories until displaced by relativity theory (which was, itself, dependent upon the development of differential geometry for its descriptions of space and time).

It is worth emphasizing that Newton's achievement lies in his having left us a rigorous and general description of the effects of gravitational bodies upon one another. His ambivalent attempts to address the why of gravity (his much-discussed flirtation with "forces") add nothing to the picture, and his failure to solve the "why" of gravity detracts not in the least from the power and the utility of Newtonian mechanics.^[6] One might well suspect that gravity amounts to something more than the empirical regularities of how bodies move in relation to one another, and it is appealing to seek some insight into this "something more," but such insight is not needed in order to make Newtonian mechanics "good science."

In brief, Newtonian mechanics provides for the mathematical maturity of a large portion of physics without providing any microexplanation for gravitational attraction in terms of some subgravitational level of explanation. Gravitation is treated as fundamental . And the lack of such an explanatory connection is not generally viewed as a fatal objection to Newtonian mechanics as good science, even though it is in some ways dissatisfying. Moreover, it displaced a Cartesian physics which did offer a microexplanation of gravitation in terms of mechanical interactions of particles.^[7]