How Did Galileo Contribute to Physics?
Galileo's physics: the law of falling bodies, the parabolic trajectory, inclined plane experiments, the principle of inertia, and the Two New Sciences.
How Did Galileo Contribute to Physics?
The work for which Galileo is best known in the popular imagination is the telescopic discoveries of 1610. The work for which he is best known among historians of science is something different: the establishment of the science of motion. The two bodies of work are related, of course. The telescopic observations destroyed the Aristotelian cosmology, and the work on motion destroyed the Aristotelian physics. Together, they cleared the ground on which Newton would build. This page looks at Galileo’s contributions to physics: the law of falling bodies, the parabolic trajectory of projectiles, the inclined plane experiments, the principle of inertia, and the Two New Sciences of 1638. The astronomical work is treated in What Did Galileo Discover With His Telescope?. The biographical context is on the Galileo page. The longer-term influence on Newton is described in What Is in Newton’s Principia Mathematica? and in The Laws of Motion and Gravity.
The Aristotelian Physics That Galileo Attacked
To understand what Galileo did, it helps to see the system he was attacking. The Aristotelian physics, which dominated the European universities well into the seventeenth century, was a sophisticated system that integrated the motion of bodies on Earth with the motion of the heavens. The system rested on four kinds of “natural” motion: heavy bodies (those made mostly of the element earth) naturally moved downward, toward the center of the universe; light bodies (those made mostly of fire) naturally moved upward, away from the center; celestial bodies (made of the fifth element) naturally moved in circles around the center; and “violent” motion, like the motion of a thrown stone, was motion contrary to nature, imposed by a mover in direct contact with the moving body. The Aristotelian system could explain a great deal. It could explain why a stone falls, why a flame rises, why the Moon orbits the Earth, and why a thrown stone eventually stops. It also made several specific predictions that could be tested: heavier bodies should fall faster than lighter ones, in proportion to their weight; a body in motion should come to rest as soon as the force moving it is removed; the motion of a projectile should be a compound of an initial violent motion and a natural motion toward the center, resulting in a curve that approaches the ground asymptotically. The system was, however, vulnerable on a number of points. The most embarrassing was the question of what keeps a projectile moving after it has left the thrower’s hand. Aristotle had suggested that the air, displaced by the projectile, rushes around behind it and pushes it forward; this was not a good explanation, and it had been criticized since antiquity. Galileo attacked it in his Two New Sciences. Other points of vulnerability included the absence of any clear account of the speed of falling bodies (had anyone measured it?), and the failure of the system to give precise predictions for the trajectories of projectiles.
The Law of Falling Bodies
The most famous of Galileo’s contributions is the law of falling bodies: that the distance fallen by a body starting from rest is proportional to the square of the time of fall, d = ½ at², where a is the acceleration due to gravity. The law holds, in a vacuum, for all bodies regardless of their weight. (In air, the law is modified by air resistance, and light bodies do fall more slowly than heavy ones, as a consequence of buoyancy and drag.) Galileo did not, in the famous story, drop two different weights from the Leaning Tower of Pisa. The story is almost certainly apocryphal. What Galileo did do was a series of experiments with inclined planes, in which he rolled bronze balls down a smooth groove cut into a wooden beam, and measured the distances and times of the rolling. To measure the times accurately, he used a water clock: a large vessel of water, with a small pipe at the bottom, was arranged so that the water flowing out during a run could be collected and weighed. The weight of the water was proportional to the time. The inclined plane had two advantages over a free-fall experiment. First, it slowed the motion, making the times easier to measure. Second, by varying the inclination of the plane, Galileo could test his conjecture that the speed gained by a body rolling down a plane of a given height was the same, regardless of the inclination. This was, in effect, the principle that the speed of a falling body depends only on the height of fall, not on the path. It was a version of what be called the conservation of energy, and it was a key step in the analysis of motion. The results of these experiments, published in the Two New Sciences (1638), showed clearly that the distance traveled was proportional to the square of the time, as the law predicts. The same law held for a wide range of inclinations and weights of the rolling body. Galileo concluded that the law held for free fall as well, and that, contrary to Aristotle, all bodies fall with the same acceleration, regardless of their weight.
The Parabolic Trajectory
A second major contribution was the parabolic trajectory of projectiles. Galileo argued, in the Two New Sciences and in the Dialogue Concerning the Two Chief World Systems, that the motion of a projectile is composed of two independent motions: a uniform horizontal motion (in the direction of the initial throw) and a uniformly accelerated vertical motion (in the direction of gravity). The two motions, superposed, give a parabola. The argument was the first clear application of the principle of superposition of motions, which would become central to Newtonian mechanics. It also gave a precise mathematical description of projectile trajectories that was of immediate practical use. Military engineers could use Galileo’s results to design better artillery; indeed, Galileo himself had written on ballistics earlier in his career, in a treatise titled Le mecaniche (c. 1600) and in his work on the geometric and military compass. The parabolic trajectory was, in addition, an argument against the Aristotelian physics. The Aristotelian account of projectile motion was, as noted, a mess. The superposed horizontal and vertical motions gave a clean, simple, mathematically tractable account, and they fit the experimental data. The contrast with Aristotle was a one-sided contest.
The Inclined Plane and the Principle of Inertia
A third contribution, related to the law of falling bodies, was the principle of inertia, or something close to it. In the Two New Sciences, Galileo asked what would happen to a body sliding on a smooth horizontal surface, with no friction. He argued, on the basis of his inclined plane experiments, that the body would continue to slide forever, at a constant speed. The horizontal surface, in the absence of friction, offered no resistance to motion. The only thing that would stop a body in motion, in the absence of friction, was the resistance of the medium through which it moved. This is not, in so many words, Newton’s first law of motion — that every body continues in a state of rest or of uniform motion in a straight line, unless compelled to change that state by impressed forces. But it is a clear step toward it. Galileo, in the Two New Sciences, did not quite state the principle in its full generality. He did not, for instance, explicitly deny that the natural motion of bodies in the absence of external forces is circular. (He seems to have retained some of the older prejudice that circular motion is more “perfect” than straight-line motion.) But the principle that a body in motion stays in motion, in the absence of resistance, was, in Galileo’s work, clear enough to be taken up by Descartes and Huygens and, eventually, Newton.
The Two New Sciences (1638)
The full expression of Galileo’s mature work on physics is the Discorsi e dimostrazioni matematiche intorno a due nuove scienze — the Discourses and Mathematical Demonstrations Concerning Two New Sciences — published in 1638 in Leiden. The book is structured as a conversation among the same three characters as the Dialogue: Salviati, Sagredo, and Simplicio. It is divided into four “days,” the first three of which treat the strength of materials and the resistance of solids to fracture, and the fourth of which treats the motion of projectiles and uniformly accelerated motion. The “two new sciences” of the title are the science of strength of materials (the “first new science”) and the science of motion (the “second new science”). The first is the first systematic treatment of what be called engineering mechanics. Galileo asked why beams break, and he gave an answer in terms of the cohesive strength of the material and the geometry of the loading. He derived the now-familiar result that the strength of a beam, for a given material, is proportional to the cross-sectional area and inversely proportional to the length. The result was important for engineers, shipbuilders, and architects, and it was the foundation of a long tradition of work on the strength of materials. The second science — the science of motion — was more philosophical. It set out the law of falling bodies, the parabolic trajectory, the inclined plane experiments, and the principle of inertia. It was, in essence, the foundation of classical kinematics. The book’s debt to Archimedes is conspicuous, particularly in the treatment of solids in equilibrium. The book is also striking for its literary qualities. Galileo wrote in a clear, vigorous Italian, with dialogue that brings the abstract arguments to life. The book was widely read across Europe, and it had a formative influence on the natural philosophers of the next generation.
Galileo’s Method
Galileo’s contributions to physics are inseparable from his method. He was, in his own way, the first systematic practitioner of the combination of experiment and mathematical analysis that would become the prototype of natural philosophy in the seventeenth century. He did not run controlled experiments in the modern sense — he did not, for instance, isolate variables, vary them one at a time, and average over many trials. But he did use experiment, both real and imagined, to test his mathematical hypotheses. He did argue from the experiments to general principles, and from the principles to predictions. He did insist on the priority of mathematics in the description of natural phenomena. And he did defend the new approach in a series of brilliant polemical works that established it, in the eyes of the European reading public, as a serious competitor to the Aristotelian tradition. The combination of empirical detail, mathematical argument, and aggressive public defense is the inheritance of modern science, and Galileo is its prototype. The fact that the method is not, in the strictest sense, the method that we now use does not diminish the achievement. The fact that the law of falling bodies was first stated as d ∝ t² and not as d = ½gt² (the constant of proportionality was not measured accurately) is, similarly, a sign of how much remained to be done. But the broad shape of the work — the use of experiment to test mathematical claims about motion — was new, and it was Galileo’s.
The Long-term Influence
The immediate influence of Galileo’s work on motion was, less than one might expect. The Two New Sciences was published in 1638, when Galileo was seventy-four and under house arrest, and it circulated mostly in manuscript form for some time. Descartes, who workeding on his own mechanical philosophy in Holland, engaged with Galileo’s ideas but disagreed with some of his conclusions. The French Jesuits in the colleges were slow to adopt the new physics. In Italy, the Aristotelian tradition held on in the universities for decades. however, the influence of the Two New Sciences was enormous. The book was the most important source for Newton’s work on motion, and Newton’s debt to Galileo is explicit in the Principia. Newton’s first law, in particular, is a direct descendant of the principle of inertia that Galileo had stated, almost. The second law — that the change of motion is proportional to the impressed force — is a generalization of Galileo’s analysis of falling bodies. The third law — that action and reaction are equal and opposite — was not in Galileo, but the analytical framework that made it possible was. The full reception of Galileo’s work, and its incorporation into the Newtonian synthesis, is the central narrative of the Newton page and of What Is in Newton’s Principia Mathematica?. The empirical content of Newton’s laws is treated in The Laws of Motion and Gravity. The relationship between the Galilean and Newtonian physics is one of the great stories in this history.