Dynamics Enters Astronomy: From Galileo to Newton

Abstract

We have seen how Galileo, the physicist, described the free fall of bodies and suggested the possibility of the existence of inertia. Clearly, through his experiments, Galileo was one of the founders of modern mechanics. However, the situation was far from simple. Galileo did indeed succeed in describing motion in a way which approached a mathematical description of the kinetic reality. Nonetheless, Galileo, in his effort to arrive at a complete explanation, to actually build a dynamic model of the observed kinematics, was often unsuccessful. His basic principle of a proportionality between the velocity of the moving body and the path already covered was obviously wrong, although it was almost true in a small number of cases, such as that of the almost uniform motion of slowly falling bodies. The truth, expressed in our mathematical language, is that in the uniformly accelerated motion (γ = constant), the velocity v is equal to K (t−t₀) hence the acceleration γ (the derivative of u with respect to time t) is constant, equal to K. Galileo would have written υ = K (x−x₀); hence γ = Kυ (υ being the derivative of space with respect to time t), which is clearly wrong! Note that the constant K is, in the case of falling bodies, the acceleration of weight. If one attributes this acceleration to a force f, this force is equal to mγ, where m represents the inertial mass of the quantity of matter put in an accelerated motion. This is the way Galileo’s experiments were expressed, not by him but later, notably by Newton.