Galileo Galilei (1564-1642) | A Particle in Motion...Galileo's Life | The Parabolic Path...A Modern View
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The Parabolic Path...Galileo's View
Vincent W. Lau

The modern view of projectile motion requires one to study modern concepts such as velocity and acceleration. The irony is that Galileo himself is responsible for these ``modern'' concepts. So by studying how we explain projectile motion today, we are really studying Galileo's explanation as well. What is of interest, though, is how Galileo came to the conclusions that we study today.

Galileo exposed the world to his physical findings in a book entitled Dialogues Concerning Two New Sciences. In this book, Galileo had three characters (Salviati, Sagredo and Simplicio) discuss his findings with each other. This method of indirectly teaching through the dialogue of characters allowed Galileo to shed some of the responsibilty of his findings. This was the time of great church influence in all aspects of European life. As Galileo would have surely known, those who dared to expound ideas contrary to Church held beliefs were ridiculed and punished.

In Two New Sciences, Galileo begins his examination of falling objects by discussing the drawing of parabolas.

Sagredo: ...a fine thing if you were able to give some quick and easy rule by which a mechanician might draw a parabola upon a plane surface?

Salviati: There are many ways of tracing curves; I will mention merely the two which are the quickest of all. One of these is really remarkable... I take a perfectly round brass ball about the size of a walnut and project it along the surface of a metallic mirror held in a nearly upright position, so that the ball in its motion will press slightly upon the mirror and trace out a fine sharp parabolic line; this parabola will grow longer and narrower as the angle of elevation increases.

What is interesting is the conclusion that Galileo draws from his simple, yet effective, method of drawing parabolas above:

Salviati: ...[the] experiment furnished clear and tangible evidence that the path of a projectile is a parabola.

In the Fourth Day (chapter) of Two New Sciences, Galileo returns to the discussion above to lay down the scientific groundwork for the proof of a projectile's motion. As Galileo explains in the introduction of the Fourth Day:

Imagine any particle projected along a horizontal plane without friction; then we know...that this particle will move along this same plane with a motion that is uniform and perpetual [constant velocity with no acceleration], provided the plane has no limits. But if the plane is limited and elevated, then the moving particle...will on passing over the edge of the plane acquire, in addition to its previous uniform and perpetual motion, a downward propensity due to its own weight [gravity]; so that the resulting motion which I call projection, is compounded of one which is uniform and horizontal and of another which is vertical and naturally accelerated [which is the same as our results in Eqns. (6), (7), (8) and (9)].

The statement above is just a wordy version of the equations obtained in the previous section. Galileo puts it all together and what results is the theorem we have spent our time discussing:

Theorem 1 : A projectile which is carried by a uniform horizontal motion compounded with a naturally accelerated vertical motion describes a path which is a semi-parabola.

It is amazing that Galileo, through experiment, found this result that we still use and teach today. We are fortunate to have been allowed to reap the rewards of his genius, and although Galileo is best known for his work in astronomy, we must be grateful that he chose to lead us onto the right path in physics.

Galileo Galilei (1564-1642) | A Particle in Motion...Galileo's Life | The Parabolic Path...A Modern View
The Parabolic Path...Galileo's View | References | Back to the front page