June 27, 2016

Galileo

Galileo and the Pisa Tower (around 1600)

Galileo did not release different objects from the top of the Pisa Tower, but he analyzed this fall from a theoretical point of view and suggested other ways of comparing falling bodies.

Galileo has said repeatedly that all falling bodies have the same motion (as long as air resistance is negligible) in the Earth’s gravitational field. Did he carry out the experiment from the Tower of Pisa, where he supposedly checked that two different bodies fall at the same speed? He talked a lot about this experiment and studied the effect of friction on movement, which proves that he was aware of the main issues of this experiment. However, he probably did not conduct the experiment as he knew its accuracy to be insufficient at the time. To test the validity of the universality of free fall, Galileo proposed alternatives based on fine analysis of the accelerated movement of mobile bodies and on pendulums swings.

Portrait of Galileo
Portrait of Galileo painted by Ottavio Leoni.

pendulums beat time (1638)

Galileo used pendulums to compare the movement of bodies of different natures

Galileo knew that the universality of free fall would be difficult to check owing to frictions, which is why he sought alternatives to dropping objects from a height. At first, as the potential difference between two different objects was probably weak, he suggested to conduct short falls, so as to add several times the short gap between the arrivals of the two bodies. As a consequence, the total time gap would be easily noticeable. Then, he minimized friction by selecting very slow movements, such as inclined planes. He went even further when he proposed a practical test on which were based all subsequent tests for the three following centuries: he compared the number of oscillations of two pendulums. He did not observe any difference as he wrote “coincidence is such that whether one thousand swings or on one hundred, the first is not ahead of the other in the slightest way”. It was the first test of the equivalence principle whose relative accuracy could be estimated at 10-2.

Galileo Pendulum
Reconstitution of the pendulums used by Galileo. On the left, four pendulums with different spheres were used to check the isochronism of the pendulums. On the right, pendulums of variable lengths allowed to link the period of oscillation of a pendulum and its length.