Galileo's Leaning Tower of Pisa experiment

Between 1589 and 1592,[1] the Italian scientist Galileo Galilei (then professor of mathematics at the University of Pisa) is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass, according to a biography by Galileo's pupil Vincenzo Viviani, composed in 1654 and published in 1717.[2][3]:19–21[4][5]

According to the story, Galileo discovered through this experiment that the objects fell with the same acceleration, proving his prediction true, while at the same time disproving Aristotle's theory of gravity (which states that objects fall at speed proportional to their mass). Most historians consider it to have been a thought experiment rather than a physical test.[6]

Galileo's experiment

At the time when Viviani asserts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He had, however, formulated an earlier version which predicted that bodies of the same material falling through the same medium would fall at the same speed.[3]:20 This was contrary to what Aristotle had taught: that heavy objects fall faster than the lighter ones,and in direct proportion to their weight.[3]:9[7] While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is accepted by most historians that it was a thought experiment which did not actually take place.[8][9] An exception is Stillman Drake, who argues that it took place, more or less as Viviani described it, as a demonstration for students.[3]:19–21, 414–416

Galileo set out his ideas about falling bodies, and about projectiles in general, in his book Two New Sciences. The two sciences were the science of motion, which became the foundation-stone of physics, and the science of materials and construction, an important contribution to engineering. Galileo arrived at his hypothesis by a famous thought experiment outlined in his book On Motion.[10] This experiment runs as follows: Imagine two objects, one light and one heavier than the other one, are connected to each other by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter object retards the fall of the heavier object. But the system considered as a whole is heavier than the heavy object alone, and therefore should fall faster. This contradiction leads one to conclude the assumption is false.
Other performances
The Nieuwe Kerk in Delft, where the experiment by Stevin and de Groot took place

A similar experiment took place some years earlier in Delft in the Netherlands, when the mathematician and physicist Simon Stevin and Jan Cornets de Groot (the father of Hugo de Groot) conducted the experiment from the top of the Nieuwe Kerk. The experiment is described in Simon Stevin's 1586 book De Beghinselen der Weeghconst (The Principles of Statics), a landmark book on statics:

Let us take (as the highly educated Jan Cornets de Groot, the diligent researcher of the mysteries of Nature, and I have done) two balls of lead, the one ten times bigger and heavier than the other, and let them drop together from 30 feet high, and it will show, that the lightest ball is not ten times longer under way than the heaviest, but they fall together at the same time on the ground. (...) This proves that Aristotle is wrong.[11][12][13]

File:Apollo 15 feather and hammer drop.ogvPlay media
Hammer and Feather Drop by astronaut David Scott, Apollo 15 (1.38 MB, ogg/Theora format)

Astronaut David Scott performed a version of the experiment on the Moon during the Apollo 15 mission in 1971, dropping a feather and a hammer from his hands. Because of the negligible lunar atmosphere, there was no drag on the feather, which hit the ground at the same time as the hammer.
See also

Terminal velocity (An object dropped through air from a sufficient height will reach a steady speed, called the terminal velocity, when the aerodynamic drag force pushing up on the body balances the gravitational force (weight) pulling the body down.)
Nordtvedt effect
Newton's second law
Law of Inertia

Notes

Some contemporary sources speculate about the exact date; e.g. Rachel Hilliam gives 1591 (Galileo Galilei: Father of Modern Science, The Rosen Publishing Group, 2005, p. 101).
Vincenzo Viviani (1717), Racconto istorico della vita di Galileo Galilei, p. 606: [...dimostrando ciò con replicate esperienze, fatte dall'altezza del Campanile di Pisa con l'intervento delli altri lettori e filosofi e di tutta la scolaresca... [...Galileo showed this [all bodies, whatever their weights, fall with equal speeds] by repeated experiments made from the height of the Leaning Tower of Pisa in the presence of other professors and all the students...].
Drake, Stillman (2003). Galileo at Work: His Scientific Biography (Facsim. ed.). Mineola (N.Y.): Dover publ. ISBN 9780486495422.
"Sci Tech : Science history: setting the record straight". The Hindu. June 30, 2005. Retrieved May 5, 2009.
Vincenzo Viviani on museo galileo
"El experimento más famoso de Galileo probablemente nunca tuvo lugar". The Conversation. May 16, 2019. Retrieved May 17, 2019.
Sharratt, M. (1994). Galileo: Decisive Innovator. Cambridge University Press. p. 31. ISBN 0-521-56671-1.
Groleau, R. (July 2002). "Galileo's Battle for the Heavens".
Ball, P. (30 June 2005). "Science history: Setting the record straight". The Hindu.
Van Helden, Albert (1995). "On Motion". The Galileo Project.
Laet nemen (soo den hoochgheleerden H. IAN CORNETS DE GROOT vlietichste ondersoucker der Naturens verborghentheden, ende ick ghedaen hebben) twee loyen clooten d'een thienmael grooter en swaerder als d'ander, die laet t'samen vallen van 30 voeten hooch, op een bart oft yet daer sy merckelick gheluyt tegen gheven, ende sal blijcken, dat de lichste gheen thienmael langher op wech en blijft dan de swaerste, maer datse t'samen so ghelijck opt bart vallen, dat haer beyde gheluyden een selve clop schijnt te wesen. S'ghelijcx bevint hem daetlick oock also, met twee evegroote lichamen in thienvoudighe reden der swaerheyt, daerom Aristoteles voornomde everedenheyt is onrecht. In: Simon Stevin, De Beghinselen der Weeghconst, 1586.
Asimov, Isaac (1964). Asimov's Biographical Encyclopedia of Science and Technology. ISBN 978-0385177719

E. J. Dijksterhuis, ed., The Principal Works of Simon Stevin. Amsterdam, Netherlands: C. V. Swets & Zeitlinger, 1955 vol. 1, pp. 509, 511.