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Galileo's Refutation of the Speed-Distance Law of Fall Rehabilitated

Norton, John D. and Roberts, Bryan W. (2012) Galileo's Refutation of the Speed-Distance Law of Fall Rehabilitated. [Published Article or Volume]

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Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this ‘equal time’ property, instantaneous motion.

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Item Type: Published Article or Volume
Norton, John
Roberts, Bryan
Additional Information: Published in Centaurus
Keywords: acceleration, freefall, foundations of physics, Galileo, history of physics
Subjects: Specific Sciences > Physics
Depositing User: Bryan Roberts
Date Deposited: 26 May 2012 13:09
Last Modified: 26 May 2012 13:09
Item ID: 9123
Journal or Publication Title: Centaurus
Official URL:

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