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Gravitational Force

We are all familiar with the force of gravity. It is a fundamental observed property of our universe that any two masses $ m_1$ and $ m_2$ experience an attracting force $ f$ given by the formula

$\displaystyle f(t) = G\frac{m_1 m_2}{r^2(t)} \protect$ (B.2)

where $ r(t)$ is the distance between the centroids of the masses $ m_1$ and $ m_2$ at time $ t$ , and $ G$ is the gravitation constant.B.2

The law of gravitation Eq.$ \,$ (B.2) can be accepted as an experimental fact which defines the concept of a force. B.3 The giant conceptual leap taken by Newton was that the law of gravitation is universal--applying to celestial bodies as well as objects on earth. When a mass is ``dropped'' and allowed to ``fall'' in a gravitational field, it is observed to experience a uniform acceleration proportional to its mass. Newton's second law of motion (§B.1) quantifies this result.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2018-01-17 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University