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

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

where $r(t)$ is the distance between the centers of the masses $m_1$ and $m_2$ at time $t$, and $G$ is the gravitation constant.^E.3

The law of gravitation Eq. (E.2) can be accepted as an experimental fact which defines the concept of a force.^E.4 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 (§E.1) quantifies this result.