# Acceleration Due to Gravity/Earth's Surface

## Physical Law

Let a body $B$ be situated in a uniform gravitational field $M$ given rise to by a body $P$.

When the body $P$ of mass $M$ is the Earth, and the body $B$ of mass $m$ is located at or near its surface, it is usual to use $g$ for the quantity $\dfrac {G M} {r^2}$.

Therefore the force on $B$ can be expressed as:

- $F = m g$

Its value is approximately:

\(\ds \) | \(\) | \(\ds 9.8 \, \mathrm m \ \mathrm s^{-2}\) | in SI units | |||||||||||

\(\ds \) | \(\) | \(\ds 32 \, \mathrm f \ \mathrm s^{-2}\) | in FPS units. |

## Historical Note

This result famously contradicts Aristotle, who taught that heavier objects fall faster than light ones.

There exists a well-known story about how Galileo proved this law by dropping two objects of different weights from a height (supposedly the Leaning Tower of Pisa).

Apparently this never actually happened.

However, Simon Stevin did perform a similar experiment some time before Galileo started experimenting.

The fact that in the general case air resistance can not be ignored goes some way to explaining how the truth was not arrived at earlier.

Even children notice how leaves, for example, flutter gently down from on high, whereas stones tend to plummet.

## Sources

- 1966: Isaac Asimov:
*Understanding Physics*... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $2$: Falling Bodies: Free Fall - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 1$: Introduction: $(2)$