Michael Fowler 1/22/07
Terrestrial Gravity: Galileo Analyzes a Cannonball Trajectory
From the earliest times, gravity meant the tendency of most bodies to fall to earth.
things that leaped upwards, like flames of fire, were said to have “levity”.
Aristotle was the first
writer to attempt a quantitative description of falling motion: he wrote that an object fell at a
constant speed, attained shortly after being released, and heavier things fell faster in proportion
to their mass. Of course this is nonsense, but in his defense, falling motion is pretty fast—it’s
hard to see the speed variation when you drop something to the ground.
Aristotle most likely
observed the slower motion of things falling through water, where buoyancy and fluid resistance
dominate, and assumed that to be a slowed-down version of falling through air—which it isn’t.
Galileo was the first to get it right.
(True, others had improved on Aristotle, but Galileo was the
first to get the big picture.)
He realized that a falling body
picked up speed at a constant rate
in other words, it had constant
(as he termed it, the word means “addition of speed”
He also made the crucial observation that, if air resistance and buoyancy can be
all bodies fall with the same acceleration
, bodies of different weights dropped
together reach the ground at the same time.
This was a revolutionary idea—as was his assertion
that it should be checked by
rather than by the traditional method of trying to
decipher what ancient authorities might have meant.
Galileo also noted that if a ball rolls without interference on a smooth horizontal surface, and
friction and air resistance can be neglected, it will move with constant speed in a fixed
direction—in modern language, its velocity remains constant.
He considered the motion of an object when not subject to interference as its “
Using his terminology, then,
natural horizontal motion
is motion at
natural vertical motion
is falling at
But he didn’t stop there—he took an important further step, which made him the first in history
to derive useful quantitative results about motion, useful that is to his boss, a duke with military
The crucial step was the realization that for a cannonball in flight,
the horizontal and
vertical motions can be analyzed independently
Here’s his picture of the path of a horizontally