Galileo discovered that all objects fall at the same rate regardless of their weight, overturning nearly 2,000 years of accepted wisdom. He also worked out the mathematical relationship governing how falling objects accelerate: the distance an object falls is proportional to the square of the time it’s been falling. These two insights, along with his discovery that projectiles follow a curved parabolic path, laid the groundwork for modern physics and directly influenced Isaac Newton’s later theory of universal gravitation.
Why Aristotle’s Theory Was Wrong
Before Galileo, the dominant view of gravity came from Aristotle, who claimed that heavier objects fall faster than lighter ones in direct proportion to their weight. A stone ten times heavier than another would, by Aristotle’s reasoning, fall ten times faster. This seemed intuitive, and nobody seriously challenged it for roughly 1,900 years.
Galileo dismantled this idea with a brilliant thought experiment. Imagine tying a heavy stone and a light stone together with a rope. Under Aristotle’s logic, two contradictory things would have to be true at the same time. First, the lighter stone should act as a drag on the heavier one, slowing it down. So the combined system should fall slower than the heavy stone alone. But second, the two stones tied together weigh more than the heavy stone by itself, so by Aristotle’s own rule, the combined system should fall faster. You can’t have the same object falling both faster and slower, which means the original assumption is broken. The only way to resolve the contradiction is to conclude that weight doesn’t determine falling speed at all.
The Inclined Plane Experiments
Galileo couldn’t easily measure objects in free fall because they accelerate too quickly. A ball dropped from a tower hits the ground in a couple of seconds, far too fast for the timing tools available in the early 1600s. His solution was elegant: slow gravity down by rolling balls along a tilted wooden track. A gentle incline stretches the fall over a longer period, making the motion measurable while preserving the same underlying physics.
He placed a smooth rail at a slight angle, released balls from various heights, and timed their descent. Without a stopwatch, he relied on methods like water clocks (measuring how much water flowed during a run) or possibly his own musical sense of rhythm to mark equal intervals of time. He repeated each trial multiple times and averaged the results.
What he found was striking. The distance a ball traveled wasn’t simply proportional to the time it rolled. It was proportional to the square of the time. A ball rolling for two seconds covered four times the distance it covered in one second. After three seconds, it had covered nine times that distance. This square relationship held consistently across different incline angles and, crucially, across balls of different masses. A steel ball and a lighter ball rolled down the same track accelerated at the same rate.
The Law of Falling Bodies
From those inclined-plane results, Galileo formulated what’s now called the law of falling bodies. Expressed as a formula, the distance an object falls equals one half times the acceleration times the time squared. In plain terms, falling objects don’t move at a constant speed. They accelerate uniformly, gaining the same amount of speed with every passing second. The velocity increases linearly with time, while the distance covered increases much faster, following that squared relationship.
This was a radical departure from Aristotle, who believed each object had a “natural speed” fixed by its weight, a speed that couldn’t change without applying an outside force. Galileo showed the opposite: gravity continuously accelerates falling objects, and it does so at the same rate for everything, heavy or light. The modern value for this acceleration near Earth’s surface is about 9.8 meters per second per second, meaning a falling object gains roughly 9.8 m/s of speed every second. Galileo didn’t calculate that precise figure with his equipment, but his experiments established the constant-acceleration principle behind it.
Projectile Motion and the Parabola
Galileo also tackled a question that had puzzled natural philosophers for centuries: what path does a cannonball or thrown object follow through the air? In 1609, he proved mathematically that the answer is a parabola, the same U-shaped curve you might remember from algebra class.
His key insight was that projectile motion is really two separate motions happening at the same time. Horizontally, a launched object moves at a constant speed (assuming air resistance is negligible). Vertically, gravity pulls it downward with uniform acceleration. Combine those two independent motions and the result is a smooth parabolic arc. Galileo confirmed this experimentally by rolling balls off the edge of a table, tracking where they landed, and sketching their trajectories in his notebook. The paths consistently matched the parabolic shape his math predicted.
This decomposition of motion into independent horizontal and vertical components was a genuinely new way of thinking about physics. It meant you could analyze a complex path by breaking it into simpler parts, a technique that remains fundamental in physics today.
Early Ideas About Inertia
Galileo’s gravity work also led him toward the concept of inertia, the idea that an object in motion will keep moving unless something acts on it. Through experiments with pendulums and balls rolling on smooth surfaces, he noticed that a ball rolling on a perfectly level surface would, in theory, keep rolling forever if nothing slowed it down. Friction was the only reason it stopped.
This was another break from Aristotle, who thought objects naturally came to rest and needed a continuous push to keep moving. Galileo recognized that gravity was one of those forces that changes an object’s motion, altering its speed and trajectory depending on how it’s launched. Without gravity, a horizontally thrown ball would keep going in a straight line forever. With gravity, it curves downward into that parabolic path. This intuitive understanding of inertia became the foundation of Newton’s first law of motion decades later.
How Galileo’s Work Shaped Newton’s Theory
Galileo’s discoveries about gravity were essential building blocks for Isaac Newton’s universal law of gravitation, published in 1687, about 45 years after Galileo’s death. The most important piece Galileo contributed was the observation that gravity accelerates all objects equally regardless of mass. Newton took that fact and, combined with his third law of motion (every action has an equal and opposite reaction), showed something profound: if Earth accelerates all objects toward it at the same rate regardless of their mass, then the gravitational pull an object exerts on other things must be proportional to its own mass.
Newton extended Galileo’s ideas in three major ways. First, he recognized that gravity isn’t unique to Earth. Every object in the universe attracts every other object. Second, he worked out that gravitational attraction weakens with the square of the distance between two objects. Third, he invented calculus partly to prove that a large, spread-out body like Earth could be treated mathematically as though all its mass were concentrated at its center. But the starting point for all of this, the observation that gravity accelerates everything equally, was Galileo’s contribution. Without it, Newton’s framework wouldn’t have come together the way it did.