Galileo and the Free Fall of Bodies: Experiments That Challenged Aristotle

Galileo Galilei argued that everything happening in nature must be confirmed by experiment — and it was on that basis that he overturned the teaching of the ancient Greek philosopher Aristotle on how bodies fall. Aristotle held that a heavier object falls faster than a lighter one, but Galileo showed through both reasoning and demonstration that, setting aside air resistance, all bodies fall with the same acceleration regardless of weight. Because Aristotle's physics rested on contemplation and reflection rather than measurement, Galileo insisted that observation and controlled testing were the only reliable path to natural truth.

How did Galileo continue his scientific work after leaving university?

Galileo kept up his scientific studies at home, using wide reading to fill the gaps in the education that poverty had cut short. During these years he published a short work on the laws governing how bodies float and a method for determining their density using a specially designed balance. This early research already reflected his conviction that physical properties should be measured, not merely asserted.

Galileo wrote this treatise in living Italian rather than in the dead Latin that scholars of the time normally used, and it drew wide attention. Readers of the work recognised that this unfinished student stood on a level with the leading scientists of the age.

How did Galileo become a professor of mathematics at Pisa?

Galileo was appointed professor of mathematics at the University of Pisa — the very institution where he had once studied — on a three-year contract at a salary of sixty florins a year, secured through the patronage of the nobleman Guidobaldo del Monte. In this post he was required by the syllabus to expound Aristotle. The young scholar was not initially hostile to the ancient Greek philosopher; he only occasionally added small corrections and supplements to Aristotle's arguments, while preparing for prolonged battles with the philosopher's followers, then called the Peripatetics.

Aristotle's theory: force as the cause of a falling body's speed

Aristotle's theory of falling bodies held that an object's speed of fall is directly proportional to its weight and inversely proportional to the resistance of the medium, so that a ten-pound stone should reach the ground ten times faster than a one-pound stone. In Aristotelian physics motion required a continuous cause: heavy things move toward their "natural place" more forcefully than light things, and this distinction between natural and forced motion underpinned two thousand years of teaching. The same framework fed Aristotle's arguments against the Earth's rotation, since he treated weight as an absolute tendency rather than a relationship between bodies.

Objections to this scheme predate Galileo. In the sixth century John Philoponus argued against Aristotelian physics by contending that two unequal weights dropped together reach the ground at nearly the same moment, and in the sixteenth century the Spanish theologian Domingo de Soto and the Italian mathematician Giambattista Benedetti advanced similar precursor arguments. Galileo inherited this critical tradition and pressed it toward a decisive test.

Galileo's first attack on the Peripatetic doctrine

Galileo's first attack targeted Aristotle's claim that heavy objects fall faster than light ones. His student experiments with pendulums of different weights had shown that heavy and light bobs hung on threads swing in exactly the same way: the duration of a single swing depended only on the length of the thread, not on the weight of the pendulum.

Galileo's pendulum experiments and the independence of weight

The pendulum result already suggested that the speed of fall does not depend on the weight of the falling object, because a swinging bob is a body falling along a constrained arc. Galileo hesitated to use this example directly, since the Peripatetics could object that swinging is one thing and free fall another. The demonstration nonetheless anticipated a principle later made exact: the period of a pendulum is set by its length and by gravitational acceleration, and identical pendulums keep time identically whatever their mass. This weight-independence is an early hint of what physicists now call the equivalence of inertial and gravitational mass.

How did Galileo logically refute Aristotle's theory?

Galileo decided to fight the Aristotelians with their own weapon — reasoning — and constructed a thought experiment that exposed a contradiction inside Aristotle's own premises. Because the Peripatetics prized argument above all, he met them on that ground rather than appealing first to observation.

The thought experiment with two tied stones

"Aristotle asserts that a stone weighing ten pounds falls ten times faster than a stone weighing one pound. Very well, let us grant it. But tell me, what will happen if we tie both stones together? At what speed will they fall? Suppose we harness to a single cart a swift racehorse and an old nag that can barely drag its legs. How fast will that cart go? Surely you will say the old nag only holds the racehorse back. In the same way the small stone, which falls ten times more slowly than the large one, will brake the fall of the large stone, hinder it, and so the two stones tied together will fall more slowly than the single large stone. Is that not so, gentlemen?"

"Yes, of course!"

replied the Peripatetics, not noticing the trap.

"You agree with me? But consider for yourselves: we tied the two stones together so that they form a single object weighing eleven pounds. And this eleven-pound object is heavier than the ten-pound one, so, according to Aristotle, it must fall not more slowly but faster than the ten-pound stone! Is that not so, gentlemen?"

The Peripatetics fell silent, with nothing to answer. For if Aristotle were right, the two tied stones would have to fall at some undefined speed — on one account faster, on the other slower. Galileo drew the conclusion at once:

Aristotle was mistaken. The speed of fall does not depend on the weight of the falling objects. All objects, regardless of their weight, fall equally fast.

Analysis of the logical flaw in Aristotle's reasoning

The force of Galileo's thought experiment lies in showing that Aristotle's rule generates two contradictory predictions from one situation, which no consistent theory can do. Treating the tied pair as a single heavy body predicts it falls faster than either stone; treating it as a slow stone dragging on a fast one predicts it falls at an intermediate speed. A rule that yields a value both greater than and less than the same quantity is logically invalid, and it is this internal contradiction — not any measurement — that condemns the Aristotelian law. Modern commentators such as Gendler, Brown, Atkinson and Conifold have debated whether Galileo's argument works purely as a priori reasoning or quietly smuggles in an empirical assumption.

Additivity of physical quantities and composite bodies

The hidden premise in Galileo's argument concerns the additivity of physical quantities: he assumes that two stones bound together really do form one body whose weight is the sum of the parts. Analysts including Leonardo Levinas of the Universidad de Buenos Aires and CONICET, along with Quentin Ruyant and others writing on ResearchGate, note that weight behaves as an extensive magnitude — it adds when bodies combine — while the speed Aristotle attaches to it does not add consistently. Distinguishing weight as an extensive property from acceleration as an intensive one is exactly what dissolves the paradox: it is acceleration, shared by all falling bodies, that stays the same when masses are joined.

"Tie two stones of equal weight together and drop them from the same height. If your view is right, then bound together they will fall twice as fast as each alone. In short, if one horse covers the distance between two towns in two hours, you will presumably say that two such horses harnessed to a cart will cover that same distance in one hour. Gentlemen, where have you seen such remarkable horses?"

The Peripatetics dispersed, angered by Galileo's mockery, muttering that this ignorant youth dared to criticise Aristotle, whom the greatest minds had revered as the wisest of men for two thousand years. Galileo tried to offer fresh arguments and examples, but they no longer wished even to listen.

The famous experiment at the Leaning Tower of Pisa

Convinced that reasoning alone would never move the Peripatetics, the twenty-five-year-old Galileo resolved on a bold and decisive experiment that would let them see their error with their own eyes. In the town square of Pisa still stands the famous leaning bell-tower, built in 1174. According to Galileo's pupil and biographer Vincenzo Viviani, Galileo used this tower — conveniently tall at fifty-seven and a half metres (a hundred cubits in Florentine measure) and inclined — climbing to the platform of the seventh storey and dropping objects of various weights to watch how they fell.

Two iron cannonballs were hauled onto the platform: one weighing a hundred pounds and a small one weighing a single pound. These weights were not chosen at random, since Aristotle had discussed objects of precisely this weight in his own arguments. It is worth adding that historians treat Viviani's account with caution — no independent contemporary record confirms the public spectacle, and many scholars regard the Leaning Tower demonstration as a dramatised version of experiments Galileo carried out more carefully with inclined planes.

A crowd gathered at the tower: Peripatetic professors hoping to catch Galileo in some slip, students drawn by the dispute, and mere onlookers. One old professor in a dark academic cap, a zealous supporter of Aristotle, stood almost directly beneath the spot where the balls would land and, tilting his beard upward, watched for the experiment to begin. With a single push Galileo let the balls go.

Everyone saw them roll off the platform together and fly down side by side — the heavy and the light — as though tied by a string. The Peripatetic professor, Galileo's fiercest opponent, holding his grey beard with one hand, followed the flight of the balls intently.

At the moment of impact he crouched down, almost flattening himself on the ground, so eager was he not to miss the instant the balls touched earth. There came a dull thud. The Peripatetic sprang up and, forgetting his venerable age and professorial rank, shouted like a schoolboy:

"It lagged! It lagged!"

— and held up two fingers. The pound ball had indeed fallen behind its heavier companion by about the thickness of two fingers, striking the ground not simultaneously with the large ball but a fraction later. Many saw it. Aristotle's supporters whistled and jeered, and the idlers, who understood nothing of the affair, roared for the sheer pleasure of the noise.

The students, who loved Galileo's daring speeches, threw their caps into the air and cheered, for a two-finger gap seemed to them a trifle. But Galileo went home vexed by that cursed little ball. Within the university walls the dispute flared anew, and the Peripatetics went on the offensive, repeating with embittered stubbornness that the small ball had, after all, lagged behind — bowing politely to Galileo when they met and holding up two fingers.

Galileo answered his opponents by turning the numbers against them:

"Why do you rejoice? Aristotle claimed that a hundred-pound object dropped from a height of a hundred cubits reaches the ground in the time it takes the little ball to fall just one cubit! So the distance between them at that moment should have been ninety-nine cubits. Yet you observed that the large ball outstripped the small one not by ninety-nine cubits but by only two fingers. And you fasten on this trifling discrepancy to hide Aristotle's error of ninety-nine cubits. Harping on my utterly insignificant error, you pass over Aristotle's greatest error in silence!"

The small residual lag was in truth caused by air resistance, which acts more strongly, relative to its weight, on the lighter ball — an effect Galileo could not yet quantify but correctly judged to be a minor disturbance rather than a vindication of Aristotle.

The Delft tower experiment of Simon Stevin and Jan Cornets de Groot

A few years before the events attributed to Pisa, the Flemish engineer Simon Stevin and his collaborator Jan Cornets de Groot carried out a documented drop test from a church tower in Delft, releasing two lead balls of very different weight and reporting that they struck a wooden board below at what sounded like a single impact. Stevin published the result in his 1586 work De Beghinselen der Weeghconst, giving one of the earliest firmly recorded experimental refutations of Aristotle's claim and lending weight to the physics Galileo argued for.

How is the law of free fall formulated?

Galileo's law of free fall states that a body released from rest falls with constant acceleration, so that the distance travelled is proportional to the square of the elapsed time rather than to the body's weight. This is often called the law of parabolic fall because a projectile combining horizontal motion with this vertical acceleration traces a parabola. Galileo set out these results in his 1638 masterwork Two New Sciences (the Discorsi), which laid a foundation for the whole later development of mechanics.

Constant acceleration and the acceleration due to gravity (9.81 m/s²)

Near the surface of the Earth every freely falling body gains speed at a constant rate of about 9.81 metres per second every second, the acceleration due to gravity denoted g. Because this acceleration is the same for all bodies, a feather and a hammer released together in a vacuum keep pace exactly; only in air do their differing shapes separate them. In modern terms the free-fall relations follow directly: velocity grows as v = g·t and distance as s = ½·g·t², so after one second a body has fallen about 4.9 metres and after two seconds about 19.6 metres.

The principle of constant acceleration and distances in successive intervals

A striking consequence of constant acceleration, first stated by Galileo, is that the distances a body falls in equal successive time intervals stand in the ratio of the odd numbers 1, 3, 5, 7, and so on. In the first unit of time it falls one part, in the second three parts, in the third five parts; the cumulative totals then reproduce the squares 1, 4, 9, 16, confirming that total distance grows with the square of time. This odd-number rule is easy to check with a ball rolling down a gentle slope and became one of Galileo's most convincing quantitative arguments.

How does air resistance affect falling bodies?

Air resistance is the reason that in ordinary experience light objects fall more slowly than heavy ones, which is exactly what misled Aristotle. A falling object pushes air aside, and the air pushes back with a drag force that grows with speed until it balances the object's weight; from that point the object stops accelerating and descends at a constant terminal velocity. Only when air is removed does Galileo's law appear in its pure form and all bodies fall together.

Why light objects really do fall more slowly in air

A light object such as a feather reaches its terminal velocity almost at once because its weight is tiny compared with the drag its surface generates, so it drifts down slowly. A dense object such as an iron ball must reach a far higher speed before drag matches its weight, so over a short drop it barely slows at all. The difference is therefore an effect of the medium, not of any weight-dependence in gravity itself — remove the air and the feather and the ball accelerate identically.

Shape and cross-section as factors in air resistance

The drag on a falling body depends strongly on its cross-sectional area and shape, which is why a flat sheet of paper flutters down while the same paper crumpled into a ball drops quickly. Two objects of identical weight but different cross-section will reach the ground at noticeably different times in air, a counterexample that shows shape — not weight — governs the resistive force. Streamlined bodies with a small frontal area cut through the air and reach higher terminal velocities, while broad, flat bodies are held back.

The hammer and feather drop on the Moon (Apollo 15)

Astronaut David Scott demonstrated Galileo's law directly on the Moon during the Apollo 15 mission in 1971, releasing a geological hammer and a falcon feather at the same instant in front of a live television camera. With no lunar atmosphere to create air resistance, the two objects fell side by side and struck the surface together, exactly as Galileo had predicted more than three centuries earlier. NASA filmed the event as a deliberate public confirmation that, in a vacuum, gravitational acceleration is the same for every body whatever its mass or shape.

Why do Galileo's discoveries matter for the development of physics?

Galileo's insistence on experiment and measurement, combined with his law of free fall, transformed physics from a discipline of authority into one of testable law, and his verbal clashes at Pisa cost him a reputation as a "troublemaker" among the university's professors. His result that all bodies share one acceleration is the seed of the equivalence principle, which Isaac Newton built into his laws of motion — where force equals mass times acceleration and inertial mass appears to equal gravitational mass — and which Albert Einstein later raised to the founding postulate of general relativity. Modern torsion-balance and satellite experiments now test the equality of inertial and gravitational mass to better than one part in a trillion, and it is the same universality of acceleration that keeps satellites in orbit and shapes the way gravity governs their paths. Readers interested in how these ideas ripple outward can follow the broader story of how science shapes everyday life, and Galileo's habit of questioning inherited authority remains a model of the scientific method itself.

Classroom demonstrations for studying free fall

Free fall is one of the most teachable topics in physics because the key ideas can be shown with simple apparatus, and inclined planes remain the safest way to slow the motion enough to measure it — the same trick Galileo used to "dilute" gravity. Instructors aligning lessons with the Next Generation Science Standards often reach for ramps and timing gates, and purpose-built kits such as Packard's Acceleration Ramp, developed by John Packard, let students verify the odd-number distance rule for themselves.

• Drop a coin and a flat piece of paper together, then crumple the paper and repeat, to reveal the role of air resistance and cross-section.
• Roll balls down a ramp and mark their positions at equal time intervals to confirm distances in the ratio 1, 3, 5, 7.
• Time pendulums of equal length but different mass to show that period is independent of weight.
• Show the Apollo 15 hammer-and-feather footage to connect the classroom result to a real vacuum demonstration.
• Use a ball rolling off a table to trace the parabolic path predicted by the law of parabolic fall.

These activities help students meet clear learning objectives — describing constant acceleration, relating distance to the square of time, and separating the effect of gravity from that of the surrounding medium — while echoing the reasoning that first let Galileo overturn two thousand years of Aristotelian physics.