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Galileo Galilei The Law of the Pendulum

 Italian mathematician, astronomer, physicist and inventor Galileo Galilei lived from 1564 to 1642. Galileo discovered the "isochronism of the pendulum" aka the "law of the pendulum". Galileo demonstrated at the Tower of Pisa that falling bodies of different weights descend at the same rate. He invented the first refracting telescope, and used that telescope to discover and document Jupiter's satellites, sunspots, and craters on the Earth's moon. He is considered to be the "Father of the Scientific Method".

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The painting above depicts a  young twenty year old Galileo observing a lamp swinging from a cathedral ceiling. Believe it or not Galileo Galilei was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same.

Galileo Galilei had discovered the law of the pendulum, which gained the young scientist considerable notoriety in the academic world. The law of the pendulum would later be used in the construction of clocks, as it could be used to regulate them.

Proving Aristotle Was Wrong

While Galileo Galilei was working at the University of Pisa, there was a popular discussion occurring about a long dead scientist and philosopher called Aristotle . Aristotle believed that heavier objects fell faster than lighter objects. Scientists in Galileo's time still agreed with Aristotle. However, Galileo Galilei did not agree and set up a public demonstration to prove Aristotle wrong.

As depicted in the illustration above, Galileo used the Tower of Pisa for his public demonstration. Galileo used a variety of balls of different sizes and weights, and dropped them off of the top of the Tower of Pisa together. Of course, they all landed at the same time since Aristotle was wrong. Objects of different weights all fall to earth at the same speed.

Of course, Gallileo's smug reaction to being proven right won him no friends and he was soon forced to leave the University of Pisa.

The Thermoscope

By 1593 after his father's death, Galileo Galilei found himself with little cash and lots of bills, including the dowry payments for his sister. At that time, those in debt could be placed in prison.

Galileo's solution was to start inventing in hopes of coming up with that one product which everyone would want. Not much different from the thoughts of inventors today.

Galileo Galilei invented a  rudimentary thermomete r called the thermoscope, a thermometer which lacked a standardized scale. It was not a big success commecially.

Galileo Galilei - Military and Surveying Compass

In 1596, Galileo Galilei made headway into his debtor's problems with the successful invention of a military compass used to accurately aim cannonballs. A year later in 1597, Galileo modified the compass so that it could be used for land surveying. Both inventions earned Galileo some well-needed cash.

Galileo Galilei - Work With Magnetism

The photo above is of the armed lodestones, used by Galileo Galilei in his studies on magnets between 1600 and 1609. They are made of iron, magnetite and brass. A lodestone by definition is any naturally magnetized mineral, able to be used as a magnet. An armed lodestone is an enhanced lodestone, where things are done to make the lodestone a stronger magnet, such as combining and placing additional magnetic materials together. 

Galileo's studies in magnetism began after the publication of William Gilbert's De Magnete in 1600. Many astronomers were basing their explanations of planetary motions on magnetism. For example Johannes Kepler , believed that the Sun was a magnetic body, and the motion of the planets was due to the action of the magnetic vortex produced by the Sun's rotation and that the Earth's ocean tides were also based on the magnetic pull of the moon.

Gallileo disagreed but never the less spent years conducting experiments on magnetic needles, magnetic declination, and the arming of magnets.. 

Galileo Galilei - First Refracting Telescope

In 1609, during a holiday in Venice Galileo Galilei learnt that a Dutch spectacle-maker had invented the spyglass ( later renamed the telescope ), a mysterious invention that could make distant objects appear closer.

The Dutch inventor had applied for a patent, however, much of the details surrounding the spyglass were being kept hush-hush as the spyglass was rumored to hold a military advantage for Holland.

Galileo Galilei - Spyglass, Telescope

Being a very competitive scientist, Galileo Galilei set out to invent his own spyglass, despite never having seen one in person, Galileo only knew what it could do. Within twenty-four hours Galileo had built a 3X power telescope, and later after a bit of sleep built a 10X power telescope, which he demonstrated to the Senate in Venice. The Senate praised Galileo publicly and raised his salary.

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Galileo's experiment at the leaning tower of pisa.

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Bringing Classical Physics Into The Modern World With Galileo’s Leaning Tower Of Pisa Experiment

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If you drop a light object and a heavy object from a tower, which one reaches the ground first? As you may recall from high school physics, this is a trick question. Neglecting air resistance, they both fall the same way and reach the ground at the same time – gravity means that their speeds increase at 9.8 meters per second squared, no matter what their mass.

That’s the premise behind  Galileo Galilei’s  Leaning Tower of Pisa experiment, a classic thought experiment in the field of dynamics.

Dynamics is the physics specialization that studies motion and force. A “dynamicist,” one who studies dynamics, can do everything from improve a basketball player’s  free throw  to help design spacecraft for  interstellar travel .

As a  dynamicist , I’ve spent much of my career helping students make sense of modern dynamics. The  Leaning Tower of Pisa experiment  is one good way to do this. It can explain how classical mechanics – the field that engineers and educators employ every day – was brought into the modern world.

Galileo’s Leaning Tower of Pisa experiment

The Leaning Tower of Pisa experiment led to the curious realization that objects fall with the same accelerations regardless of their mass. But what happens when you place objects of different masses on a smooth table and push each of them with the same force?

Even without accounting for friction , the objects’ accelerations are now different. The lighter objects accelerate more than the heavy ones. When falling, their accelerations are the same, yet when sliding, they’re different.

Let’s now place the two objects  in orbit . Imagine one of them is the Sun and the other is the Earth. In classical mechanics, the Sun exerts a force on the Earth equal in magnitude to the force that the Earth exerts back on the Sun.

But  the Sun is huge compared with the Earth . Shouldn’t the magnitude of the larger object’s force be larger? And while we’re at it, how would the magnitude of the Sun’s force on the Earth come to be equal to the magnitude of the Earth’s force on the Sun?

Heavy and light objects have equal accelerations when falling but different accelerations when sliding, and objects in space exert equal gravitational forces on each other despite having different masses. This all seems inconsistent, and a little confusing, right?

Modern mechanics

The problems above came from an ambiguity in the concept of force in classical mechanics. In classical mechanics, the  force is an interaction  between two objects, involving both objects. The magnitudes of the gravitational forces by the Sun and by the Earth depend on the masses of both bodies. The force was never just by the Sun or just by the Earth without regard to the other.

But  modern mechanics  – the physics of light, atoms, quantum mechanics and curved space-time – changed this concept of force. The modern force by the Sun and the modern force by the Earth are two separate forces, and they depend only on their own masses, excluding  relativistic effects .

In modern mechanics, the force is now an  action by an object , not an interaction between them. It is viewed as a  force field  that radiates outward from its source, whose magnitude grows smaller the farther it is from its source. Modern mechanics is a  field theory  – it deals with objects and the accelerations their force fields create.

So, what happened to the interaction force? Was it discarded? The answer is no, but it is no longer the most fundamental definition of force, either. In modern mechanics, the interaction force, represented by the letter F, is defined in terms of the action force field, represented by the letter P. The interaction force is now the  action force  P times the mass m on which P acts, so F = mP.

Newton’s  second law of motion , a fundamental part of classical mechanics, sets the interaction force F by an object equal to the mass m on which the object acts multiplied by its acceleration, so F = ma. The modern version sets the action force P by an object equal to the other object’s acceleration, so P = a. When multiplying P = a by m we get back F = ma.

Notice it was not about the math in classical mechanics being wrong – but more about the fundamental force being an action force and not an interaction force.

The modern thinking

The modern thinking reinterprets Galileo’s  Leaning Tower of Pisa experiment , the sliding blocks, the orbiting of the Earth around the Sun – and interactions in general.

In Galileo’s Leaning Tower of Pisa experiment, the light and heavy objects were falling due to the Earth’s action force, which does not depend on the masses of the falling objects, so their accelerations are naturally the same.

The light and heavy objects sliding on the smooth table were acted on by the same interaction forces. But the fundamental forces – the action forces – are different, so their accelerations are naturally different, too.

In the orbiting of the Earth around the Sun, the action forces by the Sun and by the Earth are no longer equal. The action force by the Sun, with its huge mass, is proportionally larger than the force by the Earth – as intuition suggests.

Science takes many years to evolve as it edges closer to revealing the nature of reality. One sees this in the evolution that led to modern mechanics – where scientists now embrace a theory of force fields that predicts the dynamics of objects, despite it being almost against common sense.

Larry M. Silverberg is a Professor of Mechanical and Aerospace Engineering at North Carolina State University. This article is republished from  The Conversation  under a  Creative Commons license . Read the  original article .

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Galileo

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Galileo

Who was Galileo?

Galileo was a natural philosopher, astronomer, and mathematician who made fundamental contributions to the sciences of motion , astronomy , and strength of materials and to the development of the scientific method . He also made revolutionary telescopic discoveries, including the four largest moons of Jupiter .

What did Galileo invent?

Galileo invented an early type of thermometer . Although he did not invent the telescope , he made significant improvements to it that enabled astronomical observation.

What discoveries did Galileo make?

In 1610 Galileo discovered the four biggest moons of Jupiter (now called the Galilean moons ) and the rings of Saturn .

Did the Roman Catholic Church execute Galileo?

No, the Roman Catholic Church did not execute or torture Galileo. For his heresy in claiming that Earth orbits the Sun, the church sentenced him to life imprisonment in 1633. Galileo served his sentence under house arrest and died at home in 1642 after an illness.

Galileo influenced scientists for many decades after his death, not least in his willingness to stand up to authority—in this case, the Roman Catholic Church—to defend his findings. His improvements to the telescope led to advances in the field of astronomy. Sir Isaac Newton later expanded on Galileo's work when coming up with his own theories.

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Galileo (born February 15, 1564, Pisa [Italy]—died January 8, 1642, Arcetri, near Florence) was an Italian natural philosopher, astronomer, and mathematician who made fundamental contributions to the sciences of motion , astronomy , and strength of materials and to the development of the scientific method . His formulation of (circular) inertia , the law of falling bodies , and parabolic trajectories marked the beginning of a fundamental change in the study of motion. His insistence that the book of nature was written in the language of mathematics changed natural philosophy from a verbal, qualitative account to a mathematical one in which experimentation became a recognized method for discovering the facts of nature. Finally, his discoveries with the telescope revolutionized astronomy and paved the way for the acceptance of the Copernican heliocentric system , but his advocacy of that system eventually resulted in an Inquisition process against him.

Galileo was born in Pisa , Tuscany , on February 15, 1564, the oldest son of Vincenzo Galilei , a musician who made important contributions to the theory and practice of music and who may have performed some experiments with Galileo in 1588–89 on the relationship between pitch and the tension of strings. The family moved to Florence in the early 1570s, where the Galilei family had lived for generations. In his middle teens Galileo attended the monastery school at Vallombrosa , near Florence, and then in 1581 matriculated at the University of Pisa, where he was to study medicine . However, he became enamoured with mathematics and decided to make the mathematical subjects and philosophy his profession, against the protests of his father. Galileo then began to prepare himself to teach Aristotelian philosophy and mathematics, and several of his lectures have survived. In 1585 Galileo left the university without having obtained a degree, and for several years he gave private lessons in the mathematical subjects in Florence and Siena . During this period he designed a new form of hydrostatic balance for weighing small quantities and wrote a short treatise , La bilancetta (“The Little Balance”), that circulated in manuscript form. He also began his studies on motion , which he pursued steadily for the next two decades.

In 1588 Galileo applied for the chair of mathematics at the University of Bologna but was unsuccessful. His reputation was, however, increasing, and later that year he was asked to deliver two lectures to the Florentine Academy, a prestigious literary group, on the arrangement of the world in Dante’s Inferno . He also found some ingenious theorems on centres of gravity (again, circulated in manuscript) that brought him recognition among mathematicians and the patronage of Guidobaldo del Monte (1545–1607), a nobleman and author of several important works on mechanics . As a result, he obtained the chair of mathematics at the University of Pisa in 1589. There, according to his first biographer, Vincenzo Viviani (1622–1703), Galileo demonstrated, by dropping bodies of different weights from the top of the famous Leaning Tower , that the speed of fall of a heavy object is not proportional to its weight, as Aristotle had claimed. The manuscript tract De motu ( On Motion ), finished during this period, shows that Galileo was abandoning Aristotelian notions about motion and was instead taking an Archimedean approach to the problem. But his attacks on Aristotle made him unpopular with his colleagues, and in 1592 his contract was not renewed. His patrons , however, secured him the chair of mathematics at the University of Padua , where he taught from 1592 until 1610.

Although Galileo’s salary was considerably higher there, his responsibilities as the head of the family (his father had died in 1591) meant that he was chronically pressed for money. His university salary could not cover all his expenses, and he therefore took in well-to-do boarding students whom he tutored privately in such subjects as fortification . He also sold a proportional compass, or sector, of his own devising, made by an artisan whom he employed in his house. Perhaps because of these financial problems, he did not marry, but he did have an arrangement with a Venetian woman, Marina Gamba, who bore him two daughters and a son. In the midst of his busy life he continued his research on motion, and by 1609 he had determined that the distance fallen by a body is proportional to the square of the elapsed time ( the law of falling bodies ) and that the trajectory of a projectile is a parabola , both conclusions that contradicted Aristotelian physics .

Alberto Santos-Dumont. Postcard of Brazilian aviator Alberto Santos-Dumont's (1873-1932) airship or dirigible and Eiffel Tower. The Santos Dumont Air-Ship rounding the Eiffel Tower; on Octoboer 19th 1901. airplane

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Galileo Galilei

By: History.com Editors

Updated: June 6, 2023 | Original: July 23, 2010

Galileo GalileiCirca 1610, Italian physicist, mathematician and astronomer Galileo (Galilei) (1564 - 1642). (Photo by Stock Montage/Getty Images)

Galileo Galilei (1564-1642) is considered the father of modern science and made major contributions to the fields of physics, astronomy, cosmology, mathematics and philosophy. Galileo invented an improved telescope that let him observe and describe the moons of Jupiter, the rings of Saturn, the phases of Venus, sunspots and the rugged lunar surface. His flair for self-promotion earned him powerful friends among Italy’s ruling elite and enemies among the Catholic Church’s leaders. Galileo’s advocacy of a heliocentric universe brought him before religious authorities in 1616 and again in 1633, when he was forced to recant and placed under house arrest for the rest of his life.

Galileo’s Early Life, Education and Experiments

Galileo Galilei was born in Pisa in 1564, the first of six children of Vincenzo Galilei, a musician and scholar. In 1581 he entered the University of Pisa at age 16 to study medicine, but was soon sidetracked by mathematics. He left without finishing his degree. In 1583 he made his first important discovery, describing the rules that govern the motion of pendulums.

Did you know? After being forced during his trial to admit that the Earth was the stationary center of the universe, Galileo allegedly muttered, "Eppur si muove!" ("Yet it moves!" ). The first direct attribution of the quote to Galileo dates to 125 years after the trial, though it appears on a wall behind him in a 1634 Spanish painting commissioned by one of Galileo's friends.

From 1589 to 1610, Galileo was chair of mathematics at the universities of Pisa and then Padua. During those years he performed the experiments with falling bodies that made his most significant contribution to physics.

Galileo had three children with Marina Gamba, whom he never married: Two daughters, Virginia (Later “Sister Maria Celeste”) and Livia Galilei, and a son, Vincenzo Gamba. Despite his own later troubles with the Catholic Church, both of Galileo’s daughters became nuns in a convent near Florence.

Galileo, Telescopes and the Medici Court

In 1609 Galileo built his first telescope, improving upon a Dutch design. In January of 1610 he discovered four new “stars” orbiting Jupiter—the planet’s four largest moons. He quickly published a short treatise outlining his discoveries, “Siderius Nuncius” (“The Starry Messenger”), which also contained observations of the moon’s surface and descriptions of a multitude of new stars in the Milky Way. In an attempt to gain favor with the powerful grand duke of Tuscany, Cosimo II de Medici, he suggested Jupiter’s moons be called the “Medician Stars.”

“The Starry Messenger” made Galileo a celebrity in Italy. Cosimo II appointed him mathematician and philosopher to the Medicis , offering him a platform for proclaiming his theories and ridiculing his opponents.

Galileo’s observations contradicted the Aristotelian view of the universe, then widely accepted by both scientists and theologians. The moon’s rugged surface went against the idea of heavenly perfection, and the orbits of the Medician stars violated the geocentric notion that the heavens revolved around Earth.

Galileo Galilei’s Trial

In 1616 the Catholic Church placed Nicholas Copernicus ’s “De Revolutionibus,” the first modern scientific argument for a heliocentric (sun-centered) universe, on its index of banned books. Pope Paul V summoned Galileo to Rome and told him he could no longer support Copernicus publicly.

In 1632 Galileo published his “Dialogue Concerning the Two Chief World Systems,” which supposedly presented arguments for both sides of the heliocentrism debate. His attempt at balance fooled no one, and it especially didn’t help that his advocate for geocentrism was named “Simplicius.”

Galileo was summoned before the Roman Inquisition in 1633. At first he denied that he had advocated heliocentrism, but later he said he had only done so unintentionally. Galileo was convicted of “vehement suspicion of heresy” and under threat of torture forced to express sorrow and curse his errors.

Nearly 70 at the time of his trial, Galileo lived his last nine years under comfortable house arrest, writing a summary of his early motion experiments that became his final great scientific work. He died in Arcetri near Florence, Italy on January 8, 1642 at age 77 after suffering from heart palpitations and a fever.

What Was Galileo Famous For? 

Galileo’s laws of motion, made from his measurements that all bodies accelerate at the same rate regardless of their mass or size, paved the way for the codification of classical mechanics by Isaac Newton . Galileo’s heliocentrism (with modifications by Kepler ) soon became accepted scientific fact. His inventions, from compasses and balances to improved telescopes and microscopes, revolutionized astronomy and biology. Galilleo discovered craters and mountains on the moon, the phases of Venus, Jupiter’s moons and the stars of the Milky Way. His penchant for thoughtful and inventive experimentation pushed the scientific method toward its modern form.

In his conflict with the Church, Galileo was also largely vindicated. Enlightenment thinkers like Voltaire used tales of his trial (often in simplified and exaggerated form) to portray Galileo as a martyr for objectivity. Recent scholarship suggests Galileo’s actual trial and punishment were as much a matter of courtly intrigue and philosophical minutiae as of inherent tension between religion and science.

In 1744 Galileo’s “Dialogue” was removed from the Church’s list of banned books, and in the 20th century Popes Pius XII and John Paul II made official statements of regret for how the Church had treated Galileo.

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Today, we ask how fast things fall, and we rewrite science. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

W hen Galileo was young, one of his contemporaries used these words to describe Aristotle's idea of how objects fall:

There is a natural place for everything to seek, as: Heavy things go downward, Fire upward, And rivers to the sea.

dropball.jpg

Galileo took an interest in rates of fall when he was about 26 years old and a math teacher at the University of Pisa. It seemed to him that -- with no air resistance -- a body should fall at a speed proportional to its density. He decided to test this modified Aristotelian view by making an experiment.

There was no tradition of describing experimental research in Galileo's day. Controlled experiments were almost unknown. So Galileo's report was pretty skimpy. He seems to have dropped different balls from a tower. But what weights? What tower? We can be pretty sure it was the Leaning Tower of Pisa. But we end up doubting whether or not he really did the experiment. Maybe he just reported what he thought should have happened.

One result of the experiment surprised Galileo, and one surprises us. Galileo found that the heavy ball hit the ground first, but only by a little bit. Except for a small difference caused by air resistance, both balls reached nearly the same speed. And that surprised him. It forced him to abandon Aristotelian ideas about motion. If he really did the experiment, it was surely a turning point in the history of science.

But what surprises us is what Galileo says happened just after he released the two balls. He says the lighter ball always started out a little bit faster than the heavy ball. Then the heavy ball caught up. That sounds crazy.

So Thomas Settle and Donald Miklich reran Galileo's tower experiment in front of a camera. An assistant held four-inch iron and wooden balls at arm's length -- as Galileo would have to have held them to clear the wide balustrate atop the Pisa tower. It turns out that when you try to drop them both at once, your strained muscles fool you. You consistently let go of the lighter one, the one you've been gripping less intensely, first. That means Galileo accurately reported what he seen happening. And we're left with no doubt that he actually did do the experiment. Galileo went on to become the first real challenger of Aristotle. His tower experiment was no fable -- no apple falling on Newton's head. This was one of the first controlled scientific experiments. Like most of today's experiments, it was imperfect. But this experiment changed Galileo, and it changed history. I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

Settle, T. B., Galileo and Early Experimentation, Springs of Scientific Creativity , (F. Aris, H.T. Davis, and R.H. Stuewer, eds.). Minneapolis: University. of Minnesota Press, 1983, pp. 3-20.

pisa.jpg

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Galileo's Leaning Tower of Pisa experiment

Between 1589 and 1592,[1] the Italian scientist Galileo Galilei (then professor of mathematics at the University of Pisa) is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass, according to a biography by Galileo's pupil Vincenzo Viviani, composed in 1654 and published in 1717.[2][3]:19–21[4][5]

According to the story, Galileo discovered through this experiment that the objects fell with the same acceleration, proving his prediction true, while at the same time disproving Aristotle's theory of gravity (which states that objects fall at speed proportional to their mass). Most historians consider it to have been a thought experiment rather than a physical test.[6] Galileo's experiment

At the time when Viviani asserts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He had, however, formulated an earlier version which predicted that bodies of the same material falling through the same medium would fall at the same speed.[3]:20 This was contrary to what Aristotle had taught: that heavy objects fall faster than the lighter ones,and in direct proportion to their weight.[3]:9[7] While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is accepted by most historians that it was a thought experiment which did not actually take place.[8][9] An exception is Stillman Drake, who argues that it took place, more or less as Viviani described it, as a demonstration for students.[3]:19–21, 414–416

Galileo set out his ideas about falling bodies, and about projectiles in general, in his book Two New Sciences. The two sciences were the science of motion, which became the foundation-stone of physics, and the science of materials and construction, an important contribution to engineering. Galileo arrived at his hypothesis by a famous thought experiment outlined in his book On Motion.[10] This experiment runs as follows: Imagine two objects, one light and one heavier than the other one, are connected to each other by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter object retards the fall of the heavier object. But the system considered as a whole is heavier than the heavy object alone, and therefore should fall faster. This contradiction leads one to conclude the assumption is false. Other performances The Nieuwe Kerk in Delft, where the experiment by Stevin and de Groot took place

A similar experiment took place some years earlier in Delft in the Netherlands, when the mathematician and physicist Simon Stevin and Jan Cornets de Groot (the father of Hugo de Groot) conducted the experiment from the top of the Nieuwe Kerk. The experiment is described in Simon Stevin's 1586 book De Beghinselen der Weeghconst (The Principles of Statics), a landmark book on statics:

Let us take (as the highly educated Jan Cornets de Groot, the diligent researcher of the mysteries of Nature, and I have done) two balls of lead, the one ten times bigger and heavier than the other, and let them drop together from 30 feet high, and it will show, that the lightest ball is not ten times longer under way than the heaviest, but they fall together at the same time on the ground. (...) This proves that Aristotle is wrong.[11][12][13]

File:Apollo 15 feather and hammer drop.ogvPlay media Hammer and Feather Drop by astronaut David Scott, Apollo 15 (1.38 MB, ogg/Theora format)

Astronaut David Scott performed a version of the experiment on the Moon during the Apollo 15 mission in 1971, dropping a feather and a hammer from his hands. Because of the negligible lunar atmosphere, there was no drag on the feather, which hit the ground at the same time as the hammer. See also

Terminal velocity (An object dropped through air from a sufficient height will reach a steady speed, called the terminal velocity, when the aerodynamic drag force pushing up on the body balances the gravitational force (weight) pulling the body down.) Nordtvedt effect Newton's second law Law of Inertia

Some contemporary sources speculate about the exact date; e.g. Rachel Hilliam gives 1591 (Galileo Galilei: Father of Modern Science, The Rosen Publishing Group, 2005, p. 101). Vincenzo Viviani (1717), Racconto istorico della vita di Galileo Galilei, p. 606: [...dimostrando ciò con replicate esperienze, fatte dall'altezza del Campanile di Pisa con l'intervento delli altri lettori e filosofi e di tutta la scolaresca... [...Galileo showed this [all bodies, whatever their weights, fall with equal speeds] by repeated experiments made from the height of the Leaning Tower of Pisa in the presence of other professors and all the students...]. Drake, Stillman (2003). Galileo at Work: His Scientific Biography (Facsim. ed.). Mineola (N.Y.): Dover publ. ISBN 9780486495422. "Sci Tech : Science history: setting the record straight". The Hindu. June 30, 2005. Retrieved May 5, 2009. Vincenzo Viviani on museo galileo "El experimento más famoso de Galileo probablemente nunca tuvo lugar". The Conversation. May 16, 2019. Retrieved May 17, 2019. Sharratt, M. (1994). Galileo: Decisive Innovator. Cambridge University Press. p. 31. ISBN 0-521-56671-1. Groleau, R. (July 2002). "Galileo's Battle for the Heavens". Ball, P. (30 June 2005). "Science history: Setting the record straight". The Hindu. Van Helden, Albert (1995). "On Motion". The Galileo Project. Laet nemen (soo den hoochgheleerden H. IAN CORNETS DE GROOT vlietichste ondersoucker der Naturens verborghentheden, ende ick ghedaen hebben) twee loyen clooten d'een thienmael grooter en swaerder als d'ander, die laet t'samen vallen van 30 voeten hooch, op een bart oft yet daer sy merckelick gheluyt tegen gheven, ende sal blijcken, dat de lichste gheen thienmael langher op wech en blijft dan de swaerste, maer datse t'samen so ghelijck opt bart vallen, dat haer beyde gheluyden een selve clop schijnt te wesen. S'ghelijcx bevint hem daetlick oock also, met twee evegroote lichamen in thienvoudighe reden der swaerheyt, daerom Aristoteles voornomde everedenheyt is onrecht. In: Simon Stevin, De Beghinselen der Weeghconst, 1586. Asimov, Isaac (1964). Asimov's Biographical Encyclopedia of Science and Technology. ISBN 978-0385177719

E. J. Dijksterhuis, ed., The Principal Works of Simon Stevin. Amsterdam, Netherlands: C. V. Swets & Zeitlinger, 1955 vol. 1, pp. 509, 511.

Further reading

Adler, Carl G. (1978). "Galileo and the Tower of Pisa experiment". American Journal of Physics . 46 (3): 199–201. Bibcode:1978AmJPh..46..199A. doi:10.1119/1.11165. Crease, Robert P. (2006). "The Legend of the Leaning Tower". In Hall, Linley Erin (ed.). The laws of motion : an anthology of current thought. Reprint of an article in Physics World , February 2003. (1st ed.). New York: Rosen Pub. Group. pp. 8–14. ISBN 9781404204089. Segre, Michael (1989). "Galileo, Viviani and the tower of Pisa". Studies in History and Philosophy of Science Part A. 20 (4): 435–451. doi:10.1016/0039-3681(89)90018-6.

External links

Galileo experiment on the Moon Galileo and the Leaning Tower of Pisa The Hammer-Feather Drop in the world’s biggest vacuum chamber

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  10. Galileo's Leaning Tower of Pisa experiment - Hellenica World

    Between 1589 and 1592,[1] the Italian scientist Galileo Galilei (then professor of mathematics at the University of Pisa) is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass, according to a biography by Galileo's pupil Vincenzo Viviani ...