# What Were Galileo's Contributions to Physics?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

## The Beginning

To fully understand Galileo's accomplishments in physics, it is important to see the timeline of his life. Galileo’s work in physics and astronomy can be best split up into three main phases:

• 1586-1609: mechanics and other types of related physics
• 1609-1632: astronomy

It was during that first phase that he developed the field we call dynamics, in which Newton and others made huge bounds a century later. But it was our buddy Galileo who began the line of thought and the formalization of experimentation, and we might not have known about it had he forgone publishing his main works, which he eventually did in 1638. Much of Galileo’s work was rooted in logic. In fact, he set up many of the techniques we consider necessary in science, including experimentation and recording of the results. It wouldn’t be until around 1650 that this became a standard amongst scientists (Taylor 38, 54).

Supposedly, Galileo was thinking about physics from an early age. A frequently circulated story from his youth is as follows. When he was 19, he went to a cathedral in Pisa and looked up at the bronze sanctuary lamp hanging from the ceiling. He took note of the swinging action and saw that no matter how high or low the level of oil in the lamp was, the time it took to swing back and forth never varied. Galileo was noting a pendulum property, namely that mass doesn't play a role in the period of the swing! (Brodrick 16).

One of Galileo’s first published works came in 1586, when, at age 22, he wrote La Bilancetta, a short work expounding on Archimedes' development of hydrostatic balance. Using the lever law, Galileo was able to show that if you have a rod with a pivot point, you can measure the specific gravity of an object by immersing it in water and having a counterweight balanced on the other unsubmerged side. By knowing the masses and distances to the pivot point and comparing it to the balance out of water, one needed only to utilize the lever law, and the specific weight of the unknown object could then be computed (Helden “Hydrostatic Balance”).

He continued to investigate other areas of mechanics after this. Galileo’s major breakthrough came in the study of the center of gravity of solids when he was a lecturer in Pisa in 1589. As he wrote about his findings, he would frequently find himself in heated discussions with other physicists of the time. Unfortunately, Galileo would often enter these situations without any experiments to back up his rebuke of Aristotelian physics. But that would change – eventually. It was during this stay in Pisa that Galileo, the scientist, was born (Taylor 39).

## Building the Scientific Method

Initially, in his studies, Galileo contended with two of Aristotle’s theses. One was the notion that bodies which move up and down have a velocity that is directly proportional to the weight of the object. The second was that speeds are inversely proportional to the resistance of the medium they move through. These were the cornerstones of the Aristotelian theory, and if they were wrong, down goes the house of cards. Simon Stevin, in 1586, was one of the first to bring up the experiment that would be done by Galileo just a few years later (40, 42-3).

In 1590, Galileo performed his first experiment to test these ideas. He went to the top of the Leaning Tower of Pisa and dropped two objects with significantly different weights. Despite the seemingly common-sense notion that the heavier one should hit first, both struck the ground at the same time. Of course, Aristotelians were scientists too and had skepticism about the results, but maybe we should be skeptical of the story itself (40-1).

You see, Galileo never mentioned this drop from the tower in any of his correspondences or manuscripts. Viviani, in 1654 (64 years after the supposed experiment), only says that Galileo performed the experiment in front of lecturers and philosophers. We are still not 100% sure if Galileo really performed the feat as history has recollected. But based on second-hand accounts talking about some form of experiment being done, we can be confident that Galileo did do a test of the principle even if the account is fictitious (41).

In Galileo’s findings, he determined that the speed of the falling object was not directly proportional to the height. Therefore, velocity isn’t proportional to the resistance of the medium and therefore, some ratio of air to vacuum isn’t proportional to velocity in air over velocity in vacuum but more like the difference between them over the velocity in vacuum (44).

But this got him thinking more about the falling bodies themselves, and so he started to look at their densities. Through this study of different objects falling, he realized that they did not fall because of air pushing down on them, as was believed at the time. Without realizing it, Galileo was setting the framework for Newton’s First Law of Motion. And Galileo was not shy about letting others know they were wrong. As one can see with Galileo, a common theme would begin to arise, and that was his bluntness getting him into trouble. It makes one wonder how much more he could have accomplished had he not dealt with these quarrels. It gained him unnecessary enemies, and though he was able to improve upon his work, those oppositions would prove to be a derailment to his life (44-5).

## Personal Issues

It would, however, be unfair to say that all the blame for the conflict in Galileo’s life resided with him alone. Abuse was prevalent in scientific talk at the time, not at all like it is today. One could have attacks upon them for personal rather than professional reasons, and such an example happened to Galileo in 1592. The illegitimate son of Cosimo de Medici built a machine to help dig a barrier, but Galileo predicted it would fail (and conveyed that thought in an unprofessional manner). He was absolutely right about that review, but because of his lack of tact, he was forced to resign from Pisa, for he had critiqued a prominent member of the local society. But perhaps it was for the best, for Galileo was given a new job by Guido Ubaldi, a friend of his, as chair of Mathematics at Padua in Venice in 1592. His connections with his time in the Il Bo senate, as well as his connection to Gianvincenzio Pinelli, an established intellect of the time, also helped. This enabled him to beat Giovanni Antonio Magini for the post, whose anger would be visited upon Galileo in later years. While at Padua, Galileo saw a higher salary and twice received a renewed contract to stay (once in 1598 and another in 1604), both of which saw increases in his salary from his base of 180 gold coins a year (Taylor 46-7, Reston 40-1).

Of course, finances are not everything, and he still faced difficulties during this time. A year before he resigned from Pisa, his father passed away, and his family needed money more than ever. His new position ended up being a big blessing in that regard, especially when his sister got married and required a dowry. And he was doing all of this while in poor health, which may have been induced by all of this stress (Taylor 47-8).

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But Galileo kept going with his research to get funding for his family, and in 1593 he began to look at fortification design in architecture. This was a big topic at the time, for Charles VIII of France used new technology at the end of the 15th century on Italy to obliterate enemy wall defenses. We call that tech today artillery shelling, and it represented a new engineering challenge to defend against. The best design the Italians had was using low walls that had dirt and rocks supporting them, with wide ditches and good displacement of guns to counterattack. By the 15th century, the Italians were the masters of this engineering, and it was mainly due to the minds of monks, a powerhouse in general at the time. It was Firenznola that Galileo critiqued in his report, in particular, his fortification of the castle at St. Angelo, which didn’t go so hot. Perhaps this, too, was some hidden motivation for his trial later on in his life (48-9).

In 1599, he wrote Treatise on Mechanics but did not publish it. That would finally happen after his death, which is a shame considering all the work he did in it. He covered levers, screws, inclined planes, and other simple machines in the work and how the then-accepted concept of using them to make big power from their little powers. Later in the work, he showed that a gain in force was accompanied by a corresponding loss in working distance. Galileo, later on, came up with the idea of virtual velocities, otherwise known as distributed forces (49-50).

1606 would see him describe uses for the geometrical and military compass (which he invented in 1597) in his The Operations of the Geometric and Military Compass. It was a complicated piece of equipment but could be used for more calculations than a slide rule of the time could. It, therefore, sold rather well and helped his family’s financial difficulties. But in 1607, Galileo had to defend his work when Baldessare Capra plagiarized it and claimed that others had stolen the idea. Galileo had dedicated this book to Prince Cosimo de Medici as a way to hopefully curry employment, so Galileo was very determined to set the record straight (Taylor 50-1, Drake).

While we cannot know for sure, historians and scientists feel that much of Galileo’s work from this period of his life ended up published in his Dialogues Concerning Two New Sciences. For example, the “accelerated motion” likely stems from 1604, where he stated in his notes his belief that objects call under “uniform accelerated motion.” In a letter written to Paolo Sarpi on Oct. 16, 1604, Galileo mentions that the distance a falling object covers is related to the time it took to get there. He also talks about the acceleration of objects on an inclined plane in that work (Taylor 51-2).

Another big invention of Galileo was the thermometer, whose utility is still known to this day. His version was primitive but still useful for the time. He had a container with a liquid that would go up and down based on the temperature of the surroundings. The big problems, though, were the scale as well as the volume of the container. Something universal was needed for both, but how to approach that? Also not considered were the effects of pressure, which changes with altitude and was not known to scientists of the time (52).

## Post Inquisition

After facing his tribunal and being sentenced to house arrest, Galileo returned his focus to physics in an attempt to further that branch of science. In 1633 he finished Dialogues Concerning Two New Sciences and was able to get it published in Lynden, but not in Italy. Really a collection of all his work in physics, it is set up much like his previous Dialogues with a 4-day discussion amongst the characters of Simplicio, Salviati, and Sagredo. Day 1 is devoted to the resistance of objects to fracturing, with the strength and size of the object being related. He was able to show that the breaking strain was reliant on the “square of the linear dimensions” as well as the weight of the object. Day 2 covers several topics, the first being cohesion and its causes. Galileo feels the source is either friction or that nature displeases a vacuum and thus remains intact as an object. After all, when an object is split apart, they create a vacuum for a brief moment. Though it has been mentioned earlier in the article that Galileo didn’t measure vacuum properties, he actually describes a setup that would allow one to measure the force of the vacuum without air pressure! (173-5, 178)

But day 3 would see Galileo discuss measuring the speed of light using two lanterns and the time it takes to see one being covered up, but he was unable to find a result. He felt like it isn’t infinity, but he couldn't prove it with the techniques he had applied. He wondered if that vacuum would come into play again in aiding him. Galileo also mentioned his dynamical work of falling objects, where he mentions he conducted his experiments from a height of 400 feet (Remember the story of Pisa from earlier? That tower is 179 feet tall. This further discredits that claim.). He knew that air resistance must play a role because he found a time difference in objects falling that a vacuum could not explain away. In fact, Galileo went so far as to measure air when he pumped it into a container and used grains of sand to find its weight! (178-9).

He continued his dynamics discussion with pendulums and their properties. He put forth that pendulums have a period which depends on the length of the swinging arm (in fact, a square root relation), that their period is independent of the mass of the hanging object as well as how far above the ground you start the swinging. Galileo used parallels between the idea of larger planetary orbits leading to longer orbital periods to inform his approach to pendulums (Ariotti).

Then he discusses sound waves as a vibration of air and even lays the template for the ideas of musical ratios and frequency of sound. He wraps up the day with a discussion about his ball rolling experiments, and his conclusion that distance traveled is directly proportional to the time it takes to traverse that distance squared (Taylor 182, 184-5).

Day 4 covers the parabolic path of projectiles. Here he hints at terminal velocity but also thinks about something groundbreaking: planets as free-falling objects. This, of course, greatly influenced Newton into realizing that an object that orbits is indeed in a constant state of free fall. Galileo, however, includes no math just in case he upsets someone (Taylor 187-9).

## Works Cited

Ariotti, Piero. "Galileo on the Isochrony of the Pendulum." Isis, Vol. 59, No. 4 (Winter, 1968), pp. 414-426.

Brodrick, James. Galileo: The Man, His Work, His Misfortune. Harper & Row Publishers, New York, 1964. Print. 16.

Drake, Stillman. "Was Simon Mayr Galileo's 'Ancient Adversary' in 1607?" Isis, Vol. 67, No. 3 (Sep., 1976), pp. 456-459.

Helden, Al Van. “Hydrostatic Balance.” Galileo.Rice.edu. The Galileo Project, 1995. Web. 02 Oct. 2016.

Reston Jr., James. Galileo: A Life. Harper Collins, New York. 1994. Print. 40-1.

Taylor, F. Sherwood. Galileo and the Freedom of Thought. Great Britain: Walls & Co., 1938. Print. 38-52, 54, 112, 173-5, 178-9, 182, 184-5, 187-9.

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