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In this video, he talks about the four main variables that describes any objects motion. He describes what a vector is and pointed out of the four variables which are vectors or not. There are some equations that are not simplified yet, so in this video he explains the equation while he's simplying it

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Linear Motion with Constant Acceleration (with derivations)

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We can predict the position of an object with constant acceleration.

- It explains the difference between each variable and their equation.

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On the left hand side above, the constant acceleration is integrated to obtain the velocity. For this indefinite integral, there is a constant of integration. But in this physical case, the constant of integration has a very definite meaning and can be determined as an intial condition on the movement.

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Galileo Galilei, was an Italian astronomer, physicist, engineer, philosopher, and mathematician. He was named after a relative called Galileo Bonaiuti who was a physician, university lecturer and politician. Galileo died in Arcetri, Italy, on January 8, 1642, after suffering from a fever and heart palpitations.

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In this video, she was trying out the experiment Galileo has planned. She described what will happen if she placed the car in a certain spot so that there would be a different type of speed.

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Created for Doc's Physics Class - Produced by Madison Plummer, Class of 2013

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Galileo made an hypothesis about an object falling at a certain rate. Since some objects fall naturally, its hard to figure out the speed of an object. So Galileo believes that if its falling at rest, its going to fall twice as fast. He made an experiment of having a ramp instead of the ball being thrown vertically to see if his hypothesis is correct.

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The ideas are presented in lively fashion as a dialogue involving three characters, Salviati, Sagredo and Simplicio. The official Church point of view, that is, Aristotelianism, is put forward by the character called Simplicio, and usually demolished by the others.

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Favorite Quote:

"Philosophy is written in this grand book I mean the universe which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it."

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Galileo Galilei was born in Pisa, Italy on February 15, 1564. He was the oldest of seven children. His father was a musician and wool trader, who wanted his son to study medicine as there was more money in medicine. At age eleven, Galileo was sent off to study in a Jesuit monastery.

Rerouted from Religion to Science

After four years, Galileo had announced to his father that he wanted to be a monk. This was not exactly what father had in mind, so Galileo was hastily withdrawn from the monastery.

In 1581, at the age of 17, he entered the University of Pisa to study medicine, as his father wished.

Galileo Describes the Law of the Pendulum

At age twenty, Galileo noticed a lamp swinging overhead while he was in a cathedral. Curious to find out how long it took the lamp to swing back and forth, he used his pulse to time large and small swings. Galileo discovered something that no one else had ever realized: the period of each swing was exactly the same. The law of the pendulum, which would eventually be used to regulate clocks, made Galileo Galilei instantly famous.

Except for mathematics, Galileo Galilei was bored with the university. Galileo's family was informed that their son was in danger of flunking out. A compromise was worked out, where Galileo would be tutored full-time in mathematics by the mathematician of the Tuscan court. Galileo's father was hardly overjoyed about this turn of events, since a mathematician's earning power was roughly around that of a musician, but it seemed that this might yet allow Galileo to successfully complete his college education.

However, Galileo soon left the University of Pisa without a degree.

Galileo and Mathematics

To earn a living, Galileo Galilei started tutoring students in mathematics. He did some experimenting with floating objects, developing a balance that could tell him that a piece of, say, gold was 19.3 times heavier than the same volume of water.

He also started campaigning for his life's ambition: a position on the mathematics faculty at a major university. Although Galileo was clearly brilliant, he had offended many people in the field, who would choose other candidates for vacancies.

Galileo and Dante's Inferno

Ironically, it was a lecture on literature that would turn Galileo's fortunes. The Academy of Florence had been arguing over a 100-year-old controversy: What were the location, shape, and dimensions of Dante's Inferno? Galileo Galilei wanted to seriously answer the question from the point of view of a scientist. Extrapolating from Dante's line that "[the giant Nimrod's] face was about as long/And just as wide as St. Peter's cone in Rome," Galileo deduced that Lucifer himself was 2,000 arm-length long. The audience was impressed, and within the year, Galileo had received a three-year appointment to the University of Pisa, the same university that never granted him a degree.

The Leaning Tower of Pisa

At the time that Galileo arrived at the University, some debate had started up on one of Aristotle's "laws" of nature, that heavier objects fell faster than lighter objects. Aristotle's word had been accepted as gospel truth, and there had been few attempts to actually test Aristotle's conclusions by actually conducting an experiment!

According to legend, Galileo decided to try. He needed to be able to drop the objects from a great height. The perfect building was right at hand--the Tower of Pisa, 54 meters tall. Galileo climbed up to the top of the building carrying a variety of balls of varying size and weight and dumped them off of the top. They all landed at the base of the building at the same time (legend says that the demonstration was witnessed by a huge crowd of students and professors). Aristotle was wrong.

However, Galileo Galilei continued to behave rudely to his colleagues, not a good move for a junior member of the faculty. "Men are like wine flasks," he once said to a group of students. "...look at....bottles with the handsome labels. When you taste them, they are full of air or perfume or rouge. These are bottles fit only to pee into!"Not surprisingly, the University of Pisa chose not to renew Galileo's contract.

Necessity Is the Mother of Invention

Galileo Galilei moved on to the University of Padua. By 1593, he was desperate in need of additional cash. His father had died, so Galileo was the head of his family, and personally responsible for his family. Debts were pressing down on him, most notably, the dowry for one of his sisters, which was paid in installments over decades (a dowry could be thousands of crowns, and Galileo's annual salary was 180 crowns). Debtor's prison was a real threat if Galileo returned to Florence.

What Galileo needed was to come up with some sort of device that could make him a tidy profit. A rudimentary thermometer (which, for the first time, allowed temperature variations to be measured) and an ingenious device to raise water from aquifers found no market. He found greater success in 1596 with a military compass that could be used to accurately aim cannonballs. A modified civilian version that could be used for land surveying came out in 1597 and ended up earning a fair amount of money for Galileo. It helped his profit margin that 1) the instruments were sold for three times the cost of manufacture, 2) he also offered classes on how to use the instrument, and 3) the actual toolmaker was paid dirt-poor wages.

A good thing. Galileo needed the money to support his siblings, his mistress (a 21-year-old with a reputation as a woman of easy habits), and his three children (two daughters and a boy). By 1602, Galileo's name was famous enough to help bring in students to the University, where Galileo was busily experimenting with magnets.

In Venice on a holiday in 1609, Galileo Galilei heard rumors that a Dutch spectacle-maker had invented a device that made distant objects seem near at hand (at first called the spyglass and later renamed the telescope).

A patent had been requested, but not yet granted, and the methods were being kept secret, since it was obviously of tremendous military value for Holland.

Galileo Builds a Spyglass (Telescope)

Galileo Galilei was determined to attempt to construct his own spyglass. After a frantic 24 hours of experimentation, working only on instinct and bits of rumors, never having actually *seen* the Dutch spyglass, he built a 3-power telescope. After some refinement, he brought a 10-power telescope to Venice and demonstrated it to a highly impressed Senate. His salary was promptly raised, and he was honored with proclamations.

Galileo's Observations of the Moon

If he had stopped here, and become a man of wealth and leisure, Galileo Galilei might be a mere footnote in history. Instead, a revolution started when, one fall evening, the scientist trained his telescope on an object in the sky that all people at that time believed must be a perfect, smooth, polished heavenly body-the Moon. To his astonishment, Galileo Galilei viewed a surface that was uneven, rough, and full of cavities and prominences. Many people insisted that Galileo Galilei was wrong, including a mathematician who insisted that even if Galileo was seeing a rough surface on the Moon, that only meant that the entire moon had to be covered in invisible, transparent, smooth crystal.

Discovery of Jupiter's Satellites

Months passed, and his telescopes improved. On January 7, 1610, he turned his 30 power telescope towards Jupiter, and found three small, bright stars near the planet. One was off to the west, the other two were to the east, all three in a straight line. The following evening, Galileo once again took a look at Jupiter, and found that all three of the "stars" were now west of the planet, still in a straight line!

Observations over the following weeks lead Galileo to the inescapable conclusion that these small "stars" were actually small satellites that were rotating about Jupiter. If there were satellites that didn't move around the Earth, wasn't it possible that the Earth was not the center of the universe? Couldn't the Copernican idea of the Sun at the center of the solar system be correct?

"The Starry Messenger" Is Published

Galileo Galilei published his findings-as a small book titled The Starry Messenger. 550 copies were published in March of 1610, to tremendous public acclaim and excitement.

Seeing Saturn's Rings

And there were more discoveries via the new telescope: the appearance of bumps next to the planet Saturn (Galileo thought they were companion stars; the "stars" were actually the edges of Saturn's rings), spots on the Sun's surface (though others had actually seen the spots before), and seeing Venus change from a full disk to a sliver of light.

For Galileo Galilei, saying that the Earth went around the Sun changed everything since he was contradicting the teachings of the Church. While some of the Church's mathematicians wrote that his observations were clearly correct, many members of the Church believed that he must be wrong.

In December of 1613, one of the scientist's friends told him how a powerful member of the nobility said that she could not see how his observations could be true, since they would contradict the Bible. The lady quoted a passage in Joshua where God causes the Sun to stand still and lengthen the day. How could this mean anything other than that the Sun went around the Earth?

Galileo Is Charged With Heresy

Galileo Galilei was a religious man, and he agreed that the Bible could never be wrong. However, he said, the interpreters of the Bible could make mistakes, and it was a mistake to assume that the Bible had to be taken literally.

This might have been one of Galileo's major mistakes. At that time, only Church priests were allowed to interpret the Bible, or to define God's intentions. It was absolutely unthinkable for a mere member of the public to do so.

And some of the Church clergy started responding, accusing him of heresy. Some clerics went to the Inquisition, the Church court that investigated charges of heresy, and formally accused Galileo Galilei. This was a very serious matter. In 1600, a man named Giordano Bruno was convicted of being a heretic for believing that the earth moved about the Sun, and that there were many planets throughout the universe where life-living creations of God-existed. Bruno was burnt to death.

However, Galileo was found innocent of all charges, and cautioned not to teach the Copernican system. 16 years later, all that would change.

The Final Trial

The following years saw Galileo move on to work on other projects. With his telescope he watched the movements of Jupiter's moons, wrote them up as a list, and then came up with a way to use these measurements as a navigation tool. There was even a contraption that would allow a ship captain to navigate with his hands on the wheel. That is, assuming the captain didn't mind wearing what looked like a horned helmet!

As another amusement, Galileo started writing about ocean tides. Instead of writing his arguments as a scientific paper, he found that it was much more interesting to have an imaginary conversation, or dialogue, between three fictional characters. One character, who would support Galileo's side of the argument, was brilliant. Another character would be open to either side of the argument. The final character, named Simplicio, was dogmatic and foolish, representing all of Galileo's enemies who ignored any evidence that Galileo was right. Soon, he wrote up a similar dialogue called "Dialogue on the Two Great Systems of the World." This book talked about the Copernican system.

"Dialogue" was an immediate hit with the public, but not, of course, with the Church. The pope suspected that he was the model for Simplicio. He ordered the book banned, and also ordered the scientist to appear before the Inquisition in Rome for the crime of teaching the Copernican theory after being ordered not to do so.

Galileo Galilei was 68 years old and sick. Threatened with torture, he publicly confessed that he had been wrong to have said that the Earth moves around the Sun. Legend then has it that after his confession, Galileo quietly whispered "And yet, it moves."

Unlike many less famous prisoners, he was allowed to live under house arrest in his house outside of Florence. He was near one of his daughters, a nun. Until his death in 1642, he continued to investigate other areas of science. Amazingly, he even published a book on force and motion although he had been blinded by an eye infection.

The Vatican Pardons Galileo in 1992

The Church eventually lifted the ban on Galileo's Dialogue in 1822-by that time, it was common knowledge that the Earth was not the center of the Universe. Still later, there were statements by the Vatican Council in the early 1960's and in 1979 that implied that Galileo was pardoned, and that he had suffered at the hands of the Church. Finally, in 1992, three years after Galileo Galilei's namesake had been launched on its way to Jupiter, the Vatican formally and publicly cleared Galileo of any wrongdoing.

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The Significant Contributions of Galileo Galilei, the Father of Reason

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Galileo Galilei was born in Pisa, Italy on February 15, 1564. He was the oldest of seven children. His father was a musician and wool trader, who wanted his son to study medicine as there was more money in medicine. At age eleven, Galileo was sent off to study in a Jesuit monastery.

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Galileo's first invention was the telescope. The way he improved his telescope was to make it more magnifying so that what ever someone is seeing could be exposed to more things. From this, he has created some observations about the moon. He realized that the moon had these dark spots but once time goes by, those dark spots become a different color.

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Galileo's Work

When Galileo first turned his telescope to the moon, he had no idea that he was about to see something that would cast doubt upon centuries-old beliefs. At the time of Galileo, science was based upon the teachings of Aristotle. According to Aristotle, the Earth was the center of the universe. All heavenly bodies, including the moon, were perfect spheres that moved around the Earth with circular motions (or combinations of circular motions), and the Earth was the only source of imperfection in the universe. The dark spots on the moon that been visible to man throughout the ages were explained away as parts of the moon that absorbed and emitted light differently than other parts-- the surface itself was perfectly smooth.

Copernicus's theory that the sun rather than the Earth was the center of all motion had moved the Earth into the realm of heavenly bodies. However, Copernicus's theory went against fundamental beliefs of the time, and therefore was dismissed by most learned people. One of the unacceptable notions was that of the imperfect Earth existing in the realm of the perfect heavens.

However, in November 1609 Galileo pointed his improved telescope with 20x magnification to the moon for the first time. He had decided to make an in-depth study of the moon. From November 30 until December 18 of that year, he examined and drew the moon and described that research in his book Sidereus Nuncius. Galileo's observations led him to the startling conclusion that the moon is anything but perfect. With his telescope, he noticed small dark spots that had never been seen before on the illuminated part of the moon's surface, along with similar light spots in the dark area. He observed that as time passed, these and other spots changed, either getting lighter and eventually disappearing or getting darker and more distinct. The interface between the light and dark sides of the moon was rough and uneven, rather than smooth as would be expected on a perfectly smooth sphere. Galileo also observed that the spots all "have a dark part on the side toward the Sun while on the side opposite the Sun they are crowned with brighter borders like shining ridges." ( Sidereus Nuncius, p 41)

From these and many other observations, Galileo concluded that the moon's surface consists of valleys, plains and mountains much like the surface of the Earth ( Sidereus Nuncius p 48-49). The dark spots are shadows cast by these mountains and valleys as the sun falls on them. As the moon's position relative to the sun changes, the shapes and intensities of these shadows change. Galileo's conclusion was a shocking one-- how can the moon, a heavenly body, not be perfect and spherical? If the moon is imperfect, could there be other imperfect heavenly bodies as well? If heavenly bodies can be imperfect, why can the Earth not be a heavenly body? Galileo's conclusions about the moon did not give solid proof of Copernicus' theory, but his observations paved the way for the theory's eventual acceptance.
[ Note: The page numbers in Sidereus Nuncius cited above refer to Sidereus Nuncius or the Sidereal Messenger. Translated with introduction, conclusion, and notes by Albert Van Helden. Chicago: University of Chicago Press, 1989. AVH]
Galileo's Work Today

I am a member of the Spring 1995 History 333 ("Galileo in Context") class at Rice University. Our assignment was to study Galileo's work in a particular field and then recreate his work as closely as possible. The Astronomy Group built Galilean telescopes and used them to study the same heavenly bodies that Galileo did 375 years ago.

Our group experienced many of the exciting discoveries and frustrating problems that Galileo himself may have encountered. We used modern materials to make replicas of Galileo's telescopes (click here for more information on our Galilean telescopes). One fundamental difference between our telescopes and Galileo's is the fact that ours had only about 9x magnification while Galileo used telescopes with magnifications of up to 20 to study the moon. Our attempt to rigorously recreate Galileo's work was also thwarted by the uncooporative Houston spring weather. The skies were clear for only about five nights during the semester, making it impossible to observe all the phases of the moon as Galileo did.

During my first attempt at observing the moon, I encountered problems, both expected and unforeseen. I was initially frustrated in trying to find the moon due to the small field of view the telescope. The best technique, I found, was to search until a bright light (the light of the moon) was visible on the interior surface of the tube. By moving the telescope so that this light moved down the length of the tube towards my eye, I was able to bring the moon into view. After securing the mounting so that the telescope was fixed on the moon, I was ready to begin viewing.

Before my work on this project, I had had very little experience observing the heavens with a telescope. Therefore, on my first night of observing, I felt much of the same amazement and excitement that Galileo must have felt when he first saw the detail of the moon that is invisible to the naked eye.

This is my drawing of the moon as seen through a Galilean telescope at 11pm on April 26, 1995.

The 9x magnification of our telescope brought out numerous small shadows in the lower left face of the moon, along with a distinctly rough interface between the dark and light sides of the moon. The telescope also made it possible to see the variations in the darkness of the shadows, which gave the moon the distinct three-dimensional look. Galileo's conclusions about the imperfect surface of the moon may have been revolutionary, but they are not surprising once one has looked at the moon through a telescope. Before Galileo made his 20x telescope, the strongest telescopes people had been able to make had only about 3x or 4x magnification. Presumably these telescopes were not strong enough to bring out the details of the moon as Galileo's did; It was this high magnification that allowed Galileo to make his discoveries before others. Galileo's effort to examine the moon through all its phases also played a big role in enabling him to discover and interpret the changing shadows.

As I continued my observations, a number of other problems with our telescope and mounting became obvious. At least one of these problems was one with which Galileo probably had to deal. The small field diameter of our telescopes (my telescope had a calculated field diameter of 964.8 arcseconds, or 16 arcminutes) made it impossible to see the whole face of the moon at once. In the picture

href="astrogrobs/sm2.moon1.gif">above, the concentric circles indicate the field of view visible at one time. The outer circle shows the total view possible with the telescope, while the inner circle roughly indicates the maximum field I was able to get in focus. The small field of view made it necessary to move the telescope around in order to see the whole moon when observing and drawing it. Many of Galileo's drawings of the moon indicate that he had to deal with the same problem. His pictures seem to have been drawn more as representations of the moon than as accurate replicas of what one sees through a telescope. For example, in the picture below, the size of the circular crater on the terminator (perhaps Albategnius) is greatly exaggerated. It is speculated that Galileo represented it this way in order to emphasize the effect of shadowing in creating a three-dimensional image.

From Galileo's Sidereus Nuncius (p 44)

Keeping the image withing the field of view also became a problem. In spite of our efforts to make the mounting as stable as possible, we could not entirely eliminate the wobble from the telescope. Any slight wind or shakiness of the viewer's hand, coupled with the tiny field of view, would move the telescope enough for the object under study to move out of the field. This effect made observing somewhat more difficult, although it had a more detrimental impact on observations of the more distant (and therefore smaller) planets than on observations of the moon.

Full moon observed and drawn March 16, 1995 by Nicole Peterson.

One final problem that future groups will find easily correctable is the height of the eyepiece of our telescope. Once I got the telescope angled at the moon, I discovered that the eyepiece was too high for my eye to reach while I was sitting, yet too low to see into while kneeling. The half-crouch position that I finally had to settle for became uncomfortable and made the observing much more difficult. A suggestion for the future is to design each person's mounting so that the eyepiece sits where it is most comfortable for that person in order to eliminate this annoying problem.
Ann Zumwalt

Galileo || Bibliography || Sunpots || Orion & Pleiades || Moon || Saturn || Jupiter || Venus || Mars || Telescope

We appreciate any comments or suggestions.

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When Galileo first turned his telescope to the moon, he had no idea that he was about to see something that would cast doubt upon centuries-old beliefs. At the time of Galileo, science was based upon the teachings of Aristotle. According to Aristotle, the Earth was the center of the universe.

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At the age of 8, his family moved to Florence, but he was left them for two years. He was educated in the Camaldolese Monastery at Vallombrosa. He wanted to consider the priesthood as a young man, he enrolled for a medical degree at the University of Pisa. However, he did not complete this degree, but instead studied mathematics.

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In this video, the horse represents the motion of the Earth. Galileo thought experiments were based off of motion. HE stated that when the horse is moving while the ball is being thrown at the same time, the ball will still follow the horse. He stated that we do not feel the motion of the Earth

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Galileo's Thought Experiment

The heliocentric theory holds that Earth moves around the Sun at great speed, a controversial idea in Galileo's time. Even today, many people are still perplexed by the fact that we don't experience any sense of this motion. This video segment, adapted from NOVA, shows a dramatization of one of Galileo's thought experiments designed to help prove heliocentric theory.

Visit the program page here.

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The heliocentric theory holds that Earth moves around the Sun at great speed, a controversial idea in Galileo's time. Even today, many people are still perplexed by the fact that we don't experience any sense of this motion. This video segment, adapted from NOVA, shows a dramatization of one of Galileo's thought experiments designed to help prove heliocentric theory.

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Galileo was born in PIsa,Italy on February 15, 1564. Galileo and his family were never rich but they were in a nobility. They eventually they moved. Galileo was never married but he did have someone named Marina Gamba, which sooner becomes the mother of his three kids. Two of his daughters became nuns. He also had a son but he left him.

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The Galileo Project | Biography | Early Life

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Text, design, and layout by Megan Wilde for the Electronic Text Center. This biography is based upon information culled from The Galileo Project website.

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We can predict the final velocity of

objects with constant acceleration

- This video explains what acceleration is and how we use equations to find our final velocity.

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Introduction of Motion with Constant Acceleration. How we calculate the speed

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All objects fall at the same rate

- Scientists thought that force causes speed until Galileo created this conclusion that he earth had a constant acceleration using equations

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it is important to remember that Galileo's law of fall claims that bodies fall at a constant acceleration, i.e., that their speed increases by equal increments within equal time periods, and that the distance traveled by them in equal time periods is not equal.