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BEFORE: Aristotle VIEW on the UNIVERSE was imposed by the church and by the authorities:
- EArth is at the center of the universe.
- motion has to be in a straight line, an effort is balanced by a resistance to motion. There is no acceleration.
- a large body falls faster than a less heavy one because more effort.
The speed is finite because the resistance of air is finite. So, no vacuum is possible,
other wise the speed becomes infinite.
- the theory of Democritus about atoms is rejected. Matter is not made of units. Anything is made of : fire, water, air or soil.
It took 2000 years to dismiss these views. The new science was to rely on observations, experimentation and mathematical analysis.

'aristotlle 384 BC

In aristotle's view, the one adopted by the Church, the Earth is at the center of the universe. All the planets are prefect spheres orbiting along perfect circles. Stars are plastered in a celestial sphere. All the spheres are nested into one another. There is no use to observe the heavens  because we will never reach reality but just an distorted view of it. Planets move along crystal spheres. (they didn;t know about gravity so they were try to explain why they didn't fly out). Not that for the Greek spheres and circle were perfect shapes.

Ptolemy born 90AD in Egypt

The solar of system as explained by Aristotle didn't fit the observed motion of planets as view from the Earth. Ptolemy introduces epicycles, orbits on top of orbits. Then more epicycles were added. It became very messy. Ptolemy wa a great mathematician and his system was a  computational trick to be able to predict the positions of the planets. However, he thought that we human can't only reach an imperfect reflection of a perfect reality. Sciences was not to be  based on observations and experiences. He kind of introduced Fourrier analysis showing that any periodic motion can be described by a serie of sines and cosines.

applet: retrogade motion of Mars

Nickolaus Copernicus (February 19, 1473 – May 24, 1543)

Copernicus Jordano Bruno or Giordano Bruno

The statue of Giordano Bruno at the very same place he was burnt at stake (Campo de' Fiori in Rome).. He is he 1st martyr for science. click the image. to know more.

Heliocentric system introduced by Copernicus. Uranus, Neptune and Pluto were not known yet. source, to learn more.

Copernicus was a lawyer and a doctor by trade. He found the system of Ptolemy very messy and untasteful. (see above).
He placed the Sun at the center but still used epicycles to fit the observations. The orbits were still circular (instead of ellipses)
so epicycles were necessary to fit the onservations.  He thought, as every one at the time, that planets move on Cristal spheres.
They could not other wise explain why the planets stay on their orbit instead of flying away.

He knew he could get in trouble for his work with the Church so he didn't publish his work until he was about to die.  
 (he didn't like the idea  to be tortured and killed).
He also hided his idea, in his book,  behind a lot of writing about the old ideas. Few scholars paid attention to this breakthrough.
 
But an Italian Monk Giordano Bruno did. He believed in Copernicus theory and he even believed there was life in other worlds in the Universe.
He was sentenced to be burnt at stake in Rome. You can still see his statue standing on a pillar in Rome. (see links above). Around his statue, the
story of his trial is told. (see picture above). His life and his beliefs is very interesting.
On the 400th anniversary of Bruno's death (1600), Cardinal Angelo Sodano declared Bruno's death to be a "sad episode". Despite his regret,
 he defended Bruno's persecutors, maintaining that the Inquisitors "had the desire to preserve freedom and promote the common good and did everything
possible to save his life" by trying to make him recant and subsequently by appealing the capital punishment with the secular authorities of Rome !!!
The Church seems very super slow to ackowledge its mistake !

June 2010
Nicolaus Copernicus, the Polish priest and astronomer who proposed that the Earth orbits the Sun, has been reburied with honors at Frombork Cathedral in Northern Poland,
 five centuries after he advanced his then-controversial theory. His remains had previously lain in an unmarked grave beneath the cathedral's floor.
The reburial is the culmination of a six-year effort, initiated by a local bishop, to locate the astronomer's remains and identify them using forensic reconstruction and DNA analysis
See washngton post

Galileo Galilei (15 February 1564 – 8 January 1642)

This is the "Galileo lamp" in the Duomo in Pisa. Galileo was 17 years old when he discovered the laws upon which a pendulum is built. The legend said he was using this swinging lamp in the church, using his pulse to find the period. This is not true as the lamp was hanged after the death of Galileo.

Galileo worked a lot with inclined planes. His experiments showed the principle of inertia and the laws of falling body. If you neglect friction, an incline plane dilutes gravity but you still get an uniformly accelerated motion. Galileo showed that in free-fall, bodies fall at the same rate, regardless of their mass. He shows that without friction the motion lasts for ever. (without any force needed to keep the motion going). He showed that the distance covered is proportional the the time squared. He published his work while in house arrest. He also used inclined planes to show that all body fall at the same rate regardless of their mass. (if we neglect air resistancE)

Galileo in front of the inquisition. He supported the heliocentric system of Copernicus but had to retract himself to save his life. He was considered as an heretic by the Catholic church of the time. This was the bad time to challenge the church as the counter reformation was going on/	Here some irony. In Italy, remains of  saints are exhibited in churches. But this is not the finger of a SAint, it is the middle finger of Galileo, maybe a message to those who condemned him to home arrest for the rest  of his life. This finger can be seen in Florence. History of Science Museum In 2000 the pope jean Paul II appologied  for the mistake  of the church.	The tower of Pisa and behind the Duomo. It is said that Galileo drops different objects from the top and find out that any body, regardless of its mass, falls at the same rate. This legend is probably not true either. CLICK HERE
	Galielo improved the refractive telescope built by a dutch optician. It was a toy and he made it an intrument to study the heavens. He saw the mountains on the Moon, the ring of Staturn  (he called it handles or ears), the phases of VEnus, the moons of Jupiter. Newtons later invented the reflective telescope.	DISCOVERIES of Galileo that upset the ROman Catholic Church phases of Venus can not be explained by Ptolemy system of epicycles. Only Copernicus 's view can explain the phases/ A student of Galileo suggested him to look at the phases of vEnus to decide which system was the best. (Copernicus or Ptolemy). wash study of GAlielo 1609 (museum of Florence) Moons of Jupiter. Io, Europa, Ganymede and Callisto So Earth is not the onlyplanet to have Moon. It is not in a privileged position after all. Plus if was thought that the Earth can not rotate around the sun because we would fly off. But the moons of Jupiter stay around while Jupiter is moving. So Galileo reasoned that there must be something keeping us on earth and the moon around the planets while the planets orbit the Sun. ring of Saturn. Galielo could to resolve the whole ring so he described the ring as handles. But he was the first one to see it.So the planets were not perfect spheres after all. (Church's view). mountains and valleys on the Moon. The moon is not a perfect sphere either. sunspots on the Sun . He observed the spots moving around so he reasoned that the Sun was spinning about its axis. So the EArthwas probably spinning too.

GAlileo is probably the father of modern Physics. He based his laws or finding on experiments and observations.
 He is known to have supported the heliocentric system introduced by Copernicus. He based his belief on the observation of the phases on Venus.
He used for his observations a telescope (the refractive telescope with lenses) that he had himself invented.
Actually, he didn't invent the telescope but he improved it a lot. (The real inventor was a Dutch optician) Then he let people believe he was the inventor.

 ANyway, his invention pleased so much the princes of Venice  that he was given a "tenure track" and a raise at the university of Padua (in the Venetian Republic)
 and didn't have to worry about money any more. He was able to concentrates on his experiments. Thanks to his telescope ships approaching
Venice could be seen 2 hours earlier. He improved a child toy and sold it.

Note: Galileo built a refractive telescope that use 2 lenses. The problem is that light can be spread when going through the lenses.
This is called the spreading of light or diffraction. As a result, the image is blurred. Newton invented the reflective telescope using mirrors still used today.
 You don't have this problem.

Galileo also investigated the pendulum and discovered that the period on a pendulum only depends on its length.

Galileo supported the heliocentric system of Copernicus. Unlike Copernicus, he wanted every one to know about it and wrote a book in Italian.
 This was not conformist at all. At this time, scholars would write their book in Latin so only educated people could understand.
Galileo, already popular because of his telescope, wrote in Italian on purpose and his book quickly spread out.
He got in trouble with the inquisition and had to stay in his home for the rest of his life.  (he was sentenced to home arrest. This was scientifically productive).
While in home arrest, in his Villa next to Florence, he published all his work on kinematics. (He didn't have time before).

Galileo and Kepler knew each other. They never met but they exchange some letters. Exactly 1 year after the death of Galileo, Newton.

more about him
hammer and feather on the moon
extra credits: (how Galileo figured out inertia)


LAB GALILEO-PROJECTILE MOTION

Kepler (December 27, 1571 – November 15, 1630)

Kepler. Galileo, Shakespeare, Queen Elizabeth were all contemporaries of Kepler.	Kepler was protestant and had to leave his Catholics country (Germany) to Prague in 1600. It was the 30 years war in Europe. Protestants and Catholics  were fighting. It was a very bloody period.	In Prague Kepler was hired by Tycho Brahe as a mathematician. He was in charge of processing all the data collected by Tycho. Tycho Brahe was a very gifted observer but Kepler was a better mathmatician. The 2 men could not stand each others . But they needed each other. Tycho was a weird guy. One day he had a duel with a student over who was the best mathematician. The student's sword cut Tycho's nose when he was 20. Tycho had to wear a fake nose made of copper for the rest of his life. the nose was found in his tomb in Prague. During meals Tycho had a dward under the table and fed him like a pet.
click The picture on the left shows tycho collecting data from the planets. He collected these data in a room without ceiling, in his castle in Denmark. He lived on an island given by the king of Denmark. The King has been impressed by the discovery of Tycho of a Supernova (1562). When the king died Tycho had to live Denmark for Praque.  (he was not in favor anymore). He was the first astronomer able to collect very high quality data. Only using his naked eyes. Kepler wanted these data badly.	click image Kepler discovered 3 laws regarding the motion of planets. The second law is a consequence of the conservation of angular momentum we are studying now. In equal time, planets sweep the same area.	click image. Kepler got the data of Tycho after his death. He figured out his 3 laws after years of work. He wrote a book called harmony of the world. It is a mystic about music and the motions on planets. Newtons found the 3 laws and used them for his work. Since the force of gravity was not know, Kepler thought the planets had to moved on geometric shape embedded in each other. He was very good in geometry and the ratio between the  the shapes were matching the ration between the planets distance from the Sun. This paper was an addition to his first publication. Know more.

Kepler greatest achievement was to describe the planet motion.
1) Planets move along ellipses. an ellipse is a conic section like the circle, the parabola and the hyperbola
2) Planets sweep equal area in equal time.
3)Take any 2 planets.  the orbital period squared is proportional to the orbital distance cubed. (Newton's version of Kepler's law)

That was a huge breakthrough. Newton studied these laws and was able explain them by using calculus and by introducing a  force (force of gravity)
 that holds the universe together. In addition, Newton showed that any body int he universe, under the influence of gravity, follows a conic section.
 Depending on the balance between the object Kinetic energy and potential energy. (see this chapter).

Even though Kepler wrote a book called harmony of the world , his life was not very happy. He was left by his father who was a mercenary.
His mother was trialled for witchcraft and he has to fight to save her life. Very young he was placed in a protestant institution where the activity was praying.
He was still very attracted by astronomy (at age 5 his mom took him the top of a hill to watch a comet). His problems were not over.
He lost his first wife. His second wife was terrible. He lost 7 of his 11 children. He had to flee Germany for Prague because protestants were persecuted.
(note : in 1609 Kepler observed a supernova ,)

In Prague he met Tycho Brahe, an extremely gifted astronomer who had collected extremely good data from the position of Mars and other planets.
He hired Kepler as a mathematician. They could not stand each other (they stayed together 18 months). Tycho loved to party and was very arrogant.
He played with Kepler, giving him some data only little by little. Finally, Tycho died. Funny episode. Tycho used to drink a lot.
At a party, he could not leave the room to go to the bathroom. He had to wait for the king to leave first. His balder exploded and he died.
(not 100% exact, historians are not sure about it).  Kepler managed to steal the tycho data to work on it.
The result, his famous 3 laws. He also wrote a famous almanac for the king. (the way astronomer were making money, was to work horoscopes for the rich people) .
 learn more

watch: http://www.learner.org/resources/series42.html?pop=yes&pid=551
move the movie to 14:00
quiz:
1) The conic sections are the ________________, ________________ and the _______________________
2) A)How can you get such curves geometrically ?

B) How to get a circle ? (draw)

C) How to get an ellipse ? (draw)

D) hyperbola ? (draw)

3) What is the eccentricity ?   draw to explain.

applet: Kepler's second law

Newton ( Christmas Day 1642 - 31 March 1727 )

There is a statue of Sir Isaac Newton in the chapel of Trinity College, Cambridge. When translated from the Latin, the inscription at its base reads Newton Who surpassed all men in genius. more: timelinesciences.	source : NASA website. click image A replica of Newton's 6 inch reflecting telescope of 1672 for the Royal Society.	CLICK IMAGE : Halley's comet/ Halley was a good friend of Newton. He convinced Newton to publish his work about the universal gravitational law. Newton found why the planets stay in orbit around the EArth (Inertia principle + force of gravity) but never published his work. The comet is named after Edmond Halley. He observed the comet in 1682 and realized it was the same object observed by Kepler in Prague and in 1531 by Apianus. The period is 76 years.
Robert Hooke disagree with Newton about the nature of light. Newton saw light as particles called corpuscles. Newton could not stand criticism and hated Hooke. It seems Hook was short and hunchback  and Newton wrote these famous words to Hooke: If I have seen further it is by standing on the shoulders of giants	Newton developed his infinitesimal calculus between 1664 and 1666 when he was temporarily con-fined to his estate in Woolsthorpe, quarantined from an outbreak of Bubonic plague in England. However, Newton did not publish his mathematics. Years later Leibniz published his own infinitesimal methods in a recently established scholarly journal circulated around Europe, the Acta Eruditorum. Leibniz's methods appeared in the Acta in two different articles, one in 1682 and the other in 1684. Thus, while Newton's techniques were developed first, Leibniz was the first to publish. more: http://www1.umn.edu/ships/9-1/calculus.htm	discovered the nature of light and color produced the universal theory of gravity changed ideas about space developed the laws of motion developed whole areas of mathematics including calculus disagreed violently with the deeply held religious beliefs of the day - in particular he did not believe in the Holy Trinity was an enthusiastic alchemist who - among many other feats - tasted almost all of the known heavy metals (which we now know are poisonous!) reformed the Royal Mint

applet planetary motion
applet newton's second law
slides gravity

The poet Alexander Pope, who lived at the same time as Newton, wrote

Nature and Nature's laws lay hid in night;
God said, 'Let Newton be!' and all was light.

But a English humorist added: It did not last; the devil howling "Ho!
Let Einstein be!" restored the status quo.

The 3 laws of Newton based on calculus could explain and predict any nature's  phenomena given the initial conditions. 

Newton didn't have a happy childhood. His father , an illiterate farmer, has died 3 months before his birth. His mother remarried when he was 3 and left Newton
 with his grandmother. His stepfather died when he was 10. His mother returned home with 3 other kids and a library of books.
Newton didn't go to school until he was 12 years old. He finally went to school but didn't learn any MAth or Science. His classmates didn't like him as
he was always the best. He came back home at 17 years old. His mother wanted him to be a farmer but he was really bad at it. His uncle convinced his mother
to send him to Trinity College Cambridge (his uncle's old college). There he taught himself Math and Astronomy. He became a Mathematics professor.

Soon after Newton had obtained his degree in August of 1665, the University closed down as a precaution against the Great Plague.
 For the next 2 years, Newton worked at his home in Woolsthorpe on calculus, optics and the law of gravitation.
While Newton remained at home he laid the foundations for differential and integral calculus, several years before its independent discovery by Leibniz.

In 1672 Newton was elected a fellow of the Royal Society after donating a reflecting telescope. Also in 1672 Newton published his first scientific paper on light and color in the Philosophical Transactions of the Royal Society. The paper was generally well received but Hooke and Huygens objected to Newton's attempt to prove,
 by experiment alone, that light consists of the motion of small particles rather than waves. He called the particles corpuscles.
The reception that his publication received did nothing to
 improve Newton's attitude to making his results known to the world. He was always pulled in two directions, there was something in his nature which wanted
fame and recognition yet another side of him feared criticism and the easiest way to avoid being criticized was to publish nothing.
Certainly one could say that his reaction to criticism was irrational, and certainly his aim to humiliate Hooke in public because of his opinions was abnormal.
 However, perhaps because of Newton's already high reputation, his corpuscular theory reigned until the wave theory was revived in the 19^th century.
The other theory was Huygens who believed light was a wave. This was shown later by Thomas Young. He demonstrated that light can produce
interference pattern. This theory was challenged again with modern Physics. Light is both a wave and a particle.

He didn't publish his work until his friend Halley pushed him to. He could not believe Newton kept all his discoveries for himself.
Halley persuaded Newton to write a full treatment of his new physics and its application to astronomy.
Over a year later (1687) Newton published the Philosophiae naturalis principia mathematica or Principia as it is always known.
The Philosophiæ Naturalis Principia Mathematica (Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short)
is a three-volume work by Isaac Newton published on July 5, 1687. It contains the statement of Newton's laws of motion forming the foundation of
classical mechanics, as well as his law of universal gravitation and a derivation of Kepler's laws for the motion of the planets (which were first obtained empirically). The Principia is widely regarded as one of the most important scientific works ever written.

In formulating his physical theories, Newton had developed a field of mathematics known as calculus. However, the language of calculus was largely left out of the Principia. Instead, Newton recast the majority of his proofs as geometric arguments.

There was a fight between Newton and Leibniz, both of them having invented Calculus. The notations we use now are Leibniz's one.

Over his life, Newton suffered of depression. He could not stand criticism. He hated Hooke and tried to destroy his documents from the Royal Academy after Hooke's death. 

At the end of his life, Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's great recoining, somewhat treading on the toes of Master Lucas (and securing the job of deputy comptroller of the temporary Chester branch for Edmond Halley). Newton became perhaps the best-known Master of the Mint upon Lucas' death in 1699, a position Newton held until his death. These appointments were intended as sinecures, but Newton took them seriously, retiring from his Cambridge duties in 1701, and exercising his power to reform the currency and punish clippers and counterfeiters.

In 1703 he was elected president of the Royal Society and was re-elected each year until his death. He was knighted in 1705 by Queen Anne, the first scientist to be so honored for his work. However the last portion of his life was not an easy one, dominated in many ways with the controversy with Leibniz over which had invented the calculus.

He lived for 85 years and died in agony from stones in his bladder. He refused the last sacrament on his deathbed, but is buried in state in Westminster Abbey.
Before he died , he was asked what was his greatest achievement. Surprisingly, he answered " to die a virgin".

watch that movie on Newton's law

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