Chapter 5 Gravity and Motion

Essential Question How are forces related to motion

Force and motion before Newton Kepler explained the motion of the planets but not the why they move People needed a better understanding of motion, phase one slow progress towards understanding – phase two Newton solves the problem

Galileo’s Experiments First to attempt experimental physics or do experiments instead of just observe The impetus theory – developed in the 14 th century – objects moved as long as force was applied They needed to be explainable through mathematics – to remove false or bad common knowledge

Galileo’s Experiments He used two different massed objects to roll down a ramp – No matter the weight they accelerate at the same speed Determined what caused the difference in dropping objects was the effect of air resistance Was the first to use accurate clocks in his experiments Motion was consistent and would continue unless an outside force stopped it – air resistance, friction or drag of water

Descartes and Inertial motion

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The rebirth of astronomy in Europe The Earth was still at the center Observations began with Roger Bacon 1220 – 1292, recommended experimentation as a way to get knowledge By 1400 ; Georg Prbach ( ) and Johannes Regiomontanus ( ) applied this to astronomy, discovered that current tables were off This lead to the development of new equipment and the end of comment on science and the investigation of science – 1500’s

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Essential Questions How is it possible for the heliocentric model of Copernicus to account for the diurnal motion of the celestial objects, the annual motion of the Sun, and the complicated motions of the planets? What does the heliocentric model have to say about the orbital distances and periods of the planets?

Copernicus Nicholas Copernicus ( ) Torun, Poland – lived at the height of the Renaissance Mother died when he was young and Father when he was ten, Adopted and raised by his Uncle – who was a Bishop in Ermland University of Cracow – (late Teens) was introduced to astronomy and the Ptolemaic model Receives an appointment at the cathedral in Frauenberg (early Twenties)

Copernicus Travels to Northern Italy – Studies church law, medicine, astronomy, Greek, philosophy, and mathematics – incident at Padua Returns to Ermland – works as a physician, Governor of Ermland, representative to parliament, translated Greek works into Latin, wrote on economics – capitalism and bad money theory, and published a work on trigonometry

Copernicus Wrote his first work on the heliocentric model when he first returned from Italy He sent his outline to his Friends – his outline was read years later by Georg Rheticus ( ) he traveled to Ermland to persuade Copernicus to publish his Idea He was completing a 20 year work “On the Revolutions of the Heavenly Orbs”, published 2 months before his death – received first copy on death bed

The Heliocentric model Ptolemaic model positions of Sun, Moon and Planets out of place Motions must be uniform circles Placed the Sun in the center and left the moon in orbit – explained motion as well as the Ptolemaic model did Eastward rotation of Earth – The Sun’s motion caused by the earth’s orbit Retrograde motion could also be explained.

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The Heliocentric model A Sidereal period – the time it takes to complete one orbit around the Sun Synodic period – the time it takes one planet to catch another planet To calculate a superior planet (farther away from the sun) 1/P = 1/Pearth – 1/S To calculate an inferior planet (closer to the sun) 1/P = 1/Pearth + 1/S

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The Heliocentric model Did he make his model more elegant – still needed epicycles to explain the variations in speed – people still used Aristotle’s theory of motion – observations are completely neutral The rising and setting of stars – counter argument – being close to the sun relative to the stars would explain these problem The tilt of the earth would explain the seasons and precession of the stars

Essential Question Tycho Brahe Why did Tycho Brahe, the great observational astronomer, reject the heliocentric model of the solar system?

Tycho Brahe After Copernicus’s book was published he became a highly respected astronomer – mainly for the mathematics to calculate the position of celestial objects – the heliocentric idea was ignored or disbelieved The first evidence for the heliocentric model came from Tycho Brahe (1546 – 1601) Born three years after Copernicus death, Brahe’s observations eventually became the evidence for the Heliocentric model – Brahe supported Geo

Tycho Brahe Brahe was a Danish noblemen – interested in astronomy at a young age – as a law student he would sneak out to observe the sky At 26 he wrote a book on a bright new star or “nova” – This gave him a high standing with astronomers To keep him from leaving Denmark – King Frederick 2 Gave him an island (Hveen) near Copenhagen and the money to build his observatory

Tycho Brahe Made his instruments from metal, to avoid the warping that happens with wood, and made them oversized to make the measurements more accurate. Would make his equipment fixed, take several observations at the same time, made observations daily, made ten times the observations of the ancients and correct most if not all the errors

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Tycho Brahe While looking at stellar parallax he rejected the heliocentric model – failed to detect this in stars – so either they are really far away (7000 AU) or earth did not move He then measured the angular size of stars at several minutes – if the stars are 7000 AU away they would have to be several AU in size and larger then the sun He could not believe this and therefore the earth did not move

Tycho Brahe Developed a model that incorporated both the heliocentric and geocentric models The sun and moon orbited the earth and all other planets orbited the sun – keeping the earth stationary – maintaining the regularity of the Heliocentric model This became a widely accepted model for nearly a hundred years

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Tycho Brahe In 1597 he had a falling out with the King of Denmark – Christian the 4 th – left Hveen and traveled Europe eventually ending up in Prague While in Prague he meet and worked with Johannes Kepler (1571 – 1630) In 1601 Tycho died and his 30 years of observations went to Kepler – Who used this to solve the problem of planetary motion

Essential Question How were Tycho’s observations used by Kepler to produce his laws of planetary motion? What are the shapes of planetary orbits? How does the speed of a planet’s revolution depend on its distance from the Sun?

Kepler and planetary orbits When he joined Tycho’s staff he was in his 30’s, a respected astronomer and had already published a book on the orbits of planets Tycho hired him based on this work – at Tycho death Kepler was appointed to imperial mathematician and put in charge of Tycho’s data. His set out to explain the motion of Mars – working first from the Copernican model – said he would be done in a few days, spent the next 10 years working on the problem

Essential Questions What are the shapes of planetary orbits? How does the speed of a planet’s revolution depend on its distance from the Sun?

Kepler’s first Law Planets move on an elliptical orbit with the Sun at one foci There is nothing at the other foci The closer the foci are the rounder the orbit At perihelion the planet is closest to the sun At aphelion the planet is farthest from the sun

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Kepler’s second Law The law of equal areas The distance and speed of a planet are connected The closer to the sun, the faster they move The farther away from the sun the slower they move True with a planet in it’s own orbit, 20% farther away at aphelion means 20% faster at perihelion

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Kepler’s third law That the distance from the sun is connected to the time it takes an object to orbit the sun Orbital Period (P) Average Distance from the sun (A) Mathematical (p 2 = a 3 ) A = 3.5 AU

Essential Questions How did the telescopic observations of Galileo support the heliocentric model of the solar system?

Galileo and the Telescope Galileo Galilei (1564 – 1642) Kepler’s ideas would have eventually changed the models of the solar system – helped by Galileo He did not invent the telescope and was not the first to look at the sky with it Invented by an unknown Dutch lens maker and early accounts said there where more stars then could be seen without.

Galileo and the Telescope In 1609 Galileo built his own telescope and began looking at the sky and most importantly writing down what he saw He was the first to make observations of the sun, moon, and planets His telescope do not compare to a good pair of modern binoculars

The Observations In looking at the stars Galileo noted the same unseen stars He also noted that they were not magnified like the other celestial objects – which means angular size had been overestimated In looking at the moon, he noted similar features between the earth and the moon – valleys, mountains and plains This lead him to believe the earth was just a celestial object

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The Observations When he looked at the sun He noticed that it was also not perfect That it had dark spots that moved across the surface He timed the movements and gave the sun a rotation of about 4 weeks If the sun rotated why not the earth

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The Observations When he looked at Jupiter – he noticed several smaller points of light After a few days observations – he noted that they moved with Jupiter and changed position This lead him to believe they were moons in orbit around Jupiter and they have been known as The Galilean Moons ever since.

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The Observations Phases of Venus gave even more evidence for the heliocentric model If Venus was between us and the sun – we would only see a new and crescent phases of the planet, because of reflected light If Venus was going around the sun we would see a new, crescent, quarter and gibbous phase – which is what Galileo observed

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The Dialogue After 1600 the heliocentric model was gaining popularity In 1616 the Pope decreed that it was erroneous and heretical to say the earth rotated – Galileo was called in and told to no longer teach, hold or defend the Copernican model In 1624 a new Pope and friend of Galileo gave him permission to discuss it as theory – he tore the Ptolemaic model apart in book “Dialogue Concerning the Two Chief World Systems”

The Dialogue He even questioned the Pope’s position on the concept – so in 1632 at the age of 69 he was put on trial – spared death by recanting all he said and lived the remain 9 years of his life on house arrest This slowed research in Italy – it grew outside of Italy, especially in protestant areas By 1822 (the index of 1835) the ban on Galileo’s book was lifted and by 1993 (Oct. 31, 1992) Galileo was cleared and apologized too, by the Pope It still took almost 200 years to prove the earth rotated and revolved – but the heliocentric had been proven to be the simpler and more accurate