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Unformatted text preview: "The Golden Age of Astronomy" Today's Lecture: purpose & goals 1) 2) 3) 4) 5) Review Greek Astronomy Ptolemaic (Earthcentered) model
of Planetary Motion of Planetary Motion Copernican (Suncentered) model Kepler's Laws Review Lots of motions!! The Moon revolves around the Earth (phases) Eclipses Solar, Lunar  properties the Sun, Earth and Moon must all be in a line at a precise time Early people found motions in the sky that they linked to their lives especially important were the origins of Calenders believed the Earth was the center of the Universe and that the Sun, Moon, stars and other celestial bodies revolved around the Earth. Archeoastronomy Greek Astronomy 624  548 BC Thales 560 480 BC Pythagoras of Samos Founded Ionian School of Philosophers. universe is understandable in Declared universe is understandable in terms of simple rules. terms of simple rules. Rejected superstition. Earth floats in a vast ocean. Discovered relationship between ra t ional numbe rs and musical in t e rvals. spiritual grounds that the decided upon The goal of the Philosophos, the Love r o f W isdom, was to Earth was Nature through the perfect discover rules ofspherical deep reflection. Decided upon spiritual grounds that the Earth was spherical shape. the perfect shape. Space is infinite and contains a finite, spherical, universe at space is infinite and contains a finite, the center of which lies the Earth. The visible worlduniverse at the center of spherical, is but a distorted copy of the real world of Ideas. which lies a Earth must be Earth. The shape of the spherical a sphe r e and all heavenly motion must be ci r cula r r. 428 348 BC Plato all heavenly motion must be circular. 384  322 BC Aristotle Joined Plato's Academy in 367 BC. Promoted idea of circular motion into Tutored young prince who would become A le x ande r t he a dogma of of the city of Alexandria with G r ea t , the founderastronomy along in 332 BC. Like Pythagoras, Aristotle believed that mathematics was geocentrism. the key to a true understanding of Nature. Promoted idea of cir cula r mo t ion into a dogma of astronomy along with geocent rism. 55 celestial spheres rotating each a perfect sphere. Outermost sphere primum mobile (prime mover) for the stars. Four basic elements: earth, air, fire, water 1 Greek Astronomy 2 384  322 BC Aristotle 310 BC Aristarchus of Samos 55 celestial spheres water. earth, air, fire, rotating each a perfect sphere. 55 rotating celestial spheres Outermost sphere primum mobile (prime mover) for the stars. outermost sphere air, fire, water Four basic elements: earth, primum mobile (prime mover) for the stars Last of the great Pythagoreans. heliocentrist Developed a heliocent ric model. developed a heliocentric model ; Alas his ideas all but died with him. alas his ideas all but died with This model rediscovered by Copernicus 17 him. centuries later. Determined circumference of the Earth. (next page) At the Summer Solstice the Sun is vertical at Syene but at Alexandria it is 7.25 degrees sou t h of the vertical. The greatestastronomerantiquity. greatest astronomer of of antiquity. From his precise observations he became convinced developed the magnitude motion. that Aristotle was wrong about circular scale of stellar brightness. Created a more accurate model of planetary motion in which he introduced epicycles into the geocent ric model. Wrote great textbook: T he A lmages t summarizing (later) Greek astronomy and his own astronomical theories. 276  194 BC Eratosthenes of Alexandria 190 120 BC Hipparchus 100  170 AD Claudius Ptolemeus (Ptolemy) Greek Astronomy 3 Alexandria There was a major colony of Greek scholars in Alexandria, Egypt 276  194 BC Eratosthenes of Alexandria
(head of the Greek scholarly library in Alexandria): Determined the circumference of the Earth. How would you do that?! C=2R=D Syene He noted that the Summer Solstice the Sun is vertical at Syene but at Alexandria it is 7 degrees south of the vertical. They could measure distances by pace and knew that it was 5000 stadia between Alexandria and Syene (near Aswan) 1 stadia (stadium) = 160 meters C = Earth's circumference and s = 5000 stadia S Using ratios: C/s = 360 degrees/7 degrees and C = 160*5000*360/7meters = 4.1 x 107m = 4.1 x 104 km = 25,000 miles. N o t t oo bad! Greek Astronomy 4 Alexandria There was a major colony of Greek scholars in Alexandria, Egypt 276  194 BC Eratosthenes of Alexandria (head of
the Greek scholarly library in Alexandria): Determined the circumference of the Earth. Notice that this work assumed that the Earth is a sphere!! Could you prove that the Earth is a sphere?
Yes you could, based no observations availiable long before Columbus!
1) Syene 2) 3) Ships going out to sea drop below the horizon. Different stars are visible from different places on the earth's surface. S Lunar eclipses always show a curved edge. 2 Descent into Darkness 642 AD Fall of Alexandria After a 14month siege by Arabian troops, Alexandria was all but destroyed. The great library was razed to the ground. The West enters a period of stagnation. Western history was characterized by:
"...terror and despair, in populations oppressed, famished, and wretched to a degree almost unimaginable today. To the miseries of constant war, political and social disintegration, there was added the dreadful affliction of inescapable, mysterious, and deadly disease. Mankind stood helpless as though trapped in a world of terror and peril against which there was no defense." Dark Ages (700 AD 1400 AD) The Sleepwalkers by Arthur Koestler Greek astronomy passed on to the Arabs, This knowledge is preserved and extended by Islamic scholars. The Islamic empire spreads to Spain, and GreekArabian science enters the West. Eventually, the West awakens from its long dark sleep. Planets: The Vagabond Stars
Planeti "wanderers"
 there are seven objects, five points of light and the disks of the Sun and Moon that wander among the fixed stars.  they usually move Westward against the background stars, but will reverse their course at times. Aside: Where did the names of the days of the week come from? Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday Sunday, Moonday, Tisday, Odensday, Thorsday, Friaday, Saturnday
Mercury Venus Mars(God of War) Jupiter The fundamental problem with the geocentric model of the universe with circular motion is the retrograde motion of the planets. Prograde Motion Retrograde Motion The Ptolemaic System
Geocentric Model of the Universe  Earth centered Claudius Ptolemius, Greek scholar and librarian living in Alexandria Egypt 140 AD perfectly circular orbits cycles upon cycles upon cycles (epicycles and deferents ) required great complexity to explain retrograde motion.
tied very closely to the Christian view of the centrality and importance of Man in the universe. 3 Nicholas Copernicus
Nicholas Copernicus (14731543) Polish astronomer was the first person to develop a complete theory suggesting the Earth revolved around the Sun. He suggested the planets went around in circles. didn't publish his work until the year he died. Not readily accepted; heretical! Explained retrograde motion much more simply than earthcentered Ptolemaic model! Brahe and Kepler Tycho Brahe (15461601) Brahe was a eccentric Danish nobleman. He spent over three decades observing and recording the positions and motions of the planets across the sky. the greatest pretelescope astronomer. Compared the data from Brahe to Copernicus' theory of planets revolving around the Sun in circular orbits The data did NOT support this theory Johannes Kepler (15711630) What does the scientific method say we should do? Kepler modified the model to give elliptical orbits. drawing an ellipse Historical Aside: Kepler's Laws (Orbital Motion) Keplers First Law: Planets move in orbits which are ellipses
with the Sun at one of the focal points This is an empirical theory it doesn't explain why but, it matched the data Earth's eccentricity = 0.017 Pluto's eccentricity = 0.224 Earth has a fairly circular orbit Pluto has a more elliptical orbit 4 Historical Aside: Kepler's Laws (Orbital Motion)
Kepler's Second Law: Planets sweep out equal
areas in equal times Planets move fastest when they are closest to the Sun called perihelion They move slowest when they are farthest from the Sun called aphelion comets show this property very well. Historical Aside: Kepler's Laws
Kepler's Third Law: (Orbital Motion) The square of a planet's orbital period is proportional to the cube of the orbit's semimajor axis (Pyears)2 = (AAU )3 or P2 = (42/G.M).A3 . Orbital period = time the planet takes to go around the Sun once measured in years Length of semimajor axis of orbital ellipse same as `average radius' measured in astronomical units (AU) (multiples of Earth's orbital radius) Historical Aside: Kepler's Laws (Orbital Motion)
Kepler's Second Law: Planets sweep out equal
areas in equal times
Remember that Keplers Laws are empirical they show HOW objects move, but not why. The reasons WHY objects move is GRAVITY, which will be described next class. 5 Ellipses Kepler began by assuming orbits were circles, but that didn't work so he tried ellipses An ellipse is a flattenedout circle eccentricity is a measure of how flat it is. For a circle, the distance from center is constant, eccentricity = 0 For an ellipse, the distance from one focal point to the edge to the other focal point is constant. An ellipse can be defined by its semimajor (long) axis and its eccentricity 6 ...
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 Spring '08
 gerstein
 Astronomy

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