By Ken Journigan Olympic High Astronomy-Renaissance The History of Astronomy Warm Up 1. 2. 3. 4. 5. What is a geocentric model of the Universe? According to early astronomers, what did the Universe consist of ? Aristotle said that the cosmos was composed of five fundamental properties or elements. What were they? What did Aristotle think the shape of the Earth was? Why did he think that? Name three things that Hipparchus is known for? Warm Up 1. 2. 3. 4. 5. 6. Name two discoveries made by Erastosthenes. What is an orrary? What is a heliocentric model of the Universe? What did Ptolemy include in his model of the Universe? What is an epicycle? How many epicycles did Ptolemy’s model include to work correctly? Warm Up 1. 2. 3. 4. 5. Who was Tycho Brahe? What did Tycho Brahe do? Who was Nicholas Copernicus and what did he propose? Who was Johann Kepler? Name and define his three laws. Warm Up 1. 2. 3. 4. What is Newton’s 1st law of Universal motion? What is Newton’s 2nd law of Universal motion? What is Newton’s 3rd law of Universal motion? What is the mathematical formula for gravity? Warm Up 1. 2. On Planet X, a pendulum swings 50 times in 60 seconds from a 30 cm string. What is the force of gravity on Planet X? On Planet Y, a pendulum swings 120 times in 60 seconds from a 40 cm string. What is the force of gravity on Planet Y? Astronomical History A very complete story of astronomy is told in its history. The men and women of astronomical history are synonymous with the historical evolution of this observational science. Geocentric vs. Heliocentric http://www.astro.utoronto.ca/~zhu/ast210/bo th.html Universal Models The Geocentric Model Supporters The Geocentric Model of the Universe With one mere exception (to be named later), ancient astronomers placed the Earth at the center of the known Universe. This Universal Model was known as the Geocentric Model. “Geo” meaning Earth and “centric” meaning centered. Aristotle (384 BC – March 7, 322 BC) Aristotle was an ancient Greek philosopher, a student of Plato and teacher of Alexander the Great. Aristotle had a strong influence, and his teachings carried great weight. He promoted the geocentric model. According to Aristotle the cosmos were composed of five fundamental properties Earth Air Water Fire The spherical shells of heavenly bodies with Earth at the center Aristotle Aristotle believed that everything in the regions outside the Earth was perfect and eternally unchanging. All objects in the heavens were supposed to be perfect circles, except for stars, which were featureless points of light. Celestial Sphere http://www.mathpages.com/home/star3.htm Warm Up 1. 2. 3. 4. Give three examples of evidence of early astronomy! The Universal model that places Earth at the center is called what? Aristotle said that the cosmos was composed of five fundamental properties or elements. What were they? What did Aristotle thing the shape of the Earth was? Why did he think that? Aristotle Aristotle concluded that the Earth was round and not flat as some at the time believed. He based this on his observation of lunar ellipses where a portion of the Earth’s shadow falls on the moon. Aristotle Aristotle’s beliefs about the geocentric model of the universe would pervade astronomy to such an extent, that they would not be challenged for another 1500 years. Plato and Aristotle The Greek Astronomer Hipparchus Hipparcus (c. 190 BCE--c. 120 BCE) was born in Nicaea, a city in what is now Turkey. In the year 135 BCE, he was stargazing and saw a bright point of light he didn't recognize. This star appeared in the constellation Scorpio. It turned out to be a supernova. This disproved Aristotle’s idea of the perfect, unchanging Universe The Greek Astronomer Hipparchus Developed the first catalog of stars Developed a magnitude scale where 1 represented the brightest stars and 6 represented the dimmest stars. Determined the precession of Earth based on records from the past and compared it to his own observations The Greek Astronomer Hipparchus Hipparcus cataloged the locations and brightness of over 850 stars. In addition, he calculated the length of the year to within seconds of its actual value and developed a system to predict eclipses to within hours. Stellar Magnitude Hipparchus’ invented a system to identify how bright stars are. He placed all the stars he observed on a scale that he called “magnitude”. The brightest (magnitude 1) star was Sirius. Magnitude 6 stars were just barely visible. Each level of the magnitude scale represented a change in brightness of 2.5 times. A modified version of this system is still used. Magnitude 1 stars are 100 times brighter than magnitude 6 star. The Greek Astronomer Hipparchus Hipparchus had a problem making his star chart. It was easy enough to map the surface of the Earth, because the Earth has landmarks: rivers, mountains, cities--places of known location, to which other places can be compared. The sky, however, has no landmarks, just the stars themselves. Hipparchus decided to invent "landmarks" of his own. He picked one point in the sky and drew imaginary lines radiating out from it, like the spokes of a wheel. Then he drew circles around this central point which grew larger and larger. The Greek Astronomer Hipparchus This made a grid around the sky, on which Hipparchus could locate any star he wanted. This idea soon improved Earthly mapmaking as well: the modern lines of longitude and latitude come directly from Hipparchus's method of mapping the sky. Instead of locating stars on the "celestial sphere" (the entire area visible around the Earth), later map-makers drew gridlines on their charts of the Earth's sphere. Eratosthenes Eratosthenes Eratosthenes was born in Cyrene, Greece in 276 BC (now modern day Libya. Studying in Alexandria and Athenes, he was eventually appointed as chief librarian of the great Library of Alexandria. It was during this time that he built the famous armillary sphere as a model of the celestial sphere (until the later invention of the orrery) Orrery Antikythera mechanism Many modern scholars believe that Eratosthenes was critical in the design on the Antikythera mechanism (orrery) due to his exclusive knowledge concerned the Earth’s relationship with the moon. Many consider it the first analog computer. It was part of the cargo discovered on a 2,500 year old roman sailing ship. Recreation of the Antikythera mechanism Eratosthenes and Size of the Earth About 250 BC, Eratosthenes used some of Aristotle's ideas to calculate the size of the Earth. On the summer solstice, observers at Syene, Egypt saw the sun directly overhead (the well). He also knew that in his hometown ofAlexandria, Egypt that the sun was at an angle of about 7.50 on that day. The angular displacement was measured. Using simple geometry, he calculated the distant from Syene to Alexandria represented 1/50 of a circle. Hiring someone to walk the distance to measure it 5,000 stadia, where each stadia equals about 700 m), he calculated that circumference of the Earth at around 252,000 stadia (or about 46,420 km). The result was within 1 percent accuracy of the figure known today. Eratosthenes Eratosthenes was an athlete, poet, mathematician and astronomer. In addition to figuring our the Earth’s circumference he also calculated the tilt of the Earth’s axis and invented the leap day. He is likely the astronomer to first suggest the idea of the epicycle as well. Warm Up 1. 2. 3. 4. 5. 6. 7. Name three innovative (new) things that Hipparchus did! According to Hipparchus system to classify stars, what is the brightest star? According to Hipparchus system to classify stars, what is the dimmest star? What was Eratosthenes job in Alexandria? What is he most famous for? What is an armillary sphere? What was the Antikythera mechanism? Ptolemy When I trace at my pleasure the windings to and fro of the heavenly bodies, I no longer touch the earth with my feet: I stand in the presence of Zeus himself and take my fill of ambrosia, food of the gods. (studying the star sure makes me happy) Quoted in C B Boyer, A History of Mathematics (New York 1968) Ptolemy Ptolemy’s full Latin name was Claudius Ptolemaeus (fl. AD 87-150, Alexandria), He was an ancient astronomer, geographer, and mathematician who considered the Earth the center of the universe (the "Ptolemaic system"). Virtually nothing is known about his life. Ptolemy Claudius Ptolemy lived in Rome around 100 AD. His model of the solar system and heavenly sphere was a refinement of previous models developed by Greek astronomers. Ptolemy’s major contribution, however, was that his model could so accurately explain the motions of heavenly bodies, it became the model for understanding the structure of the solar system. Nearly all the early models, including Ptolemy’s version of the solar system, assumed that the Earth was the center of the Universe. The Ptolemaic Model The Ptolemaic model accounted for the apparent motions of the planets in a very direct way, by assuming that each planet moved on a small sphere or circle, called an epicycle, that moved on a larger sphere or circle, called a deferent. The stars, it was assumed, moved on a celestial sphere around the outside of the planetary spheres. The Epicycle http://physics.syr.edu/courses/java/demos/ke nnett/Epicycle/Epicycle.html The idea of the epicycle was incorporating into Ptolemy’s universal model in order to explain retrograde motion Prograde Versus Retrograde Motion Prograde Motion: The regular west to east migration of celestial bodies across the sky. Retrograde Motion: The irregular and periodic transit of planets across the sky from east to west. Prograde Versus Retrograde Motion http://jove.geol.niu.edu/faculty/stoddard/JAV A/luminaries.html The Ptolemaic Model To accurately predict the motions of the heavens, Ptolemy used 80 epicycles to construct his model. The model was very accurate in predicting the motions of the heavens and therefore survived for around 1,400 years! Imagine what wrong ideas are around now that will last for that long! Universal Models The Heliocentric Model Supporters The Heliocentric Model Heliocentric (sun-centered) model More accurately accounted for all observations of the movement of the sun and the moon, and the planets, and the stars were good predictors of future positions of celestial bodies; models were verifiable simplicity (Occam's Razor or the Principle of Parsimony) - as few assumptions or rules as possible; no contradictions. Heliocentric Model Aristarchus of Samos, a Greek about 310-230 BC, had a heliocentric model. He proposed that all of the planets, including Earth revolved around the Sun, and that the Earth rotates on its axis once a day. His ideas did not gain widespread acceptance during his lifetime. Aristarchus of Samos Aristarchus was the first person to give the solar system scale. Nicholaus Copernicus/Mikolaj Kopernik Nicholaus Copernicus Born in Trum, Poland, Copernicus was the youngest of four children. His father was a well to do merchant (copper trader), politician and civic leader. Following college and his fathers death, Copernicus went to live with his uncle who nominated him for a position as canon (a church official with a good salary and no work). Nicholaus Copernicus and the Revival of the Heliocentric Universe. Copernicus was dissatisfied with the complexity of the geocentric model. In 1514 he anonymously published a hand-written document called the “Little Commentary” where he espoused and supported the idea of a heliocentric Universe. His beliefs would ultimately get him in trouble with the Church. Nicholaus Copernicus and the Revival of the Heliocentric Universe. His ideas included: Sun is at the center of the universe, motionless; stars are motionless around the edge Planets all revolve around the sun (6 total including Earth) Moon revolves around Earth Earth rotates on axis causing apparent daily motion of the heavens Earth revolves around sun causing sun's annual movements Retrograde motion of planets is due to relative planetary motions Planetary orbits are perfect circles Nicholaus Copernicus and the Revival of the Heliocentric Universe. Copernicus was the first to accurately determine the relative distances of the planets from the sun. Planetary Distances According to Copernicus Planet Copernican Distance Real Distance Mercury 0.38 AU 0.39 AU Venus 0.75 AU 0.72 AU Earth 1.00 AU 1.00 AU Mars 1.52 AU 1.52 AU Jupiter 5.22 AU 5.20 AU Saturn 9.17 AU 9.54 AU Copernican views marked the beginning of the modern era of astronomy. Errors The errors in Copernicus’ calculations was due to his insistence that the planets maintained circular orbits. As a result he had to resort to the use of epicycles to account for the discrepancies of his model. Two steps forward and one step back. Tycho Brahe Tycho Brahe Tycho Brahe was born in Denmark (now Sweden) in 1546 to a wealthy, noble family. At age 2 he was relinquished to his uncle Jorge by agreement. Jorge and his wife were barren. Jorges Brahe died in 1565 from pneumonia after saving King Fredrik II of Denmark from drowning. Tycho Brahe Around Christmas of 1566, while still a student, Brahe became involved in a drunken argument with a fellow noble. The argument was settled in the dark with rapiers. As a result, Brahe was relieved of most of the upper part of his nose. For the rest of his life he wore a copper prosthetic glued to his face. Tycho Brahe Tycho, who received his full inheritance from his uncle Jorge plus his fathers full inheritance in 1571, was a very wealthy man. It is estimated that at one time Brahe controlled one percent of the wealth of Denmark. Being rich and eccentric, Tycho employed a dwarf that he believed to be clairvoyant and owned an elk that he tamed. Unfortunately the elk died according to Brahe from “ingesting too much beer and plummeting down a flight of stairs” at a party. Tycho Brahe Tycho Brahe benefited greatly from King Fredrik's generous support. Brahe received an island called Hven from the king. He turned this island into his own little country. Tycho Brahe Brahe built a castle on Hven and named it Uraniborg after Urania, the goddess of the sky. He also built an observatory on the island. For over 20 years, Brahe used the island as his base from which to make astronomical observations. In 1597, Tycho Brahe lost the Danish king's support, so he went to Wandsbech in Germany. He eventually settled in Prague where he continued his astronomical observations. Prague was the capital of the Catholic Church. Tycho Brahe Over a 20 year period of time, Tycho Brahe made consistent observations which supported the heliocentric theory proposed earlier by Copernicus. These observations were made using only a compass and a sextant. Brahe catalogued over 1000 stars. Death of Brahe Astronomer Johannes Kepler suggested that Brahe died (1601) of a ruptured bladder. It was bad manners to leave a party before the end in those days. Modern science however has determined that Brahe most likely died of mercury poisoning. Some even suggest that he was murdered by Kepler for the data that he had collected?! Johannes Keplar (12/1571-11/1630) Johannes Keplar Keplar My aim is to say that the machinery of the heavens is not like a divine animal but like a clock (and anyone who believes a clock has a soul gives the work the honor due to its maker) and that in it almost all the variety of motions is from one very simple magnetic force acting on bodies, as in the clock all motions are from a very simple weight. Johannes Keplar (12/1571-11/1630) Born in present-day Germany. Pursued priesthood, but finally decided to teach math. Learned of the Copernican model in advanced astronomy. Excommunicated in 1612. Coined the term “satellite”. Johannes Keplar Keplar Sent copies of some of his work to Tycho Brahe. Tycho Brahe wrote to Kepler’s teacher that he needed a mathematical assistant and hired Kepler. Completed his work on the orbit of Mars in 1605. Created infinitesimal calculus after watching tradesmen measure the volume of wine in barrels at a wedding. Kepler's Laws The orbit of each planet is an ellipse with the sun at one focus. The square of the period of revolution of a planet about the sun is proportional to the cube of the semimajor axis of the planet’s elliptical orbit. These laws are illustrated in the following diagram: Creating an Ellipse 1. 2. 3. Chose two students to represent the ellipse’s foci. Chose one student to represent the orbiting body Chose one student to mark the path of the orbiting body. http://www.astro.utoronto.ca/~zhu/ast210/ke pler.html Kepler's First Law The orbit of each planet is an ellipse with the sun at one focus. Kepler's Second Law The line segment joining a planet to the sun sweeps out equal areas in equal time intervals. http://www.walter-fendt.de/ph11e/keplerlaw2.htm Kepler's Third Law The square of the period of revolution of a planet about the sun is proportional to the cube of the semi-major axis of the planet’s elliptical orbit. Kepler's Third Law (cont’d) The square of the period of revolution of a planet about the sun is proportional to the cube of the semi-major axis of the planet’s elliptical orbit. P2 = A3 where “P” is the orbital period (AU) and “A” is the area inscribed by the semi-major axis. Kepler's Laws Kepler provided us with a tool, accurate even by today’s standards, to understand the mechanical universe and the orbital nature of the planets. The only remaining question, was why did the planets move the way they did? The answer to that question could be provided by only one man; arguably the greatest scientist the world has ever seen……. Sir Isaac Newton Warm Up 1.) State Johannes Kepler’s 3 Laws of Planetary Motion. 2.) Explain what each one means (so that even I can understand it). Define any variables that you might use! 3.) Observations of what planet lead to Kepler’s understanding of planetary motion? 4.) How do you form an ellipse? What are foci? What is a semi-major axis? 5.) What was the one question that Kepler could not answer? …But first, what about Galileo? Galileo Galilei 1564 - 1642 Galileo Galilei Spent his childhood in Pisa, Italy Family wanted him to be a doctor. Left the University of Pisa in 1585 without his degree. Saw “Kepler’s” supernova in 1604 while teaching math at the University at Padua (Venice). Galileo Galilei Formulated “Laws of Motion” from observations and experimentation with pendulums and inclined planes. Learned of the “perspicillum” in 1609. Created his own telescope and improved on the design by teaching himself how to grind lenses . Insert: The Early Telescope tele = 'far' and skopein = 'to look or see' Invented by Dutch spectacle maker Hans Lippershey in the 1590’s. Lippershey is the only person to apply for a patent for the telescope. First paper published about use of telescope for observation was by Englishman Thomas Harriott Galileo Galilei Sold the rights to the telescope to the Venetian Senate for a better position. Laughed because he did not own them. Began nighttime observations in 1609. Galileo Galilei His observations included: Mountains on the Moon. The Galilean moons of Jupiter. The phases of Venus. Saturn and its rings (though he did not understand why they periodically disappeared). Sunspots. Galileo Galilei Convicted of heresy, Galileo was placed under house arrest for the remainder of his life, a gentle punishment for any individual convicted during the Inquisition. On 31 October 1992, 350 years after Galileo's death, Pope John Paul II gave an address on behalf of the Catholic Church in which he admitted that errors had been made by the theological advisors in the case of Galileo. The Church however never admitted that they were wrong in declaring Galileo a heretic! Sir Isaac Newton (1642-1727) Sir Isaac Newton Born in Woolsthorpe, Lincolnshire, England on Christmas Day. He was quite premature and not expected to live. (His mother said that when he was an infant, that she could fit him inside a one quart pot). Newton’s father died a few months before his birth. Sir Isaac Newton His mother remarried to a wealthy clergyman, left home, leaving Isaac to be raised by his grandmother Eight years later, she returned, with three more children and another dead husband. (She’s not having much luck with her husbands, is she?). Two years later, Newton went away to Grammar School in Grantham, where he lodged with the local apothecary, and learned his fascinated of chemicals. Sir Isaac Newton In 1661, his uncle convinced his mother to send Newton to Trinity College, Cambridge. He supported himself by working in a tavern and cleaning for other faculty and wealthy students. In the summer of 1665, the Black Plague came to Cambridge and Trinity College closed its doors. Newton returned home to Woolsthorpe. Sir Isaac Newton The two years between leaving and returning to Cambridge, mark Newton’s most remarkable and productive years. During this time he formulated his ideas on moving bodies, gravity and light. He also invented integral, differential and infinite series calculus during this time. In 1667, began his work in alchemy (explain). Sir Isaac Newton Newton disliked publishing his work and usually did so in response to other published articles. He was frequently embroiled in debates over the originality of his work. He was haphazard regarding the care of his work and frequently lost and misplaced things. Sir Isaac Newton Newton’s first major publication regarded his invention, design and construction of the first reflecting (or Newtonian) telescope. Eliminated chromatic aberration. Sir Isaac Newton Newton elected to the Royal Society. Through the 1670, Newton became obsessed with theology and alchemy. He deeply desired to understand the nature of matter. He also tried to calculate to age of the Earth using biblical texts. To do this he taught himself Hebrew. Sir Isaac Newton In 1684, three members of the Royal Society, Sir Christopher Wren, Robert Hooke and Edmond Halley, argued as to whether the elliptical orbits of the planets could result from a gravitational force towards the sun proportional to the inverse square of the distance. Halley writes: Mr. Hook said he had had it, but that he would conceal it for some time so that others, triing and failing might know how to value it, when he should make it publick. (Yea, right!!! What a load!) Sir Isaac Newton and Edmond Halley Having heard the rumor that Newton already had the solution they sought, Edmond Halley (namesake of the comet) visited the mathematician. Newton replied that he had the proof from fours years earlier, but sought in vain to find it. Newton devoted the next three months to reproducing the proof. Sir Isaac Newton Published the Principia in 1686, widely regarded as the greatest scientific work ever published. Publication made Newton a very public figure which he quickly grew accustomed to. He was appointed Master of the Mint and moved from Cambridge to London. He was responsible for many improvements to currency to control “shaving” and counterfeiting (ridges, like quarters today. The Ideas of Isaac Newton The central topic of the Principia was gravitational force. Defined by Newton as: Fg = G (M1) (M2)/ r2 where: (the inverse square law) Fg = The force of gravity G = The gravitational constant M1 = The mass of body one M2 = The mass of body two r = the distance between the centers of the two bodies Sir Isaac Newton Orbital flight was explained by Newton in a though activity called the “mountain cannon”. Is seeks to show how an object may continually fall and still never his the ground of a round body. http://galileoandeinstein.physics.virginia.edu/m ore_stuff/Applets/newt/newtmtn.html Newton’s First Law of Motion Newton’s First Law of Motion states that: F = ma F = force m = mass a = acceleration where: Newton’s Second Law of Motion Newton’s Second Law of Motion is the Law of Inertia which states that: A body in motion tends to stay in motion (in a straight line) and a body at rest tends to stay at rest, unless acted upon by some external force. Mass resists change and the natural state of matter is to be in motion! Newton’s Third Law of Motion Newton’s Third Law of Motion states: For every action there is an equal, but opposite, reaction. Or, if I push you, then you push me and if you push me then I push you! Isaac Newton Creator of: Reflecting telescope Laws of Motion Laws of Gravity Calculus Astrophysics Our understanding of the true nature of light (Not a bad resume, eh?)