Looping Planets. towards the modern view. Ptolemy s computational scheme for celestial motion

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1 Reading: Chap. 2, Sec. 2.2, 2.4 Homework 3: Due Friday/Monday Exam 1: 2 weeks from today: Tuesday, Sept. 26, in the evening Public lecture: Tomorrow night 8 p.m., Great Hall, Memorial Union "Water Exploration in the Solar System: The Restless Hunt for Life" 1 Looping Planets 2 Brief review of last time: Solar Eclipses; Early Astronomy Solar eclipses: only at New Moon length of Moon s umbra ~ mean Earth (surface)-moon dist partial eclipse: (Moon s penumbra) widely visible total eclipse: visible only from narrow, fast eclipse track annular eclipse: similar to total, but moon s umbra doesn t reach Earth Motions of the Planets: concluding the discovery of our solar system Early Science prehistoric discoveries: visual observations - motivations Philosophy + some observation culminated in 3 Ptolemy s computational scheme for celestial motion Earth -centered Uniform, circular Motion Epicycles towards the modern view s: Ptolemy s method off by several degrees response: add more epicycles : Copernicus moved sun to center -----> Revolutionary! 1580: Tycho Brahe precise positions of planets stars are fixed, therefore very distant sky is not immutable 1609: Galileo astronomer: telescope studies show Copernicus right physicist: experiments with Gravity

2 Looping Planets 5 planetary alignments (outer planet) 6 opposition (retrograde loop midpoint) Earth conjunction w/ Sun inferior conjunction planetary alignments (inner planet) greatest Eastern elongation greatest Western elongation superior conjunction 7 towards the modern view s: Ptolemy s method off by several degrees response: add more epicycles : Copernicus moved sun to center -----> Revolutionary! 1580: Tycho Brahe precise positions of planets stars are fixed, therefore very distant sky is not immutable 1609: Galileo astronomer: telescope studies show Copernicus right physicist: experiments with Gravity

3 Nicolaus Copernicus ( ) Heliocentric system, but with uniform motion & epicycles. - Placed known planets in proper order out from the Sun. - Noticed that the closer to the Sun, the greater the orbit speed. Evidences: - Phases of Venus (Copernicus didn t see them though). - Configurations of the Superior planets vs. Inferior. - Got relative distances from quadrature triangles. - Ptolemy could also account for retrograde motion, but less naturally. 9 Interesting consequence in Copernicus scheme the circular orbits (and their epicycles had to be larger than in Ptolemy s scheme. C. made the universe larger. towards the modern view s: Ptolemy s method off by several degrees response: add more epicycles : Copernicus moved sun to center -----> Revolutionary! 1580: Tycho Brahe precise positions of planets stars are fixed, therefore very distant sky is not immutable 1609: Galileo astronomer: telescope studies show Copernicus right physicist: experiments with Gravity Tycho Brahe ( ) Danish nobleman gained the patronage of King Frederick II of Denmark Built Uraniborg Observatory on island of Hveen Court astronomer for Emperor Rudolph II in Prague. Hired Kepler. Important Observations: - Observed a comet (1577), saw no parallax --> not made of luminous airey vapours. Concluded that it was > 3 times as distant as the Moon. - Very accurate positional observations ( 1 arcmin) of stars & planets. Continuous 20 yr. record of such observations. Noticed many empirical regularities.

4 Galileo Galilei ( ) Didn t finish college, but got a professorship anyway..pisa --> Padua --> Tuscany 16 Mechanics - Experiments were a new idea: pendulums, balls on planes, falling objects. - Gravitational acceleration independent of mass. - Law of inertia: bodies resist change in motion. Rest is not the only natural state. Astronomy - Made telescopes, about 30x magnification, found: - many faint stars, star clusters. - Milky Way = stars - Galilean moons of Jupiter, I.e., other centers of motion. - Phases of Venus - Structure of the Moon: maria, mountains, imperfect surf. - Sunspots, Sun is imperfect & transient too. Solar rotation. Heliocentric Cosmology: strong advocate of Copernicus.

5 Galileo s observations full set of phases of Venus Jupiter s system of moons (the Galilean satellites) a famous experiment 1612 (?) A model from history of overcoming adversity. Johannes Kepler ( ) Son of a reckless soldier of fortune and the undisciplined and ill-educated daughter of the burgomeister of Eltingen (1927 Encyclopedia Brittanica). Recovered from smallpox at age 4, with crippled hands, and eyesight permanently impaired. Enrolled in seminary at age 13, entered university at age 17. Gave up theology for science professorship (in Ptolemaic astrology) at Gratz, Austria. Because of religious disturbances in Gratz, took job with Tycho in Prague. Succeeded him in 1601 as court astronomer or mathematician. Picked up the study of Mars. Long struggle with traditional orbit models, though from early on he considered the Law of Areas. Finally stumbled on a model that behaved like an ellipse. Published Astronomia Nova in 1609 with an orbit for Mars and his first 2 laws. Got a telescope in 1610 and did optical studies (theory of refraction). Published De Harmonice Mundi in 1619 with the third law and a theory of the harmony of the spheres. Mother arrested for witchcraft in 1620 (Wurttemberg). Linz beseiged, obtained permission to move his Rudolphine Tables types to Ulm. Published in Statue in Linz (from Wikipedia)

6 Johannes Kepler mathematician and klutz used Tycho s data on the motion of Mars: with no circular motion bias to discover Kepler s Laws of Planetary Motion These are simple empirical laws explaining planetary motion, derived from data only, with no preconceptions Kepler s Law #1 Planets orbit the sun in ELLIPTICAL orbits around the sun, with the sun at one focus of the ellipse. abandonment of perfect circular motion Anatomy of an ellipse DEFINITION where your distance from two fixed points adds up to a constant FOCI - the two reference points MAJOR AXIS longest dimension of ellipse contains foci usually refer to semimajor axis a ECCENTRICITY measure of the flatness of the ellipse e= (distance between foci) / 2a e = 0 for a circle (semimajor axis = radius) 0 e 1 for an ellipse e = 1 for a parabola 23 The Earth s orbit is an ellipse 24

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