1	Astr 1050 Fri. Jan. 30, 2004 Extra credit articles Homework #1 Discussion Finish Ch. 3: Cycles in the Sky Eclipses Phases of the moon Start Ch. 4: History of Astronomy
2	Shadows and Eclipses
3	Types of eclipses
4	Solar eclipses
5	Eclipse Facts Longest possible total eclipse is only 7.5 minutes. Average is only 2-3 minutes. Shadow sweeps across Earth @ 1000 mph! (Compare with scene in The Mummy Returns!) Birds will go to roost in a total eclipse. The temperature noticeably drops. Totally predictable (even in ancient times, e.g., the Saros Cycle, eclipse pattern repeats every 6585.3 days or 18 years, 11 1/3 days).
6	Eclipses and Nodes
7	Variations in Solar Eclipses
8	Phases of the Moon and its orbit around the Earth (1).
9	Phases of the Moon and its orbit around the Earth (2).
10	Chapter 4: The Origin of Modern Astronomy The development of modern science The Aristotelian Universe The Copernican Revolution The rules of modern science References: The Beginnings of Western Science by David Lindberg Galileo’s Daughter by Dava Sobel Celestial Matters by Richard Garfinkle (fantasy)
11	The Historical Setting The Renaissance The European Discovery of the New World The Reformation
12	People and Contributions Nicolaus Copernicus 1473 - 1543 Heliocentric model Explanation of retrograde motion Tycho Brahe 1546 - 1601 Observations of changes in sky Accurate planet positions Johannes Kepler 1571 – 1630 Mathematical description of planetary orbits Galileo Galilei 1564 – 1642 Observations using telescope supporting Copernican model Isaac Newton 1642 – 1727 Physics to explain Kepler’s orbits
13	Ancient People and Contributions Plato 427 – 347 B.C. Simple motion using spheres Perfection of the heavens, Eudoxus 390 – 337 B.C. Retrograde motion Aristotle 384 – 322 B.C. Shape of Earth, Multiple Spheres Eratosthenes ~200 B.C. Size of the Earth Ptolemy ~150 A.D. Models for planetary motion
14	Aristotle’s Universe: Earth’s Shape Aristotle knew the Earth was round: Shadow of Earth during lunar eclipse Changing height of Polaris and celestial pole as you moved south Eratosthenes measured size of Earth to better than 20% ~200 BC, Greek living in Alexandria Egypt Observed that Sun was overhead at Syene on summer solstice Sun was 7^o to the south of zenith at Alexandria Circumference of Earth must be 360/7 times distance from Syene to Alexandria
15	Aristotle’s Universe: Earth’s Motion Aristotle had good reasons to think the Earth stood still: Absence of any detectable parallax If the Earth orbits the sun (rather than the reverse) then we should be able to see shifts in the positions of the stars due to parallax. The amount of parallax is proportional to We now know the distance to the nearest star is so large that even it only has a parallax of 1 second of arc = 1/3600 deg. 1 parsec = 3.26 ly.
16	Aristotle’s Universe: Planets’ Motion Heavens composed of “perfect” fifth element Elements: Earth, Air, Fire, Water, Quintessence Heavens are unchanging except for rotation: Motion produced by multiple nested spheres Rotate at constant rate Are offset and inclined in ways to produce motion of planets Our “Celestial Sphere” of stars is just the outermost of many he had. VERY complicated for a “perfect” system!
17	Planetary Motion Planets stay almost on the ecliptic Most of the time they move East (relative to stars) Rates drop from Mercury to Venus to Mars to Jupiter to Saturn. Superior planets exhibit “retrograde” motion near opposition.
18	Ptolemy’s explanation: Epicycles Uses multiple levels of “circular” motion. Planet moves on a small circle called en epicycle. Center of epicycle moves on a larger circle called a deferent. Earth is fixed near (not exactly at) the center of the deferent. Motion around deferent is only constant as seen from point called equant. Add epicycles on epicycles to refine motion.
19	People and Events Nicolaus Copernicus 1473 – 1543 De Revolutionibus Tycho Brahe 1546 - 1601 1572 Tycho’s supernova 1576-1597 Planet Positions Johannes Kepler 1571 – 1630 1609 Laws 1 & 2 publish 1611 Law 3 published Galileo Galilei 1564 – 1642 1609 Telescope 1632 Dialog published Isaac Newton 1642 – 1727 1687 Principia published
20	Copernicus: 1473 –1543 Proposed heliocentric model Circular orbits and uniform motion Less accurate for predicting positions but more “physically realistic” Simple explanation for retrograde motion De Revolutionibus Orbium Coelestium published in 1543 In some ways model was “one step back” to enable a later “two steps forward”
21	Tycho Brahe: 1546 - 1601 1563 “Conjunction” Jupiter and Saturn show problems with Ptolemaic predictions of positions. 1572 Tycho’s “supernova” challenges ideas of unchanging nature of the heavens Lack of parallax shows it was at least as far away as the moon. 1576 – 1596 Most precise observations of positions of the planets 1596 Moves to Prague, hires Johannes Kepler as assistant 1601 Collapses, requests Kepler be appointed his replacement, then dies
22	Johannes Kepler: 1571 – 1630 The nature of planetary orbits Problem: How do you find the position of a planet (say Mars) when you know its direction but not its distance. Standard surveying solution: Observe it from two different locations and use “triangulation” or parallax. Special Problem: The motion of the Earth lets you make observations from two different positions, but Mars moves too during this time. Kepler’s special insight: Find an artificial way to make Mars “stand still”
23	Kepler’s Laws, #1 and #2 1609 Published two laws showing: K1 Planets orbit the sun in ellipses, with the Sun at one focus K2 Motion is faster when they are near the Sun, in such a way that a line from the planet to the sun sweeps out equal areas in equal times
24	Properties of Ellipses Ellipse defined by two constants semi-major axis a 1/2 length of major axis eccentricity e 0=circle, 1 = line
25	Kepler’s Laws, #3 1619 Publishes third law, showing that there is a relationship orbital period and semi-major axis: Exact relationship is P² µ a³ . Outer planets orbit more slowly than inner ones Example: Earth P = 365 days, a = 1.00 AU. Mars p = 687 days, a = 1.524 AU Orbital Period of some asteroid with a = 9 AU ?
26	Galileo Galilei 1564 - 1642 Galileo’s earlier work 1590 Masses fall at same rate – heavier do not fall faster (unless affected by air resistance) 1604 Observes a supernova, no parallax Þ must be beyond the Moon Telescopes: 1609 Hears of invention of telescope, which at that point just use eyeglass lenses Works out details of better lenses and lens placement, builds improved ones himself
27	Galileo: First telescopic observations “Sidereus Nuncius” (The Starry Messenger) published in 1610 reporting: Moon isn’t “perfect” (violating Aristotelian principles for heavens) Shows mountains and valleys Uses shadows to estimate heights Milky Way made up of myriad faint stars Doesn’t directly violate Aristotelian principles, but suggests that a few simple phenomena can explain many features of the heavens Discovers 4 moons (Galilean Satellites) orbiting Jupiter Violates idea that all motion is centered on the Earth Shows that orbiting objects can “follow” a moving body 4 moons will also be seen to follow Kepler’s 3^rd law P² µa³ (but with a different proportionality constant)
28	Galileo’s additional observations Detects sunspots and the rotation of the Sun. Further evidence of the “imperfect” heavens Detects the phases of Venus Phases show that Venus must orbit the Sun. “Full” Venus when it is on far side of Sun. “Crescent” Venus when it is on near side of Sun.
29	Galileo’s critical observations Jupiter’s moons show orbits which are not earth-centered Venus’ phases show it must circle the Sun Several objects (Moon, Sun) show “imperfections” which are not supposed to be present in the heavens Galileo’s observations clearly support Copernican model, but so far his printed work has mostly been reporting what he sees, rather than directly arguing for Copernican model.
30	Galileo and the “Dialog” Written as a debate between 3 people Salviati Copernican advocate – (really Galileo) Sagredo Intelligent but uninformed Simplicio Aristotelian philosopher – not very bright Hoped to avoid earlier ruling by not directly advocating Copernican model Actually made things worse by convincing accusers they were “Simplicio” 1633 Inquisition condemns him for violating 1616 order Something like modern “contempt of court” ruling Proceeding not a re-argument of Copernican vs. Aristotelian debate But forced to recant, admitting “errors” Sentenced to life imprisonment –actually “house arrest” Dies in 1642 Pope John Paul II finally makes some amends 350 years later.
31	Newton: 1642-1727 Principia published in 1687 3 Law of motion 1. A body continues at rest or in uniform motion in a straight line unless acted upon by some force. 2. A body’s change of motion is proportional to the force acting on it and is in the direction of the force. 3. When one body exerts a force on a second body, the second body exerts an equal and opposite force back on the first body. Universal gravitation There is an attractive force between all bodies, proportional to their mass, and inversely proportional to the square of their distance.
32	Explanation for Kepler’s Laws Momentum keeps the planets moving – you do not need some force to do this. Gravity provides the force which makes orbits curve Gravity of Sun curves orbits of Planets Gravity of Earth curves orbit of moon (and also makes objects on earth fall downward) “Conservation of Angular Momentum” explains why motion is faster when closer to the sun. The inverse square law of gravity explains P² µ a³ and the details of why the orbits are ellipses.
33	Circular Orbits: Limiting case of an ellipse. Centripetal acceleration (v²/r) caused by Gravity Period found by Kepler’s 3^rd Law just comes from this Given P and a (and G) we can find the mass of a planet or star
34	Summary: People and Contributions Nicolaus Copernicus 1473 - 1543 Heliocentric model Explanation of retrograde motion Tycho Brahe 1546 - 1601 Observations of changes in sky Accurate planet positions Johannes Kepler 1571 – 1630 Mathematical description of planetary orbits Galileo Galilei 1564 – 1642 Observations using telescope supporting Copernican model Isaac Newton 1642 – 1727 Physics to explain Kepler’s orbits