Ancient Astronomy: Understanding Planetary Motion - Ptolemaic System vs. Copernican Model , Study notes of Astronomy

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Gratifizion Bnd ee aaltz of thi ie yl i % ASTR 111 – 003 Fall 2007 Lecture 03 Sep. 17, 2007 Introducing Astronomy (chap. 1-6) Introduction To Modern Astronomy I: Solar System Ch1: Astronomy and the Universe Ch2: Knowing the Heavens Ch3: Eclipses and the Motion of the Moon Ch4: Gravitation and the Waltz of the Planets Ch5: The Nature of Light Ch6: Optics and Telescope Planets and Moons (chap. 7-15) Chap. 16: Our Sun Chap. 28: Search for Extraterrestrial life Ptolemaic System: cycles on cycles • Ptolemaic system (~ 200 AD): each planet is assumed to move in a small cycle called an epicycle, whose center in turn moves in a large cycle, called a deferent, which is centered on the Earth • Both the epicycle and deferent rotates in the same direction ---- counter clock-wise 0403003.swf FLASH Ptolemaic System: cycles on cycles • When the planet is on the part of its epicycle nearest Earth, the motion of the planet along the epicycle is opposite to the motion of the epicycle along the deferent. The planet therefore appears to go backward in retrograde Heliocentric Model by Copernicus • Heliocentric (Sun- centered) model: all the planets, including the Earth, revolve about the Sun • A heliocentric model simplifies the explanation of the retrograde motion of planets • Occam’s razor: simple explanations of phenomena are most likely to be correct Nicolaus Copernicus (1473 – 1543) Planetary Configurations • Conjunction: – The Sun and planet appear together in the celestial sphere • Opposition: – Earth is between Sun and planet – Planet is highest in the sky at midnight – Planet appears brightest because it is closest to the Earth • Superior planets: Mars, Jupiter and Saturn – Their orbits are larger than the Earth – They can appear high in the sky at midnight, thus opposite the Sun with Earth in between Synodic Period and Sidereal Period • Synodic period: the time that elapses between two consecutive identical configurations as seen from the Earth – e.g., from one opposition to the next for superior planets – e.g., from one greatest eastern elongation to the next for inferior planets • Sidereal period: true orbital period, the time it takes the planet to complete one full orbit of the Sun relative to the stars • Sidereal period is deduced from observed synodic period Synodic Period and Sidereal Period • For an inferior planet, over one synoptic period Angular distance of the planet (360 / P X S) = Angular distance of the Earth (360 /E X S) + 360° SEP 111 += P = sidereal period of the planet E = sidereal period of the Earth = 1 year S = synoptic period of the planet (from observation) 0403005.swf FLASH For example: Mercury S = 0.318 year (116 days) P = 0.242 year = 88 days ASTR 111 – 003 Fall 2007 Lecture 04 Sep. 24, 2007 Introducing Astronomy (chap. 1-6) Introduction To Modern Astronomy I: Solar System Ch1: Astronomy and the Universe Ch2: Knowing the Heavens Ch3: Eclipses and the Motion of the Moon Ch4: Gravitation and the Waltz of the Planets Ch5: The Nature of Light Ch6: Optics and Telescope Planets and Moons (chap. 7-15) Chap. 16: Our Sun Chap. 28: Search for Extraterrestrial life Tycho Brahe’s Observations Tycho Brahe (1546 – 1601) • Brahe’s observations measured the positions of stars and planets with unprecedented accuracy (about 1 arcmin) (before the invention of telescope) • The data obtained by Brahe put the heliocentric model on a solid foundation. Johannes Kepler • Using data collected by Tycho Brahe, Kepler deduced three laws of planetary motion, which are about 1. Orbital shape 2. Orbital speed 3. Orbital period Johannes Kepler (1571 – 1630) Kepler’s Second Law • Kepler’s second law: a line joining a planet and the Sun sweeps out equal areas in equal interval of time • Perihelion: nearest the Sun; the planet moves fastest • Aphelion: farthest from the Sun; the planet moves slowest 0403006.swf FLASH Kepler’s Third Law • Kepler’s third law: the square of the sidereal period of a planet is directly proportional to the cube of the semimajor axis of the orbit P2 = a3 P = planet’s sidereal period, in years a = planet’s semimajor axis, in AU Kepler’s Laws • Kepler’s laws of planetary motion are a landmark in astronomy • They made it possible to calculate the motions of planets with better accuracy than any geocentric model ever had • They passed the test of Occam’s razor • They helped to justify the idea of heliocentric models Phases of Venus • Venus exhibits phases like those of the Moon • The apparent size (α) is related to the planet’s phase – Venus appears larger at crescent phase – Venus appears smaller at gibbous phase α: apparent angular size of Venus as seen through telescope. Correction: the unit should be ’’ (arcsec) instead of ° (degree) • Heliocentric model provides a natural explanation for the phases of Venus – When Venus is on the same side of the Sun as the Earth, we see it a “new” phase and with a larger angular size – When Venus is on the opposite side of the Sun from the Earth, it appears full and has a small angular size Phases of Venus • Ptolemaic geocentric model was wrong • To explain why Venus is never seen very far from the Sun, the Ptolemaic model had to assume that the deferents of Venus and of the Sun move together in lockstep, with the epicycle of Venus centered on a straight line between the Earth and the Sun • In this model, Venus was never on the opposite side of the Sun from the Earth, and so it could never have shown the gibbous phases that Galileo observed Phases of Venus Newton Second Law of Motion • Second law of motion, or law of force: The acceleration of an object is proportional to the net outside force acting on the object, and is inversely proportional to the mass of the object. F = ma F = net outside force on an object m = mass of object a = acceleration of object • Mass: total amount of material in the object, an intrinsic value independent of gravitational environment; measured in Kg (Kilogram) • Acceleration: the rate at which velocity changes • Weight: force of gravity that acts on a body; measured in Newton (1 Newton = 0.225 Pound) • Earth surface gravity = 9.8 m/s2 • Mars surface gravity = 3.7 m/s2 (0.4 gE) Newton Third Law of Motion • Third law of motion, or law of action and reaction: Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body Newton’s Law of Universal Gravitation F = gravitational force between two object m1 = mass of first object m2 = mass of second object r = distance between objects G = universal constant of gravitation: 6.67 × 10–11 newton • m2/kg2 • Law of Universal Gravitation: Two bodies attract each other with a force that is directly proportional to the mass of each body and inversely proportional to the square of the distance between them )( 2 21 r mm GF = Gravitation: Orbital Motions • Based on his gravitational law, Newton found that the orbits of an object around the Sun could be any one of a family of curves called conic sections • Some comets are found to have hyperbolic orbits Gravitation: Tidal Force • Tidal forces are differences in the gravitational pull at different points in an object • From the perspective of the center ball, it appears that the forces have pushed the 1-ball away and pulled the 3- ball toward the planets. Tidal Force • The tidal force equals the Moon’s gravitational pull at the location minus the gravitational pull of the Moon at the center of the Earth • These tidal forces tend to deform the Earth into a non- spherical shape Final Notes on Chap. 4 • There are 8 sections. All the sections are covered. • There are 4 boxes. All boxes are covered. Advanced Question Chap. 4, Q43 in P93 Suppose that you travelled to a planet with 4 times the mass and 4 times the diameter of the Earth. Would you weigh more or less on that planet than on Earth? By what factor?