Ancient Astronomy and Planetary Motion: From Geocentric to Heliocentric Models - Prof. Jie, Study notes of Astronomy

Download Ancient Astronomy and Planetary Motion: From Geocentric to Heliocentric Models - Prof. Jie and more Study notes Astronomy in PDF only on Docsity! Note (added on Sep. 25, 2006): this ppt file contains the lecture note for the whole chap. 4. Section 4.1- 4.4 was taught on Sep. 18, 2006, and the other section 4.5 – 4.8 was taught on Sep. 25, 2006 Introducing Astronomy (chap. 1-6) Introduction To Modern Astronomy I 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. 7-17) ASTR 111 – 003 Fall 2006 Lecture 03 Sep. 18, 2006 Gravitation and the Waltz of the a Planets [a= Chapter Four Planetary Motion • Like the Sun and Moon, the planets usually move slowly eastward on the celestial sphere with respect to the background of stars • This eastward progress is called direct motion • Retrograde motion: but from time to time, the planets stop, and move westward for several weeks or months The Path of Mars in 2009-2010 Ptolemaic System: cycles on cycles • Ptolemaic system: 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 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 Planetary Configurations • Greatest Eastern Elongation: – Mercury or Venus visible after sunset – Called “evening star” • Greatest Western Elongation: – Mercury or Venus visible before sunrise – Called “morning star” • Inferior planets: Mercury and Venus – Their orbits are smaller than the Earth – They are always observed near the Sun in the sky • Elongation: the angle between the Sun and a planet as viewed from Earth 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 the observed synodic period Johannes Kepler • Using data collected by Tycho Brahe, Kepler deduced three laws of planetary motion, which are about 1. shape of orbits 2. speed of orbital motion 3. Relation between orbital size and orbital period Johannes Kepler (1571 – 1630) Kepler’s First Law • Kepler’s first law: the orbit of a planet about the Sun is an ellipse, with the Sun at one focus • Semimajor axis: the average distance between the planet and the Sun • Assuming ellipse, Kepler found his theoretical calculations match precisely to Tycho’s observations. Ellipse • Eccentricity e: the measure of the deviation from the perfect circle Kepler’s Third Law • Kepler’s the law 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 Note: this ppt file contains the lecture note for the whole chap. 4. Section 4.1- 4.4 was taught on Sep. 18, 2006, and other sections 4.5 – 4.8 will be covered today (Sep. 25, 2006) Introducing Astronomy (chap. 1-6) Introduction To Modern Astronomy II 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 (Exam 1 on Oct. 2: Chap.1 – Chap.4) Ch5: The Nature of Light Ch6: Optics and Telescope Planets and Moons (chap. 7-17) ASTR 111 – 003 Fall 2006 Lecture 04 Sep. 25, 2006 Galileo’s Discoveries with Telescope • The invention of the telescope in the early 17th century led Galileo to new discoveries that permanently changed people’s view on the heavens. Galileo Galilei (1564 – 1642) • Galileo showed convincingly that the 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 Galileo’s Discoveries: Phases of Venus • Galileo discovered four moons, now called the Galilean satellites, orbiting Jupiter – Io, Europa, Ganymede and Callisto • The Earth is not at the center of all heavenly objects. • He also discovered – The Milky Way is not a featureless band of light, but “a mass of innumerable stars” – Mountains on the Moon – Sunspot on the Sun – Ring of Saturn Galileo’s Discoveries Isaac Newton • Isaac Newton, based on the insight into fundamental principles, introduced – three laws of motion • Law of Inertia • Law of Force • Law of Action and Reaction – the law of universal gravitation Isaac Newton (1642 -- 1727) 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 Gravitation: Orbital Motions • Kepler’s three laws of planetary motion can be exactly derived from Newton’s law of universal gravitation • E.g., – closer to the Sun – stronger the gravitational force – faster the orbital speed – smaller the orbital period 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. Gravitation: 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 Gravitation: Tidal Force • The positions of high tide caused by the Moon – Moon is at the upper local meridian (highest in the sky) – Moon is at the lower local meridian