Introduction To Modern Astronomy IGravitation and the Waltz of the PlanetsGuiding QuestionsAncient Geocentric modelsPlanetary MotionHeliocentric Model by CopernicusHeliocentric Model by CopernicusPlanetary ConfigurationsPlanetary ConfigurationsTycho Brahe’s ObservationsJohannes KeplerKepler’s First LawKepler’s Second LawKepler’s Third LawKepler’s Third LawIntroduction To Modern Astronomy IIGalileo’s Discoveries with TelescopeGalileo’s Discoveries: Phases of VenusGalileo’s Discoveries: Phases of VenusGalileo’s Discoveries: Phases of VenusGalileo’s DiscoveriesIsaac NewtonNewton First Law of MotionNewton Second Law of MotionNewton Third Law of MotionNewton’s Law of Universal GravitationGravitation: Orbital MotionsGravitation: Orbital MotionsGravitation: Tidal Force Final Notes on Chap. 4Note (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, 2006Introducing Astronomy (chap. 1-6)Introduction To Modern Astronomy ICh1: Astronomy and the UniverseCh2: Knowing the HeavensCh3: Eclipses and the Motion of the MoonCh4: Gravitation andthe Waltz of the PlanetsCh5: The Nature of LightCh6: Optics and TelescopePlanets and Moons (chap. 7-17)ASTR 111 – 003 Fall 2006Lecture 03 Sep. 18, 2006Gravitation and the Waltz of the PlanetsChapter FourGuiding Questions1. How did ancient astronomers explain the motions of the planets?2. Why did Copernicus (1473-1543) think that the Earth and the other planets go around the Sun?3. How did Tycho Brahe (1546-1601) attempt to test the ideas of Copernicus?4. What paths do the planets follow as they move around the Sun? Johannes Kepler (1571-1630)5. What did Galileo (1564-1642) see in his telescope that confirmed that the planets orbit the Sun?6. What fundamental laws of nature explain the motions of objects on Earth as well as the motions of the planets?7. Why don’t the planets fall into the Sun?8. What keeps the same face of the Moon always pointed toward the Earth ?• Ancient astronomers believed the Earth to be at the center of the universe, and the Earth is at rest• All the stars are fixed on the celestial sphere, rotating once a day• The Sun and Moon move slowly eastward with respect to the starsAncient Geocentric modelsPlanetary 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 2009-2010Ptolemaic 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-wisePtolemaic 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 retrogradeHeliocentric 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 correctNicolaus Copernicus (1473 – 1543)Heliocentric Model by Copernicus• Retrograde motion of a planet is caused by the Earth overtaking and passing the slow-moving planet• In the case of the Mars, it occurs during the period when the Sun, Earth and Mars are about aligned along a straight linePlanetary 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 EarthPlanetary 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 betweenSynodic 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 periodHeliocentric Model by Copernicus• Copernicus determined the sidereal period of planets• Copernicus also determined the distance of the planets from the Sun using trigonometryTycho Brahe’s ObservationsTycho Brahe(1546 – 1601)• Brahe’s observations measured the positions of stars and planets with unprecedented accuracy(about 1 arcmin)• The data obtained by Braheput the heliocentric model on a solid foundation.Johannes Kepler• Using data collected by Tycho Brahe, Keplerdeduced three laws of planetary motion, which are about1. shape of orbits2. speed of orbital motion3. Relation between orbital size and orbital periodJohannes 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’sobservations.Ellipse• Eccentricity e: the measure of the deviation from the perfect circleKepler’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;