Ancient Astronomy: Geocentric Universe vs. Heliocentric Model, Study notes of Astronomy

Download Ancient Astronomy: Geocentric Universe vs. Heliocentric Model and more Study notes Astronomy in PDF only on Docsity! If one morning you wake a couple of hours before sunrise and see the moon just over your eastern horizon, what phase is the moon in? a.  Waxing crescent b.  First quarter c.  New moon d.  Waning gibbous e.  Waning crescent Like the sun, the moon is higher in the sky at some times of year than others. During what month is the full moon likely to be lowest in the sky? (Northern hemisphere) A.  March B.  June C.  September D.  December Ancient Greek Astronomy •  Models were generally wrong because they were based on wrong “first principles”, believed to be “obvious” and not questioned: 1.  Geocentric Universe: Earth at the Center of the Universe. 2.  “Perfect Heavens”: Motions of all celestial bodies described by motions involving objects of “perfect” shape, i.e., spheres or circles. Ancient Greek Astronomers Aristotle (384 – 322 B.C.), major authority of philosophy until the late middle ages: Universe can be divided in 2 parts: 1. Imperfect, changeable Earth, 2. Perfect Heavens (described by spheres) Issues of Ancient Astronomy (I) Fundamental argument for the geocentric universe: Motion of Earth should result in an observable parallax, which was not seen. Introduced by Ptolemy (ca. A.D. 140) The Ptolemaic system was considered the “standard model” of the universe until the Copernican Revolution. The Copernican Revolution Nicolaus Copernicus (1473 – 1543): heliocentric universe (sun in the center) Copernicus’ new (and correct) explanation for retrograde motion of the planets: This made Ptolemy’s epicycles unnecessary. Retrograde (westward) motion of a planet occurs when Earth passes the planet. Tycho Brahe (1546 – 1601) Use of high-precision instruments for precise astronomical observations, meticulously reported in tables. Later used by Kepler to develop laws of planetary motion. A Quadrant designed by Brahe Used to precisely measure an object’s angular distance above the horizon Johannes Kepler (1571 – 1630) Used the precise observational tables of Tycho Brahe to study planetary motion mathematically. 1. Circular motion and •  Planets move around the sun on elliptical paths, with non-uniform velocities. Found a consistent description by abandoning both: 2. Uniform motion. Eccentricities of planetary orbits Orbits of planets are virtually indistinguishable from circles: Earth: e = 0.0167 Most extreme example: Pluto: e = 0.248 But their centers may be significantly offset from the sun. 3. A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed: Py2 = aAU3 2. A line from a planet to the sun sweeps over equal areas in equal intervals of time. (Py = period in years; aAU = distance in AU) If the orbital period of Jupiter is 11.8 years, what is its semi-major axis in AU? •  A. 11.8 AU •  B. 139 AU •  C. 40.5 AU •  D. 5.2 AU •  E. 3.4 AU P2(yr) = a3 (AU) 11.82 = a3 (AU) a (AU) = 11.82/3 = 11.8 0.66 = 5.2 AU Major discoveries of Galileo (I): •  Moons of Jupiter (4 Galilean moons) •  Rings of Saturn (What he really saw) Major discoveries of Galileo (II): •  sunspots (proving that the sun is not perfect!) •  Phases of Venus (including “full Venus”), proving that Venus orbits the sun, not Earth! Major discoveries of Galileo (III): Historical Overview 1543 99 years of astronomy 1642 1666 London Black Plague o_o Sidereal Messenger Dialogues 1610 1632 American War of Independence t Impri d x Telescope css . Ndpoleon Tycho’s nova _ invented Luther 1572 Beige tt oo 20 yrs at Hveen ‘T'i609 ul - oe Magellan's French and voyage alles nether P Indian War around the ycho Law rincipia world hires 1619 1687 JGfinMarshall Kepler 1600 Benjami(erankin) Ki | Destruction of the Voyage of mn Spanish Armada | the Mayflower oo ‘© 2006 Brooks/Cole - Thomson Isaac Newton (1643 - 1727) •  Building on the results of Galileo and Kepler Major achievements: 1.  Invented calculus as a necessary tool to solve mathematical problems related to motion •  Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler 2. Discovered the three laws of motion 3. Discovered the universal law of mutual gravitation The Universal Law of Gravity •  Any two bodies are attracting each other through gravitation, with a force proportional to the product of their masses and inversely proportional to the square of their distance: F = - G Mm r2 (G is the gravitational constant describing how strongly matter attracts each other…Isn’t such “action at a distance” odd?) Understanding Orbital Motion The universal law of gravity allows us to understand orbital motion of planets and moons: •  Earth and moon attract each other through gravitation. Example: Earth Moon v v’ Δv F •  Since Earth is much more massive than the moon , the moon’s effect on Earth is small. •  Earth’s gravitational force constantly accelerates the moon towards Earth. •  This acceleration is constantly changing the moon’s direction of motion, holding it on its almost circular orbit. Orbital Motion (II) In order to stay on a closed orbit, an object has to be within a certain range of velocities: Too slow : Object falls back down to Earth Too fast : Object escapes the Earth’s gravity Orbital Motion (Ill): Geosynchronous Orbits © 2003 Brooks/Cole Publishing a division of Thomson Learning, Inc. At a distance of 42,250 km (26,260 miles) from _ Earth's center, a satellite _ orbits with a period of 24 hours. The satellite orbits eastward, and Earth _ rotates eastward _ under the moving satellite. y The satellite remains _ fixed above a spot on _ Earth's equator.  Good morning. Here is ] bear called Corduroy.  Goodnight, Corduroy. The Tides Caused by the difference of the moon’s gravitational attraction on the water on Earth → 2 tidal maxima Excess gravity pulls water towards the moon on the near side Forces are balanced at the center of Earth → 12-hour cycle Excess centrifugal force pushes water away from the moon on the far side