John Winthrop, Observation of the Transit of Venus, June 6, 1761
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Modelling and the Transit of Venus
Modelling and the transit of Venus Dave Quinn University of Queensland <[email protected]> Ron Berry University of Queensland <[email protected]> Introduction enior secondary mathematics students could justifiably question the rele- Svance of subject matter they are being required to understand. One response to this is to place the learning experience within a context that clearly demonstrates a non-trivial application of the material, and which thereby provides a definite purpose for the mathematical tools under consid- eration. This neatly complements a requirement of mathematics syllabi (for example, Queensland Board of Senior Secondary School Studies, 2001), which are placing increasing emphasis on the ability of students to apply mathematical thinking to the task of modelling real situations. Success in this endeavour requires that a process for developing a mathematical model be taught explicitly (Galbraith & Clatworthy, 1991), and that sufficient opportu- nities are provided to students to engage them in that process so that when they are confronted by an apparently complex situation they have the think- ing and operational skills, as well as the disposition, to enable them to proceed. The modelling process can be seen as an iterative sequence of stages (not ) necessarily distinctly delineated) that convert a physical situation into a math- 1 ( ematical formulation that allows relationships to be defined, variables to be 0 2 l manipulated, and results to be obtained, which can then be interpreted and a n r verified as to their accuracy (Galbraith & Clatworthy, 1991; Mason & Davis, u o J 1991). The process is iterative because often, at this point, limitations, inac- s c i t curacies and/or invalid assumptions are identified which necessitate a m refinement of the model, or perhaps even a reassessment of the question for e h t which we are seeking an answer. -
Lomonosov, the Discovery of Venus's Atmosphere, and Eighteenth Century Transits of Venus
Journal of Astronomical History and Heritage, 15(1), 3-14 (2012). LOMONOSOV, THE DISCOVERY OF VENUS'S ATMOSPHERE, AND EIGHTEENTH CENTURY TRANSITS OF VENUS Jay M. Pasachoff Hopkins Observatory, Williams College, Williamstown, Mass. 01267, USA. E-mail: [email protected] and William Sheehan 2105 SE 6th Avenue, Willmar, Minnesota 56201, USA. E-mail: [email protected] Abstract: The discovery of Venus's atmosphere has been widely attributed to the Russian academician M.V. Lomonosov from his observations of the 1761 transit of Venus from St. Petersburg. Other observers at the time also made observations that have been ascribed to the effects of the atmosphere of Venus. Though Venus does have an atmosphere one hundred times denser than the Earth’s and refracts sunlight so as to produce an ‘aureole’ around the planet’s disk when it is ingressing and egressing the solar limb, many eighteenth century observers also upheld the doctrine of cosmic pluralism: believing that the planets were inhabited, they had a preconceived bias for believing that the other planets must have atmospheres. A careful re-examination of several of the most important accounts of eighteenth century observers and comparisons with the observations of the nineteenth century and 2004 transits shows that Lomonosov inferred the existence of Venus’s atmosphere from observations related to the ‘black drop’, which has nothing to do with the atmosphere of Venus. Several observers of the eighteenth-century transits, includ- ing Chappe d’Auteroche, Bergman, and Wargentin in 1761 and Wales, Dymond, and Rittenhouse in 1769, may have made bona fide observations of the aureole produced by the atmosphere of Venus. -
MASSACHUSETTS: Or the First Planters of New-England, the End and Manner of Their Coming Thither, and Abode There: in Several EPISTLES (1696)
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Joshua Scottow Papers Libraries at University of Nebraska-Lincoln 1696 MASSACHUSETTS: or The first Planters of New-England, The End and Manner of their coming thither, and Abode there: In several EPISTLES (1696) John Winthrop Governor, Massachusetts Bay Colony Thomas Dudley Deputy Governor, Massachusetts Bay Colony John Allin Minister, Dedham, Massachusetts Thomas Shepard Minister, Cambridge, Massachusetts John Cotton Teaching Elder, Church of Boston, Massachusetts See next page for additional authors Follow this and additional works at: https://digitalcommons.unl.edu/scottow Part of the American Studies Commons Winthrop, John; Dudley, Thomas; Allin, John; Shepard, Thomas; Cotton, John; Scottow, Joshua; and Royster,, Paul Editor of the Online Electronic Edition, "MASSACHUSETTS: or The first Planters of New- England, The End and Manner of their coming thither, and Abode there: In several EPISTLES (1696)" (1696). Joshua Scottow Papers. 7. https://digitalcommons.unl.edu/scottow/7 This Article is brought to you for free and open access by the Libraries at University of Nebraska-Lincoln at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Joshua Scottow Papers by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors John Winthrop; Thomas Dudley; John Allin; Thomas Shepard; John Cotton; Joshua Scottow; and Paul Royster, Editor of the Online Electronic Edition This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/ scottow/7 ABSTRACT CONTENTS In 1696 there appeared in Boston an anonymous 16mo volume of 56 pages containing four “epistles,” written from 66 to 50 years earlier, illustrating the early history of the colony of Massachusetts Bay. -
Transit of Venus Presentation
http://sunearthday.nasa.gov/2012/transit/webcast.php Venus visible Venus with the unaided eye: "morning star" or the Earth "evening star. • Similar to Earth: – diameter: 12,103 km – 0.95 Earth’s – mass 0.89 of Earth's – few craters -- young surface – densities, chemical compositions are similar • rotation unusually slow (Venus day = 243 Earth days -- longer than Venus' year) • rotation retrograde • periods of Venus' rotation and of its orbit are synchronized -- always same face toward Earth when the two planets are at their closest approach • greenhouse effect -- surface temperature hot enough to melt lead M ikhail Lomonosov, june 5, 1761 discovered, during a transit, that V enus has an atmosphere The atmosphere is is composed mostly of carbon dioxide. There are several layers of clouds, many kilometers thick, composed of sulfuric acid. Mariner 10 Image of Venus V enera 13 Venus’ orbit is inclined (by 3.39 degrees) relative to the ecliptic If in the same plane we would have 5 transits in 8 years Venus: 13 years , Earth: 8 years Each time Earth completes 1.6 orbits, Venus catches up to it after 2.6 of its orbits Progress of the 2004 Transit of Venus pictured from NASA's Soho solar observatory. Credit: NASA Ascending (A) or Duration since last transit Date of transit Descending (D) node (years and months) 6 December 1631 A 4 December 1639 A 8 yrs 6 June 1761 D 121 yrs 6 months 3 June 1769 D 8 yrs 9 December 1874 A 105 yrs 6 months 6 December 1882 A 8 yrs 8 June 2004 D 121 yrs 6 months 5 June 2012 D 8 yrs 11 December 2117 A 105 yrs 6 months 8 December 2125 A 8 yrs In 6000 years 81 transits only Venus’ Role in History Copernican System vs Ptolemaic System http://astro.unl.edu/classaction/animations/renaissance/venusphases.html Venus’ Role in History Size of the Solar System - Revealed! • Kepler predicted the transit of December 1631 (though not observed!) and 120 year cycle. -
History of Science Society Annual Meeting San Diego, California 15-18 November 2012
History of Science Society Annual Meeting San Diego, California 15-18 November 2012 Session Abstracts Alphabetized by Session Title. Abstracts only available for organized sessions. Agricultural Sciences in Modern East Asia Abstract: Agriculture has more significance than the production of capital along. The cultivation of rice by men and the weaving of silk by women have been long regarded as the two foundational pillars of the civilization. However, agricultural activities in East Asia, having been built around such iconic relationships, came under great questioning and processes of negation during the nineteenth and twentieth centuries as people began to embrace Western science and technology in order to survive. And yet, amongst many sub-disciplines of science and technology, a particular vein of agricultural science emerged out of technological and scientific practices of agriculture in ways that were integral to East Asian governance and political economy. What did it mean for indigenous people to learn and practice new agricultural sciences in their respective contexts? With this border-crossing theme, this panel seeks to identify and question the commonalities and differences in the political complication of agricultural sciences in modern East Asia. Lavelle’s paper explores that agricultural experimentation practiced by Qing agrarian scholars circulated new ideas to wider audience, regardless of literacy. Onaga’s paper traces Japanese sericultural scientists who adapted hybridization science to the Japanese context at the turn of the twentieth century. Lee’s paper investigates Chinese agricultural scientists’ efforts to deal with the question of rice quality in the 1930s. American Motherhood at the Intersection of Nature and Science, 1945-1975 Abstract: This panel explores how scientific and popular ideas about “the natural” and motherhood have impacted the construction and experience of maternal identities and practices in 20th century America. -
Great Cloud of Witnesses.Indd
A Great Cloud of Witnesses i ii A Great Cloud of Witnesses A Calendar of Commemorations iii Copyright © 2016 by The Domestic and Foreign Missionary Society of The Protestant Episcopal Church in the United States of America Portions of this book may be reproduced by a congregation for its own use. Commercial or large-scale reproduction for sale of any portion of this book or of the book as a whole, without the written permission of Church Publishing Incorporated, is prohibited. Cover design and typesetting by Linda Brooks ISBN-13: 978-0-89869-962-3 (binder) ISBN-13: 978-0-89869-966-1 (pbk.) ISBN-13: 978-0-89869-963-0 (ebook) Church Publishing, Incorporated. 19 East 34th Street New York, New York 10016 www.churchpublishing.org iv Contents Introduction vii On Commemorations and the Book of Common Prayer viii On the Making of Saints x How to Use These Materials xiii Commemorations Calendar of Commemorations Commemorations Appendix a1 Commons of Saints and Propers for Various Occasions a5 Commons of Saints a7 Various Occasions from the Book of Common Prayer a37 New Propers for Various Occasions a63 Guidelines for Continuing Alteration of the Calendar a71 Criteria for Additions to A Great Cloud of Witnesses a73 Procedures for Local Calendars and Memorials a75 Procedures for Churchwide Recognition a76 Procedures to Remove Commemorations a77 v vi Introduction This volume, A Great Cloud of Witnesses, is a further step in the development of liturgical commemorations within the life of The Episcopal Church. These developments fall under three categories. First, this volume presents a wide array of possible commemorations for individuals and congregations to observe. -
Predictable Patterns in Planetary Transit Timing Variations and Transit Duration Variations Due to Exomoons
Astronomy & Astrophysics manuscript no. ms c ESO 2016 June 21, 2016 Predictable patterns in planetary transit timing variations and transit duration variations due to exomoons René Heller1, Michael Hippke2, Ben Placek3, Daniel Angerhausen4, 5, and Eric Agol6, 7 1 Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany; [email protected] 2 Luiter Straße 21b, 47506 Neukirchen-Vluyn, Germany; [email protected] 3 Center for Science and Technology, Schenectady County Community College, Schenectady, NY 12305, USA; [email protected] 4 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA; [email protected] 5 USRA NASA Postdoctoral Program Fellow, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA 6 Astronomy Department, University of Washington, Seattle, WA 98195, USA; [email protected] 7 NASA Astrobiology Institute’s Virtual Planetary Laboratory, Seattle, WA 98195, USA Received 22 March 2016; Accepted 12 April 2016 ABSTRACT We present new ways to identify single and multiple moons around extrasolar planets using planetary transit timing variations (TTVs) and transit duration variations (TDVs). For planets with one moon, measurements from successive transits exhibit a hitherto unde- scribed pattern in the TTV-TDV diagram, originating from the stroboscopic sampling of the planet’s orbit around the planet–moon barycenter. This pattern is fully determined and analytically predictable after three consecutive transits. The more measurements become available, the more the TTV-TDV diagram approaches an ellipse. For planets with multi-moons in orbital mean motion reso- nance (MMR), like the Galilean moon system, the pattern is much more complex and addressed numerically in this report. -
Classical Mechanics - Wikipedia, the Free Encyclopedia Page 1 of 13
Classical mechanics - Wikipedia, the free encyclopedia Page 1 of 13 Classical mechanics From Wikipedia, the free encyclopedia (Redirected from Newtonian mechanics) In physics, classical mechanics is one of the two major Classical mechanics sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the Newton's Second Law action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of History of classical mechanics · the oldest and largest subjects in science, engineering and Timeline of classical mechanics technology. Branches Classical mechanics describes the motion of macroscopic Statics · Dynamics / Kinetics · Kinematics · objects, from projectiles to parts of machinery, as well as Applied mechanics · Celestial mechanics · astronomical objects, such as spacecraft, planets, stars, and Continuum mechanics · galaxies. Besides this, many specializations within the Statistical mechanics subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely Formulations accurate results as long as the domain of study is restricted Newtonian mechanics (Vectorial to large objects and the speeds involved do not approach mechanics) the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to Analytical mechanics: introduce the other major sub-field of mechanics, quantum Lagrangian mechanics mechanics, which reconciles the macroscopic laws of Hamiltonian mechanics physics with the atomic nature of matter and handles the Fundamental concepts wave-particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, Space · Time · Velocity · Speed · Mass · classical mechanics is enhanced by special relativity. -
A Disintegrating Minor Planet Transiting a White Dwarf!
A Disintegrating Minor Planet Transiting a White Dwarf! Andrew Vanderburg1, John Asher Johnson1, Saul Rappaport2, Allyson Bieryla1, Jonathan Irwin1, John Arban Lewis1, David Kipping1,3, Warren R. Brown1, Patrick Dufour4, David R. Ciardi5, Ruth Angus1,6, Laura Schaefer1, David W. Latham1, David Charbonneau1, Charles Beichman5, Jason Eastman1, Nate McCrady7, Robert A. Wittenmyer8, & Jason T. Wright9,10. ! White dwarfs are the end state of most stars, including We initiated follow-up ground-based photometry to the Sun, after they exhaust their nuclear fuel. Between better time-resolve the transits seen in the K2 data (Figure 1/4 and 1/2 of white dwarfs have elements heavier than S1). We observed WD 1145+017 frequently over the course helium in their atmospheres1,2, even though these of about a month with the 1.2-meter telescope at the Fred L. elements should rapidly settle into the stellar interiors Whipple Observatory (FLWO) on Mt. Hopkins, Arizona; unless they are occasionally replenished3–5. The one of the 0.7-meter MINERVA telescopes, also at FLWO; abundance ratios of heavy elements in white dwarf and four of the eight 0.4-meter telescopes that compose the atmospheres are similar to rocky bodies in the Solar MEarth-South Array at Cerro Tololo Inter-American system6,7. This and the existence of warm dusty debris Observatory in Chile. Most of these data showed no disks8–13 around about 4% of white dwarfs14–16 suggest interesting or significant signals, but on two nights we that rocky debris from white dwarf progenitors’ observed deep (up to 40%), short-duration (5 minutes), planetary systems occasionally pollute the stars’ asymmetric transits separated by the dominant 4.5 hour atmospheres17. -
The Puritan Dilemma
Library of American Biography / EDITED BY OSCAR HANDLIN 6/|l Edmund S. Morgan The Puritan Dilemma The Story ofJohn Winthrop Morgan The Puritan dilemma 3 !39 - , <, DEC 2 1974 PROSPECT FEB 2 6 1386/27-tf-t ilffiOCT 1 NOV : , -APR 171996 Edmund S. Morgan Tke Puritan Dilemma The Story of Jonn Wintnrop ^5^ ited by Ostcar Hand/in Little, Brown and Company Boston * Toronto COPYRIGHT, , 1958, BY EDMUND S. MORGAN ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRO- DUCED IN ANY FORM WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER, EXCEPT BY A REVIEWER WHO MAY QUOTE BRIEF PAS- SAGES IN A REVIEW TO BE PRINTED IN A MAGAZINE OR NEWSPAPER. LIBRARY OF CONGRESS CATALOG CARD NO. 58-6029 First Paperbac^ Printing Published simultaneously in Canada by Little, Brown & Company {Canada} Limited PRINTED IN THE UNITED STATES OF AMERICA For my mother Editor's Prerace FROM its first discovery, the emptiness of the New World made it the field for social experiment. Euro- peans, crowded in by their seeming lack of space and by a rigid social order, looked with longing across the ocean where space and opportunity abounded. Time and again, men critical of their own society hoped by migration to find the scope for working out their visions of a better order. Yet, in the actual coming, as likely as not, they en- countered the standing quandary of the revolutionary. They had themselves been rebels in order to put into prac- tice their ideas of a new society. But to do so they had to restrain the rebellion of others. -
Transit of Venus M
National Aeronautics and Space Administration The Transit of Venus June 5/6, 2012 HD209458b (HST) The Transit of Venus June 5/6, 2012 Transit of Venus Mathof Venus Transit Top Row – Left image - Photo taken at the US Naval Math Puzzler 3 - The duration of the transit depends Observatory of the 1882 transit of Venus. Middle on the relative speeds between the fast-moving image - The cover of Harpers Weekly for 1882 Venus in its orbit and the slower-moving Earth in its showing children watching the transit of Venus. orbit. This speed difference is known to be 5.24 km/sec. If the June 5, 2012, transit lasts 24,000 Right image – Image from NASA's TRACE satellite seconds, during which time the planet moves an of the transit of Venus, June 8, 2004. angular distance of 0.17 degrees across the sun as Middle - Geometric sketches of the transit of Venus viewed from Earth, what distance between Earth and by James Ferguson on June 6, 1761 showing the Venus allows the distance traveled by Venus along its shift in the transit chords depending on the orbit to subtend the observed angle? observer's location on Earth. The parallax angle is related to the distance between Earth and Venus. Determining the Astronomical Unit Bottom – Left image - NOAA GOES-12 satellite x-ray image showing the Transit of Venus 2004. Middle Based on the calculations of Nicolas Copernicus and image – An observer of the 2004 transit of Venus Johannes Kepler, the distances of the known planets wearing NASA’s Sun-Earth Day solar glasses for from the sun could be given rather precisely in terms safe viewing. -
Download a Pdf File of This Issue for Free
Issue 41: The American Puritans The American Puritans: Did You Know? Little-known or remarkable facts about the American Puritans Cassandra Niemczyk is an independent scholar who contributed to The Variety of American Evangelicalism (Tennessee, 1991). Critic H. L. Mencken once said, wrongly, “Puritanism is the haunting fear that someone, somewhere, may be happy.” On the contrary, Puritans read good books and enjoyed music. They drank beer with meals and rum at weddings. Puritans swam and skated, hunted and fished, and played at archery and bowling (as long as the games were not in a public tavern or on Sunday). The famous “Pilgrims,” who landed at Plymouth Rock in 1620, were so radical they were usually disliked and sometimes hated. Unlike most Puritans, they did not seek to reform the Church of England; they thought the church was beyond help. Most weddings in New England were performed not by ministers but by magistrates. Wedding rings, seen as “popish,” were not used. The early settlers of Massachusetts included more than 100 graduates of Oxford and Cambridge. One historian termed Massachusetts “the best-educated community the world has ever known.” In Puritan worship, a prayer could last an hour or more; a sermon, two hours. In a lifetime, a Puritan might hear 15,000 hours of preaching. Within only six years of their arrival, while still trying to hew out an existence, the Puritans founded a religious college named Harvard. Puritans wanted highly educated ministers, not “Dumme Doggs,” as they called less-trained examples. New England residents who failed to attend worship services on Sunday morning and afternoon were fined or put into stocks.