Sun Kwok Our Place in the Universe Understanding Fundamental Astronomy from Ancient Discoveries Second Edition Our Place in the Universe Sun Kwok Our Place in the Universe Understanding Fundamental Astronomy from Ancient Discoveries Second Edition Sun Kwok Faculty of Science The University of Hong Kong Hong Kong, China This book is a second edition of the book “Our Place in the Universe” previously published by the author as a Kindle book under amazon.com ISBN 978-3-319-54171-6 ISBN 978-3-319-54172-3 DOI 10.1007/978-3-319-54172-3 (eBook) Library of Congress Control Number: 2017937904 © Springer International Publishing AG 2017 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Cover image: The Nebra Disk Credit: By Dbachmann, CC BY-SA 3.0, https://commons.wikimedia.org/ w/index.php?curid=1500795 Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface There is a common perception among the general populace that astronomy is impractical and irrelevant This could not be further from the truth For thousands of years, astronomy was an extremely practical subject, and our ancestors relied on their astronomical knowledge to conduct their daily lives Most ancient people were far more familiar with the behavior of the Sun, the Moon, and the stars than the average person is today Astronomy also motivated intellectual thought and had a major impact on the social development of the human race throughout history Our evolving perception of our place in the universe helped bring about important social changes over the last two thousand years This book is not just about astronomy It uses the historical development of astronomy to illustrate the process of rational reasoning and its effect on philosophy, religion, and society Because celestial objects followed regular patterns, astronomical observations gave humans some of the first hints that Nature was understandable The complicated nature of these patterns also challenged our intellectual powers In our education system, science is often presented to our students as a series of facts In fact, science is about the process of rational thinking and creativity What we consider to be the truth is constantly evolving and has certainly changed greatly over the history of humankind The essence of science is not so much about the current view of our world but how we changed from one set of views to another This book is not about the outcome but the process I tried to achieve these goals as follows I begin with a description of basic observations, summarize the patterns observed and the problems they pose, and discuss the suggested theories and their implications The pros and cons of these theories are evaluated alongside alternate theories This approach differs from typical science textbooks, which usually take an axiomatic approach by first stating the correct theory and deriving the deductions before comparing them with experimental results I hope this historical approach allows students to better understand the scientific process and learn from this process when they tackle real-life problems in their careers v vi Preface We live in the most prosperous times in human history It is convenient to assume that everything important happened recently and that events from the distant past not matter It is also easy for us to forget or dismiss the wisdom and achievements of our ancestors A simple survey of modern university students will reveal that most of them believe we discovered the Earth was round only a few hundred years ago But in fact the Earth’s shape was well known as long as 2500 years ago With naked eye observations and some very simple instruments, ancient astronomers found out a great deal about our world By observing celestial objects, they deduced that the Earth was round They could explain the changing times and locations of sunrise They had a reasonable empirical model to forecast eclipses In spite of the apparent erratic motions of the planets, their positions could be predicted accurately with mathematical models hundreds of years into the future Although ancient civilizations occupied only a small fraction of the surface of the Earth, they had a very good estimate of the size of the entire Earth They could even determine the size of and distance to the Moon Modern humans’ disconnection from Nature also means that some common knowledge from ancient times has been lost Many people today believe that the Sun rises in the east every day, but it was common knowledge among our ancestors that the direction of sunrise changes every day The regular yet complex apparent motion of the Sun was the main motivator for the development of rational thought This book is based on a course designed for the Common Core Program of The University of Hong Kong (HKU) The HKU Common Core courses are not based on a specific discipline and are designed to help students develop broader perspectives and abilities to critically assess complex issues The classes also help students appreciate our own culture and global issues I developed this course and taught it from 2010 to 2016 Every year, the class contained about 120 students from all faculties of the University, including Architecture, Arts, Business and Economics, Dentistry, Education, Engineering, Law, Medicine, Science, and Social Sciences Because of the students’ diverse background, no mathematical derivations or calculations were used The students were, however, expected to understand qualitative concepts, develop geometric visualizations, and perform logical deductions In order to convey the concepts effectively without mathematics, I relied strongly on graphical illustrations and animations Computer simulations were used to show apparent motions of celestial objects in the sky These illustrations greatly helped students visualize the complexity of such motions For more technical readers, I have added some mathematics in this book, most of which is presented in the Appendices Nonmathematical readers can skip these parts To focus on the evolution of concepts, I have deliberately omitted certain details For example, the apparent motions of the Sun and Moon are even more complicated than I have presented here My goal is to reach a broad readership Jargons are great obstacles to learning In this book, I try to minimize the use of jargons as much as possible and some technical terms are replaced by simple words Preface vii with similar meaning Some concepts have precise definitions, and the use of technical terms is unavoidable All definitions are presented in the Glossary Every year, students ask me whether they will be handicapped by their lack of previous knowledge of physics and astronomy In fact, the reverse is true Students in science have been told all the modern notions but have never learned how we arrived at those conclusions To learn about the process of discovery, they have to give up their preconceptions, which can be hard for some students One example is the question “How we know that the Earth revolves around the Sun?” When I posed this question to students, the most common answer I got was “This is what I was told by my teacher.” In this book, we try to retrace historical steps to find out how we got to this conclusion In addition to lectures, we had weekly tutorials, quizzes, assignments, computer laboratory exercises, a planetarium show, and exams The planetarium show was developed with the assistance of the Hong Kong Space Museum to illustrate the celestial motions observed in different parts of the world and at different times in history The laboratory exercises were based on computer software so that students could have firsthand experience viewing and recording data from simulated observations The assessments were designed to test whether the students had understood the course materials, could connect material from different parts of the course, had achieved some degree of synthesis, and could apply the acquired knowledge to new situations I wish to thank Wai Wong, who skillfully drew many of the figures in this book Anisia Tang and Sze-Leung Cheung helped with background research and contributed to the laboratory exercises I thank Gray Kochhar-Lindgren, Director of the HKU Common Core Program, and Y.K Kwok, Associate Vice President (Teaching and Learning), for their unyielding support for my course Tim Wotherspoon and Bruce Hrivnak provided helpful comments on an earlier draft I thank Ramon Khanna, my editor at Springer, for encouraging me to publish this book I am particularly grateful to my wife Emily and daughter Roberta for reading various drafts of this book and giving me critical comments I also wish to thank the University of British Columbia for its hospitality during my sabbatical leave when this manuscript was completed I first became interested in this subject during my second year of undergraduate study at McMaster University, where Prof Bertram Brockhouse (Nobel Prize in Physics, 1994) introduced me to Kepler’s work in his Philosophy of Science course His teaching made me realize that physics is more than just mechanical calculations; it is a subject with philosophical and social implications Vancouver, Canada 2016 Sun Kwok Prologue 天地玄黃 , 宇宙洪荒 。日月盈昃 , 辰宿列張 。 寒來暑往 , 秋收冬藏 。閏餘成歲 , 律呂調陽 。 千字文 周興嗣 “In the beginning, there was the black heaven and the yellow earth The Universe was vast and without limit The Sun rises and sets, the Moon goes through phases, and the stars spread over distinct constellations in the sky The warm and cold seasons come and go, while we harvest in the fall and store our grains for the winter A year is composed of an uneven number of months, and harmony of music governs the cosmos” First eight verses from the “Thousand Character Essay” by Zhou Xing Si (470–521 A.D.), translated from Chinese Zhou, an official in the Court of the Liang Dynasty, was asked by the Emperor Wu 梁武帝 (reigned 502–549 A.D.) to arrange a set of 1000 characters into an essay for the education of the young princes He composed a rhymed essay of 250 four-character verses where each character was used only once From the sixth century to the early twentieth century, this essay was commonly used as a primary text to teach young children the Chinese characters The essay begins with eight verses that express humans’ desire to understand the Universe and their appreciation for the celestial objects’ orderly movements As Zhou describes it, people also recognize that observations of the Sun, Moon, and stars have led to the development of calendars and that the structure of the Universe can be understood by theoretical models These verses exemplify the yearning for knowledge of our place in the Universe, which is shared by all ancient cultures Through tireless observations, our ancestors on different continents observed the behavior of the Sun, Moon, planets and the stars They were aware that these patterns were regular but by no means simple Although the data collected were similar across cultures, the interpretations of the celestial patterns differed These interpretations were incorporated into social, religious, and philosophical structures Throughout history, the evolution of our models of the Universe led to changes in these structures This book is an attempt to tell the story of the evolution of astronomical development over two millennia and its effect on our society ix Contents Humans and the Sky 1.1 Repeating Days and Nights 1.2 Cycles of the Seasons 1.3 Early Sky Watchers 1.4 Worship of the Sun 1.5 The Orderly Heaven 1.6 Questions to Think About 4 Effects of Celestial Motions on Human Activities 2.1 Daily Motion of the Sun 2.2 The Annual Motion of the Sun 2.3 The Seasons 2.4 Regular But Not Simple 2.5 Questions to Think About 11 12 12 14 15 15 Ancient Models of the Universe 3.1 A Spherical Heaven 3.2 Chasing the Shadows 3.3 Not All Directions Are Equal 3.4 Path of the Sun 3.5 Where Does the Sun Go at Night? 3.6 Questions to Think About 17 17 18 18 21 22 24 Turning of the Heavens 4.1 The Pole of Heaven 4.2 The Heaven Is Tilted 4.3 A Free Floating Earth 4.4 Questions to Think About 25 26 29 31 31 A Spherical Earth 5.1 The Sun Moves in Complete Circles 5.2 A Different Show for Everyone 33 33 35 xi xii Contents 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 Evidence for a Non-flat Earth The Changing Horizon How High Can the Sun Go? Different Lengths of Daylight Pole Star and Latitude Celestial Navigation Are There Stars We Can’t See? Success of the Round-Earth Hypothesis Questions to Think About 35 37 41 42 42 44 46 47 48 Journey of the Sun Among the Stars 6.1 The Sun Moving Through the Stars 6.2 Two Kinds of Motion of the Sun 6.3 Inclination of the Ecliptic 6.4 Placing Stars on the Celestial Sphere 6.5 An Asymmetric Universe 6.6 Questions to Think About 49 49 53 54 56 58 59 A Two-Sphere Universe 7.1 An Inner Sphere for Humans, an Outer Sphere for Celestial Objects 7.2 The Armillary Sphere 7.3 Armillary Spheres as Observing Instruments 7.4 The Two-Sphere Cosmology 7.5 Questions to Think About 61 61 63 67 67 69 Dance of the Moon 8.1 Shifting Locations of Moonrise 8.2 Two Different Lengths of a Month 8.3 Eclipses and Phases of the Moon 8.4 Size and Distance to the Moon 8.5 The Self-spinning Moon 8.6 Questions to Think About 71 72 75 77 78 80 81 The Calendars 9.1 How Long Is a Year? 9.2 Star Calendar 9.3 What Defines a Year? 9.4 Different Calendars Around the World 9.5 Reform of the Julian Calendar 9.6 What Is so Special About a 24-hour Day? 9.7 Questions to Think About 83 84 84 86 87 89 90 91 10 The Wanderers 93 10.1 The Ten Patterns of Venus 96 10.2 Mars at Opposition 100 250 Laboratory Exercises observe more frequently at certain points, add these observations to the data and the curve.] (3) Repeat Step above for two other locations at different latitudes, preferably one north of and one south of your location Plot the azimuth of sunrise of for these two locations in Graph 1, and plot the time of sunrise of these locations in Graph Questions and Discussion (1) Count the number of days between Day and Day Also count the number of days between Day and Day Discuss the significance of these numbers (2) From Graph 1, calculate the difference in angular position between the northernmost and the southernmost rising Sun for your local location Also roughly estimate the differences for the other two locations What can you say about these differences? Why you think this is the case? (3) From Graph 2, compare the shapes of the sunrise time curves for the three locations Discuss the possible causes of the shapes B Observation of Moonset and Moon Phase Aim: to find out the variation of direction of moonset Exercise: (1) From an observing location that has a clear view to the west, preferably with a background of flat land or sea, mark the time of the Moon when it hits the horizon Start from a date shortly after a new Moon Repeat this measurement once every two or three days over the period of a month On a piece of graph paper, plot the time of moonset against the date Also label the phase of the Moon for each measurement (2) Mark the position of moonset with a cell phone equipped with an electronic compass Make measurements once every two or three days over the period of month (3) Plot the azimuth of the setting Moon as a function of time (4) As the Moon goes through its phases over a month, note the direction of the bright side of the Moon Compare this to the direction (or inferred direction) of the Sun Laboratory Exercises 251 C Synodic Month Aim: to determine the length of the synodic month Exercise (1) From your local location, find the day that the crescent moon is first visible in the western horizon after sunset (2) Repeat this search for the next 12 months (3) Count the number of days between each of these first sightings Average the result to find the length of the synodic month D The Metonic Cycle Aim: to confirm the Metonic cycle Exercise (1) Beginning with the year 2000, find the date of the first new moon of the year for the following 20 years (2) Find the length of the period that the pattern of the dates of the first new moon of the year repeat themselves (3) Predict the date of the first new moon of the year for the year 2050 E The Geminus Calendar Aim: to appreciate the difficulty of designing a calendar that reconciles the solar cycle and the moon phase Exercise (1) Based on the principle of Geminus, design a calendar system of 125 30-day months and 110 29-day months (2) Specifically, when will the switch between 30-day and 29-day months occur? Discussion (1) What are the desirable and undesirable features of your calendar system? (2) What is the problem with our present system of more-or-less alternating 30 and 31 day months? 252 Laboratory Exercises (3) What is the problem of the Chinese calendar of alternating 29 and 30 day months? F Observations of Venus Aims (1) To learn what kinds of observations of Venus that ancient civilizations could and could not make (2) To reveal how observations of Venus can be used as evidence for the heliocentric model of Copernicus Exercise (1) Observe Venus from the location of your home town once every 15 days either at sunrise or at sunset for one complete cycle between maximum angular separations with the Sun along ecliptic For each observation, write down (1) the position of Venus on the ecliptic, i.e its ecliptic longitude (assume the deviation of Venus from the ecliptic is small, i.e its ecliptic latitude can be neglected), and (2) the angular separation between Venus and the Sun Also record whether Venus is seen at sunrise or at sunset for each observation Notes: If Venus is in front of the Sun (i.e Venus is towards east of the Sun) on the ecliptic, treat the angular separation as positive Otherwise, treat it as negative (2) Plot (a) the angular separation between Venus and the Sun against date (Graph 1); (b) the position of Venus on the ecliptic against date (Graph 2) (3) By making more frequent observations wherever necessary, identify the day (s) on which: (a) Venus disappears and reappears (If the angular separation between Venus and the Sun is within 7 , the sky will be too bright for Venus to be seen.) (b) the angular separations between Venus and the Sun are the greatest (c) Venus is stationary on the ecliptic (4) Zoom in on Venus by setting the field of view to arc minutes Observe its phases on each of the dates that you have identified in question Print screen to show the phases in order of the dates with the size of Venus in proportion Discussion From this exercise, describe what you have learnt about the cycle of Venus Laboratory Exercises 253 G Synodic Period of Mars Aim: to determine the synodic period of Mars Exercise: using a planetarium software, look up the positions of the Sun and Mars at your current time Find next five consecutive occurrences of Mars in opposition Determine the length of the synodic period of Mars to the best accuracy possible Glossary A.D Altitude Ante meridiem Aphelion Arc minute Arc second Autumnal equinox Azimuth B.C Celestial equator Celestial pole Celestial sphere Conjunction Day Deferent Anno Domini Year in the Julian calendar after the birth of Christ A.D immediately follows B.C There is no year zero Recently, the term Common Era (C.E.) is used to avoid the religious connotations The angle measured along the great circle perpendicular to the horizon It is measured from the horizon, positive to the zenith (90 degrees), and negative to the nadir (À90 degrees) It is sometimes called the elevation a.m., the period of a solar day before the Sun crosses the local celestial meridian A point in a planet’s orbit which is farthest from the Sun One sixtieth of a degree See Degree One sixtieth of an arc minute See Degree Spatial definition: The intersection of the ecliptic and the celestial equator where the Sun goes from positive to negative declination Temporal definition: date on which the Sun crosses the celestial equator moving southward, occurring on or near September 22 Angle measured on the horizon with north as the zero point, through east, south, and west Since east is 90 degrees around the horizon from north, its azimuth is 90 degrees, that of south and west are respectively 180 degrees and 270 degrees The year Before Christ The year B.C is immediately followed by year A.D There is no year zero Recently, the term Before Common Era (B.C.E.) is used to avoid the religious connotations The projection of Earth’s equator onto the celestial sphere Projection of Earth’s north or south pole onto the celestial sphere An imaginary sphere surrounding Earth to which all stars were once considered to be attached Orbital configuration in which a planet lies in the same direction as the Sun, as seen from Earth The value of elongation at conjunction is (1) The time when the Sun is above horizon Opposite of night (2) The length of time from noon to noon, see Solar day and Mean solar day The large circle upon which the center of the epicycle moves (continued) © Springer International Publishing AG 2017 S Kwok, Our Place in the Universe, DOI 10.1007/978-3-319-54172-3 255 256 Declination Degree ( ) Diurnal motion East Ecliptic Elongation Epicycle Geocentric Gnomon Heliacal rising Heliacal setting Heliocentric Horizon Hour Inferior conjunction Inferior planet Law Leap year Local celestial meridian Glossary The elevation of the point on the celestial sphere from the plane of the celestial equator The celestial equator therefore has declination 0 , and the north and south celestial poles have declinations 90 and À90 , respectively It is the equivalent of latitude on the celestial sphere The unit of angular measure defined such that an entire rotation is 360 degrees This unit dates back to the Babylonians, who used a base 60 number system The number 360 likely arose from the Babylonian year, which was composed of 360 days (12 months of 30 days each) The degree is subdivided into 60 arc minutes per degree, and 60 arc seconds per arc minute 1 ¼ 600 and 10 ¼ 6000 The daily motion of the Sun and the stars One of the two intersection points of the celestial equator and the horizon If we face north, east is 90 degrees to the right The path of the Sun on the celestial sphere over the course of a year Angular separation between a planet and the Sun The angle between the line joining the planet and Earth and the line joining the Sun and Earth A circle whose center is on the boundary of another circle Earth-centered A vertical stick used to measure the length and direction of the Sun’s shadow When a star rises on the eastern horizon before sunrise for the first time following a solar conjunction The occasion when a star is seen for the last time to set in the west after the Sun in the evening sky Sun-centered The maximum visible extent of the horizontal plane on which an observer stands (1) The unit of time measure defined such that the period is one twentyfourth of a mean solar day The hour is subdivided into 60 minutes per hour, and 60 seconds per minute 1h ¼ 60m and 1m ¼ 60s (2) The unit of measure of right ascension representing 15 degrees, or one twenty-fourth of a great circle 1h ¼ 15 , 1m ¼ 150 , and 1s ¼ 1500 Hence, 100 ¼ 0.0667s Orbital configuration in which an inferior planet lies closest to Earth Planets whose orbits lie between Earth and the Sun, i.e Mercury and Venus An empirical relationship between two or more observable quantities Year in which an additional day is inserted into the calendar in order to keep the calendar year synchronized with the length of the tropical year There is a leap year in every years except in years which are multiples of 100, but not multiples of 400 This makes a total of 146,097 days in every 400 years, or 365.2425 days per year which is close to the 365.2422 days in a tropical year The most recent modern corrections are that the years which are multiples of 4000 will not be leap years so that there are 7,304,845 days in 20,000 years, which is 365.24225 days per year The great circle that passes through the north and south celestial poles and the zenith and nadir (continued) Glossary Mean solar day Meridian Minute Month Night Noon North Obliquity of the ecliptic Opposition Parallax Perihelion Planetary conjunction Planetary transit Pole star Polyhedron Post meridiem Precession Principle Quadrature Right ascension Scientific notation 257 Average length of time from one noon to the next, taken over the course of a year An imaginary line on the celestial sphere through the north and south celestial poles, passing directly overhead at a given location A meridian is a line of constant longitude (1) The unit of time, one sixtieth of an hour See Hour definition (2) The unit of angle, one sixtieth of a degree See Degree (3) The unit of angle, one sixtieth of an hour See Hour definition See Synodic month The time when the Sun is below the horizon Opposite of day See day The instance when the Sun is the highest in the sky in one day It is also the time when the Sun crosses the local (celestial) meridian Found by locating the north celestial pole and dropping a vertical line from it to the horizon The angle between the plane of the ecliptic relative the celestial equator A modern interpretation of this term is the tilt of the earth’s rotation axis relative to the orbital plane of the Earth around the Sun Orbital configuration in which a planet lies in the opposite direction from the Sun, as seen from Earth The value of elongation at opposition is 180 degrees The change in the relative positions of stars as the result of the changing position of the observer The point in a planet’s orbit which is closest to the Sun Planets coming together sharing similar apparent positions in the sky Orbital configuration in which an inferior planet is observed to pass directly in front of the Sun The bright star closest to the celestial pole Currently the Pole Star in the north is Polaris There is no pole star in the south Three-dimensional solids with flat polygonal faces and straight edges p.m., past the local (celestial) meridian, after noon The slow gyration of the rotation axis of the rotation axis of the Earth relative to the ecliptic polar axis as the result of external gravitational influence It makes the vernal equinox drift slowly around the zodiac This drift is in clockwise direction as seen over the north ecliptic pole An idea that is assumed to be universal For example, the principle of relativity refers to the idea that all motions are relative Orbital configuration in which a planet is at 90 degrees from the Sun, as seen from Earth Elongation is 90 degrees The arc of the celestial equator measured eastward (anti-clockwise as viewed over the north celestial pole) from the vernal equinox to the foot of the great circle passing through the celestial poles and a given point on the celestial sphere, expressed in hours It is the equivalent of longitude on the celestial sphere The zero point (0 hour) is the position of the Sun at the vernal equinox The expression of a number in the form a  10p, where p is an integer called the “order of magnitude” For example, the scientific notation of 101325 is 1.01325  105 The order of magnitude is (continued) 258 Second Sidereal day Sidereal month Sidereal orbital period Sidereal period (of a planet) Sidereal year Solar day South Summer solstice Superior conjunction Superior planet Synodic month Synodic period Time zone Transit Tropic of Cancer Tropic of Capricorn Tropics Glossary (1) The unit of time, one sixtieth of a minute See Hour definition (2) The unit of angle, one sixtieth of an arc minute See Degree and Hour definition The time between successive risings of a given star, or the time for a star to pass the celestial meridian on successive nights One sidereal day ¼ 23h56m4.091s which is roughly minutes shorter than a solar day Time required for the Moon to complete one trip around the celestial sphere (27.32166 days, 27d7h43m11.5s) See Sidereal period Time required for a planet to complete one cycle around the Sun and return to the starting position on the orbit It is also called the sidereal orbital period Time required for the constellations to complete one cycle around the sky and return to their starting points, as seen from a given point on Earth Earth’s orbital period around the Sun is sidereal year (365.256 mean solar days), or 20 minutes longer than the tropical year because of precession The period of time between one noon and the next The opposite direction (180 degrees) from north Spatial definition: point on the ecliptic where the Sun is at its northernmost point above the celestial equator Temporal definition: the date on which the Sun reverses direction from going north to going south, occurring on or near June 21 Orbital configuration in which an inferior planet lies farthest from Earth (on the opposite side of the Sun) Planets whose orbits lie outside that of Earth, i.e Mars, Jupiter, Saturn, Neptune and Uranus Time required for the Moon to complete a full cycle of phases (29.53059 days) Time required for a planet to return to the same apparent position relative to the Sun, e.g., from opposition to opposition, or from inferior conjunction to inferior conjunction Region on Earth in which all clocks keep the same time, regardless of the precise position of the Sun in the sky, for consistency in travel and communications The standard time zones have been adopted around the world since 1884 The time of each zone is defined to be the local mean solar time of the central longitude of the zone except some curving of the time zone boundaries is introduced to cater for the non-straight boundaries of some countries See Planetary transit The northern most latitude that the Sun can be seen directly overhead For the year 2013 it is at the latitude of 23 260 1400 N The southern most latitude that the Sun can be seen directly overhead For the year 2013, it is at latitude 23 260 1500 S The geographical region between latitudes of 23.5 N and 23.5 S, between the Tropic of Cancer and Tropic of Capricorn (continued) Glossary Tropical year Tropical period Universal time West Winter solstice Vernal equinox Year Zodiac Zodiac signs 259 The time interval between one vernal equinox and the next It is approximately 365.2422 mean solar days In terms of hours and minutes, it is 365 days, hours, 48 minutes, 45.19 seconds the amount of time for a planet to go once around the ecliptic Local mean solar time at Greenwich (0 longitude) One of the intersections of the celestial equator and the horizon If we face north, west is 90 degrees to the left Spatial definition: point on the ecliptic where the Sun is at its southernmost point below the celestial equator Temporal definition: the date on which the Sun reverses direction from going south to going north, occurring on or near December 21 Spatial definition: one of the two intersections of the ecliptic and the celestial equator when the Sun passes from negative to positive declination Temporal definition: date on which the Sun crosses the celestial equator moving northward, occurring on or near March 21 See tropical year The 12 constellations on the ecliptic With modern constellation boundaries defined by the International Astronomical Union (IAU) in 1930, the ecliptic also goes through the modern constellation of Ophiuchus The ecliptic is divided into 12 equal zones, each is assigned a sign, in the order of Aires, Pisces, Aquarius, Capricornus, Sagittarius, Scorpius, Libra, Virgo, Leo, Cancer, Gemini, and Taurus Further Reading Aveni, A 1993, Ancient Astronomers, St Remy Press Aveni, A 1999, Stairways to the Stars, Wiley Aveni, A 2002, Conversing with the Planets, University Press of Colorado Campion, N 2009, A History of Western Astrology Volume II: the medieval and modern worlds, Bloomsbury Academic Chan, K.H 2007, Chinese Ancient Star Maps, Hong Kong Space Museum publications Chen, C.Y 1995, Early Chinese Work in Natural Science: a re-examination of the physics of motion, acoustics, astronomy and scientific thought, Hong Kong University Press Couprie, D.L 2011, Heaven and Earth in Ancient Greek Cosmology, Springer Crowe, M.J 2001, Theories of the world from antiquity to the Copernican revolution (2nd edition), Dover Danielson, Dennis Richard (ed.) 2000, The Book of the Cosmos, Persus Evans, J 1998, The History and Practice of Ancient Astronomy, Oxford University Press Ferguson, K 2002 Tycho and Kepler: the unlikely partnership that forever changed our understanding of the heavens, Walker Books Fowles, G.R 1962, Analytical Mechanics, Holt, Rinehart and Winston Gingerich, O 1997, The Eye of Heaven: Ptolemy, Copernicus, Kepler, Sprinter Gingerich, O 2005, The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus, Walker & Co Heilbron, J.L 2010, Galileo, Oxford University Press Hoskin, M 1997, Cambridge Illustrated History of Astronomy, Cambridge University Press Hoyle, F 1973, Nicolaus Copernicus, Harper & Row Kelley, D.H., & Milone, E.F 2011, Exploring Ancient Skies: a survey of ancient and cultural astronomy, Springer Kaler, J 1996, The Ever Changing Sky: a guide to the celestial sphere, Cambridge University Press Koestler, A 1959, The Sleepwalkers, Hutchinson Krupp, E.C 1983, Echoes of the Ancient Skies: the astronomy of lost civilizations, Harper & Row Kuhn, T.S 1957, The Copernican Revolution, Harvard University Press Leverington, D 2003, Babylon to Voyager and Beyond: a history of planetary astronomy, Cambridge University Press Motz, L & Duveen, A 1968, Essentials of Astronomy, Wadsworth Selin, H 2000, Astronomy Across Cultures, Kluwer Thurston, H 1994, Early Astronomy, Springer Walker, C 1996, Astronomy Before the Telescope, British Museum Press Yip, Chee-kuen, 2001, Moving Stars and Changing Scenes, Hong Kong Science Museum Zeilik, M., & Gregory, S.A 1998, Introductory Astronomy & Astrophysics, Brooks/Cole © Springer International Publishing AG 2017 S Kwok, Our Place in the Universe, DOI 10.1007/978-3-319-54172-3 261 Index A Abu Raihan al-Biruni, 132 Acceleration, 202, 206 Action-in-a-distance, 209 Afonso VI, 153 Agriculture, 2, 11 Alexander the Great, 128, 145 Alexandria, 33, 128, 129, 138, 145 Almagest, 113, 138, 149, 153, 154, 159, 177 Al-Maʾmun, 131, 151 Altair, 57 Altitude, 12, 22, 49 Anaxagoras, 74, 111, 143 Anaximander, 31, 34, 111, 112, 143 Anaximenes, 111 Anglican church, 90 Annual motion, 14, 53, 112, 114 Ante meridiem (AM), 21 Aphelion, 190 Apollonius of Perga, 137, 141, 146, 191 Apollonius of Rhodes, 128 Apparition, 98 Archimedes, 113, 145 Arctic Circle, 42, 63 Aristarchus, 78, 79, 113, 114, 116, 131, 145, 154, 161 Aristotle, 127, 137, 143, 149, 152, 153, 179, 194, 201, 202 Armillary sphere, 63, 65, 67, 128 Artificial satellites, 207 Astrolabe, 151 Astrology, 108 Astronomical unit, 131, 151, 167, 192 Athens, 29, 33, 112, 113, 128, 144 Aurora, Autumnal equinox, 12, 56, 62, 120 Azimuth, 22, 39 B Bandwagon effect, 157 Bible, 152 Big Horn Medicine Wheel, Bishop of Warmia, 159 Bruno, G., 181 C Calculus, 205 Calendar, 7, 26, 83, 116, 124 Calendar reform, 161 Callanish Stones, 7, 73 Callippus, 117 Canopus, 127 Caracol temple, Cardinal Sch€ onberg, 167 Cathedral of Frombork, 159 Celestial equator, 42, 56, 58, 83, 120, 172 Celestial meridian, 44 Celestial navigation, 45, 58 Celestial poles, 26, 83 Celestial sphere, 17, 21, 56, 109, 137, 143, 147, 178 Central force, 206 Centrifugal force, 207 Chiche´n Itza´, Chinese calendar, 88, 119 Christianity, 146, 157, 182 © Springer International Publishing AG 2017 S Kwok, Our Place in the Universe, DOI 10.1007/978-3-319-54172-3 263 264 Christmas, 89, 90 Circumnavigation, 133 Circumpolar, 57 Clay tablets, 111 Columbus, C., 44, 134, 135 Comets, 2, 15, 108, 185 Confucius, 133, 152, 182 Conic section, 141, 192 Conjunction, 101, 161, 188 Constantine I, 146 Constellations, Copernicus, 113, 131, 153, 159, 167, 170, 173, 177, 179, 182, 194, 198 Cosmology, 17, 108, 201 Council of Nicaea, 89 D Day, 3, 19, 83 Declination, 56, 57, 67 Deferent, 137, 141, 149, 169 Dias, B., 153 Dingqi 定氣, 119 Diurnal motion, 53, 68, 74, 83, 112, 137 Dresden Codex, 96 Duke Cosimo II, 198 Dynamics, 202 E Earth, size of, 129, 131 Easter, 89, 160 Eccentric, 118, 125, 139, 169, 190, 194 Eccentricity, 161 Ecliptic, 50, 56, 64, 65, 75, 77, 83, 93, 101, 114, 118, 120, 156, 172 Ecliptic pole, 57, 172 Egyptian system, 115 Einstein, A., 209 Ellipse, 141, 191, 193, 195 Elongation, 95, 154, 161, 165 Emperor Rudolph II, 188, 193 Emperor Theodosius I, 146 Epicycles, 118, 125, 137, 139, 149, 154, 161, 166, 167, 169–171, 177, 193, 194 Equant, 139, 149, 154, 161, 167, 169, 190 Equator, 14, 38, 63 Equatorial system, 56, 67 Equinoxes, 19 Eratosthenes, 128, 129, 131, 134, 151 Ether, 144, 205, 208 Euclid, 145 Index Eudoxus of Cnidus, 17, 84, 114 Evening star, 96, 101 F Fixed stars, 75, 109, 150, 179 Friction, 202, 205 G Galileo, 181, 197, 205 Geminus of Rhodes, 88 Geocentric model, 166, 169, 172, 198 Geometry, 111 Gerard of Cremona, 153 Giese, T., 167 Gnomon, 18, 22, 33, 47 Goethe, 181 Gravitational mass, 209 Gravity, 206 Greece, 111 Gregorian calendar, 89, 90, 205 Guo Shoujing, 67, 88 Gutenberg, J., 153 H Harrison, J., 46 Heliacal rising, 52, 84, 125 Heliocentric model, 113, 161, 166, 167, 169, 172, 174, 177, 190 Hellenistic period, 145 Herakleides of Pontus, 113, 115, 134, 154, 161, 179 Hesiod, 85 Hesperus, 96, 112 Hicetas of Syracuse, 113, 161, 179 Hipparchus, 78, 86, 115, 117, 120, 137, 146, 154, 166, 173, 185, 188 Homer, 84 Hooke, R., 205 Horizon, 3, 12, 17, 26, 29, 37, 47, 49, 61, 64, 127, 178 Horoscopes, 193 House of Wisdom, 131 Hyperbola, 141 I Index of Forbidden Books, 200 Inertia, 205 Inertial force, 205 Index Inertial mass, 209 Inferior conjunction, 161 Inferior planets, 93, 105, 154, 161 Inner planets, 93 Intercalary month, 87, 88 International Astronomical Union, 123 Inverse-square law, 206 Islamic calendar, 87 J Jewish calendar, 88 Jian yi, 67 Julian calendar, 84, 87, 89, 160, 205 Julian the Apostate, 154 Julius Caesar, 84 Jupiter, 108 Jupiter, moons of, 198 K Kepler, J., 188 Kepler, planetary laws of, 190, 191, 206 King Christian IV, 188 King Frederick II, 187 Kochab, 120 Koestler, A., 170, 181 Kuhn, T., 68 L Lactantius, 146 Lascaux Cave, Latitude, 38, 41, 44, 57 Leap year, 87 Li Zhi Zao, 88 Library of Alexandria, 113, 128, 151 Lippershey, H., 197 Longitude, 39, 41 Lunar eclipse, 37, 77, 116, 127 M Magellan, 134 Makahiki, 85 Mars, 100, 190 Mercury, 95, 114, 115, 163, 170 Meridian, 20, 25, 49, 63 Mesopotamia, 4, 96 Metaphysics, 145, 149 Meteors, 2, 15, 108 Meton of Athens, 87 Metonic cycle, 88 265 Midnight, 74 Milky Way, Moon, 2, 71, 154, 197, 206 distance to, 79, 117, 131 far side of, 80 phases of, 71 rise, 72 size of, 79 Morning star, 96, 98 Music, 112 N Nadir, 38 Natural motion, 145 Navigation, 46 Nebra Sky Disk, Newton, I., 205 Night, Noon, 12, 19, 46, 74 North, 18, 26 North celestial pole, 26, 49, 56, 63, 120 North Pole, 63 Novae, O Obliquity of the ecliptic, 55, 59, 86, 125, 129, 151 Opposition, 95, 101, 106, 109, 161 Orthodox Church, 90 Osiander, A., 167 Outer planets, 95, 114 P Parabola, 141, 202 Parallax, 188 Parmenides of Elea, 111 Perihelion, 190 Phosphorus, 96, 112 Pingqi 平氣, 119 Planetary orbits, size of, 165, 177 Planets, 2, 93 motion of, 137, 149 Plato, 112, 114, 137, 143 Pleiades, 5, 85 Polar axis, 29, 59, 63, 65, 120 Polaris, 26, 46, 120 Pole Star, 25 Polyhedra, 189 Polynesians, 2, 14 Polytheism, 146 266 Pope Gregory XIII, 89 Pope John Paul II, 200 Pope Leo X, 160 Pope Paul III, 167 Pope, Urban VIII, 200 Post meridiem (PM), 21 Precession of the equinox, 120, 123–125, 173, 188 Prime meridian, 39 Prograde motion, 101, 154 Projectiles, 202 Ptolemy, 41, 113, 115, 118, 138, 140, 149, 154, 161, 166, 169, 170, 177 Pyramids, 111 Pythagoras, 96, 112, 113, 127, 143, 154 R Ramadan, 87 Reductionism, 210 Reflecting telescope, 205 Renaissance, 153, 159 Retrograde motion, 101, 103, 106, 109, 139, 141, 154, 159, 164 Rheticus, G.J., 167 Rho, G., 88 Right ascension, 56, 67 S Saros, 78 Saturn, 108 Scaliger, J., 92 Schall von Bell, J.A., 88 Seasonal markers, 119 Seasons, 2, 4, 14, 83, 113, 125, 172 origin of, 55 Seven luminaries, 95 Sidereal day, 83, 173 Sidereal month, 58, 75, 173 Sidereal period, 162, 192 Sidereal year, 124 Sirius, 26, 57, 84, 85, 125, 127 Solar day, 83, 173 Solar eclipse, 77 South, 18 South celestial pole, 27, 42, 56, 63 Southern Cross, 27, 124 Spica, 120 Stars, distance to, 181 St Thomas Aquinas, 146, 152 Stjerneborg, 188 Stonehenge, Index Strabo, 134 Sub-lunary, 144, 180, 186 summer solstice, 12, 14, 20, 34, 63, 98, 116, 119 Sun, 2, 11, 195, 198 distance to, 130 size of, 130 Sundial, 18 Sunrise, 5–7, 11–13, 26, 65, 71, 73, 85, 95, 152 Sunspots, 198 Superior conjunction, 161 Superior planets, 95, 101, 154, 161 Super-lunary, 144, 180, 185 Syene, 129 Synodic month, 71, 78, 87, 88, 115 Synodic period, 75, 101, 104, 105, 162, 163 T Telescope, 197 Terrenz, J., 88 Thales of Miletus, 17, 111, 143 Thuban, 120 Tides, Time zones, 90 Timocharis, 120 Tower of Pisa, 201 Tropic of Cancer, 14, 63, 64, 123 Tropic of Capricorn, 14, 63, 65, 123 Tropical period, 104, 105, 114, 150, 174 Tropical year, 86, 88, 89, 103, 115, 116, 124 Trundholm Sun chariot, Turkey, 111 Twilight, 23 Two-sphere universe, 61–63, 68, 137, 178 Tycho Brahe, 185, 188, 190, 201 Tychonic system, 188, 201 U UFO, 96 Unevenness of the seasons, 117, 118, 125, 137 Universe, size of, 150, 179 Uraniborg, 187 V Vatican, 90, 200 Vega, 57, 120 Venus, 7, 95, 96, 112, 114, 115, 162, 170 phase of, 198 Verbiest, F., 67, 89 Index 267 Vernal equinox, 13, 62, 64, 84, 86, 89, 119, 120, 123 Violent motion, 145, 208 Vision, 90 Y Yang Guang Xian, 89, 133 Year, length of, 84, 86, 89, 116 Yi Shin, 133 W Week, 95 Winter solstice, 12, 14, 20, 34, 88, 89 Z Zenith, 17, 20, 38, 44 Zodiac, 51, 75, 83, 93, 123 Zodiac signs, 64, 123 X Xu Guangqi, 88 .. .Our Place in the Universe Sun Kwok Our Place in the Universe Understanding Fundamental Astronomy from Ancient Discoveries Second Edition Sun Kwok Faculty of Science The University... of the stones have been suggested to mark the cycles of the Sun and the Moon, the astronomical purpose of the stones is less definite than in the Stonehenge case In the Americas, the Plains Indians... see the Sun, the Moon, and the stars and speculated that other worlds were out there, much further away than people could travel If we define everything in existence as the Universe”, then the