Answers to Chapter Review Questions and Problems for the Amateur Astronomer's Introduction to the Celestial Sphere
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Unit 2 Basic Concepts of Positional Astronomy
Basic Concepts of UNIT 2 BASIC CONCEPTS OF POSITIONAL Positional Astronomy ASTRONOMY Structure 2.1 Introduction Objectives 2.2 Celestial Sphere Geometry of a Sphere Spherical Triangle 2.3 Astronomical Coordinate Systems Geographical Coordinates Horizon System Equatorial System Diurnal Motion of the Stars Conversion of Coordinates 2.4 Measurement of Time Sidereal Time Apparent Solar Time Mean Solar Time Equation of Time Calendar 2.5 Summary 2.6 Terminal Questions 2.7 Solutions and Answers 2.1 INTRODUCTION In Unit 1, you have studied about the physical parameters and measurements that are relevant in astronomy and astrophysics. You have learnt that astronomical scales are very different from the ones that we encounter in our day-to-day lives. In astronomy, we are also interested in the motion and structure of planets, stars, galaxies and other celestial objects. For this purpose, it is essential that the position of these objects is precisely defined. In this unit, we describe some coordinate systems (horizon , local equatorial and universal equatorial ) used to define the positions of these objects. We also discuss the effect of Earth’s daily and annual motion on the positions of these objects. Finally, we explain how time is measured in astronomy. In the next unit, you will learn about various techniques and instruments used to make astronomical measurements. Study Guide In this unit, you will encounter the coordinate systems used in astronomy for the first time. In order to understand them, it would do you good to draw each diagram yourself. Try to visualise the fundamental circles, reference points and coordinates as you make each drawing. -
Basic Principles of Celestial Navigation James A
Basic principles of celestial navigation James A. Van Allena) Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242 ͑Received 16 January 2004; accepted 10 June 2004͒ Celestial navigation is a technique for determining one’s geographic position by the observation of identified stars, identified planets, the Sun, and the Moon. This subject has a multitude of refinements which, although valuable to a professional navigator, tend to obscure the basic principles. I describe these principles, give an analytical solution of the classical two-star-sight problem without any dependence on prior knowledge of position, and include several examples. Some approximations and simplifications are made in the interest of clarity. © 2004 American Association of Physics Teachers. ͓DOI: 10.1119/1.1778391͔ I. INTRODUCTION longitude ⌳ is between 0° and 360°, although often it is convenient to take the longitude westward of the prime me- Celestial navigation is a technique for determining one’s ridian to be between 0° and Ϫ180°. The longitude of P also geographic position by the observation of identified stars, can be specified by the plane angle in the equatorial plane identified planets, the Sun, and the Moon. Its basic principles whose vertex is at O with one radial line through the point at are a combination of rudimentary astronomical knowledge 1–3 which the meridian through P intersects the equatorial plane and spherical trigonometry. and the other radial line through the point G at which the Anyone who has been on a ship that is remote from any prime meridian intersects the equatorial plane ͑see Fig. -
2. Disc Resources
An early map of the world Resource D1 A map of the world drawn in 1570 shows ‘Terra Australis Nondum Cognita’ (the unknown south land). National Library of Australia Expeditions to Antarctica 1770 –1830 and 1910 –1913 Resource D2 Voyages to Antarctica 1770–1830 1772–75 1819–20 1820–21 Cook (Britain) Bransfield (Britain) Palmer (United States) ▼ ▼ ▼ ▼ ▼ Resolution and Adventure Williams Hero 1819 1819–21 1820–21 Smith (Britain) ▼ Bellingshausen (Russia) Davis (United States) ▼ ▼ ▼ Williams Vostok and Mirnyi Cecilia 1822–24 Weddell (Britain) ▼ Jane and Beaufoy 1830–32 Biscoe (Britain) ★ ▼ Tula and Lively South Pole expeditions 1910–13 1910–12 1910–13 Amundsen (Norway) Scott (Britain) sledge ▼ ▼ ship ▼ Source: Both maps American Geographical Society Source: Major voyages to Antarctica during the 19th century Resource D3 Voyage leader Date Nationality Ships Most southerly Achievements latitude reached Bellingshausen 1819–21 Russian Vostok and Mirnyi 69˚53’S Circumnavigated Antarctica. Discovered Peter Iøy and Alexander Island. Charted the coast round South Georgia, the South Shetland Islands and the South Sandwich Islands. Made the earliest sighting of the Antarctic continent. Dumont d’Urville 1837–40 French Astrolabe and Zeelée 66°S Discovered Terre Adélie in 1840. The expedition made extensive natural history collections. Wilkes 1838–42 United States Vincennes and Followed the edge of the East Antarctic pack ice for 2400 km, 6 other vessels confirming the existence of the Antarctic continent. Ross 1839–43 British Erebus and Terror 78°17’S Discovered the Transantarctic Mountains, Ross Ice Shelf, Ross Island and the volcanoes Erebus and Terror. The expedition made comprehensive magnetic measurements and natural history collections. -
Constellations with Prominent Stars That Can Be Found Near the Meridian at 10 Pm on January 15
ONSTELLATIONS C Altitude Ruler The rotation of the Earth on its axis causes the stars to rise and set each evening. In addition, the orbit of the Earth around the Sun places different regions of the sky in our Horizon night-time view. The PLANISPHERE is an extremely useful tool for finding stars and 10 constellation in the sky, depicting not only what is currently in the sky but it also allows the 20 prediction of the rising and setting times of various celestial objects. 30 THE LAYOUT OF THE PLANISPHERE 40 50 The outer circumference of the dark blue circular disk (which is called the star wheel) you’ll notice that the wheel is divided into the 12 months, and that each month is divided into 60 individual dates. The star wheel rotates about the brass fastener, which represents the 70 North Celestial Pole. The frame of the planisphere has times along the outer edge. 80 Holding the planisphere on the southern corner you'll see "midnight" at the top. Moving Zenith counterclockwise, notice how the hours progress, through 1 AM, 2 AM, and so on through "noon" at the bottom. The hours then proceed through the afternoon and evening (1 PM, 2 PM, etc.) back toward midnight. Once you have the wheel set properly for the correct time and day, the displayed part represents what you see if you stand with the star and planet locator held directly over your head with the brass fastener toward the north. (Notice that the compass directions are also written on the corners of the frame.) Of course, you don't have to actually stand that way to make use of the Star and Planet Locator--this is just a description to help you understand what is displayed. -
Equatorial and Cartesian Coordinates • Consider the Unit Sphere (“Unit”: I.E
Coordinate Transforms Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. declination the distance from the center of the (δ) sphere to its surface is r = 1) • Then the equatorial coordinates Equator can be transformed into Cartesian coordinates: right ascension (α) – x = cos(α) cos(δ) – y = sin(α) cos(δ) z x – z = sin(δ) y • It can be much easier to use Cartesian coordinates for some manipulations of geometry in the sky Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. the distance y x = Rcosα from the center of the y = Rsinα α R sphere to its surface is r = 1) x Right • Then the equatorial Ascension (α) coordinates can be transformed into Cartesian coordinates: declination (δ) – x = cos(α)cos(δ) z r = 1 – y = sin(α)cos(δ) δ R = rcosδ R – z = sin(δ) z = rsinδ Precession • Because the Earth is not a perfect sphere, it wobbles as it spins around its axis • This effect is known as precession • The equatorial coordinate system relies on the idea that the Earth rotates such that only Right Ascension, and not declination, is a time-dependent coordinate The effects of Precession • Currently, the star Polaris is the North Star (it lies roughly above the Earth’s North Pole at δ = 90oN) • But, over the course of about 26,000 years a variety of different points in the sky will truly be at δ = 90oN • The declination coordinate is time-dependent albeit on very long timescales • A precise astronomical coordinate system must account for this effect Equatorial coordinates and equinoxes • To account -
Capricious Suntime
[Physics in daily life] I L.J.F. (Jo) Hermans - Leiden University, e Netherlands - [email protected] - DOI: 10.1051/epn/2011202 Capricious suntime t what time of the day does the sun reach its is that the solar time will gradually deviate from the time highest point, or culmination point, when on our watch. We expect this‘eccentricity effect’ to show a its position is exactly in the South? e ans - sine-like behaviour with a period of a year. A wer to this question is not so trivial. For ere is a second, even more important complication. It is one thing, it depends on our location within our time due to the fact that the rotational axis of the earth is not zone. For Berlin, which is near the Eastern end of the perpendicular to the ecliptic, but is tilted by about 23.5 Central European time zone, it may happen around degrees. is is, aer all, the cause of our seasons. To noon, whereas in Paris it may be close to 1 p.m. (we understand this ‘tilt effect’ we must realise that what mat - ignore the daylight saving ters for the deviation in time time which adds an extra is the variation of the sun’s hour in the summer). horizontal motion against But even for a fixed loca - the stellar background tion, the time at which the during the year. In mid- sun reaches its culmination summer and mid-winter, point varies throughout the when the sun reaches its year in a surprising way. -
Chapter 7 Mapping The
BASICS OF RADIO ASTRONOMY Chapter 7 Mapping the Sky Objectives: When you have completed this chapter, you will be able to describe the terrestrial coordinate system; define and describe the relationship among the terms com- monly used in the “horizon” coordinate system, the “equatorial” coordinate system, the “ecliptic” coordinate system, and the “galactic” coordinate system; and describe the difference between an azimuth-elevation antenna and hour angle-declination antenna. In order to explore the universe, coordinates must be developed to consistently identify the locations of the observer and of the objects being observed in the sky. Because space is observed from Earth, Earth’s coordinate system must be established before space can be mapped. Earth rotates on its axis daily and revolves around the sun annually. These two facts have greatly complicated the history of observing space. However, once known, accu- rate maps of Earth could be made using stars as reference points, since most of the stars’ angular movements in relationship to each other are not readily noticeable during a human lifetime. Although the stars do move with respect to each other, this movement is observable for only a few close stars, using instruments and techniques of great precision and sensitivity. Earth’s Coordinate System A great circle is an imaginary circle on the surface of a sphere whose center is at the center of the sphere. The equator is a great circle. Great circles that pass through both the north and south poles are called meridians, or lines of longitude. For any point on the surface of Earth a meridian can be defined. -
3.1 Discipline Science Results
CASSINI FINAL MISSION REPORT 2019 1 SATURN Before Cassini, scientists viewed Saturn’s unique features only from Earth and from a few spacecraft flybys. During more than a decade orbiting the gas giant, Cassini studied the composition and temperature of Saturn’s upper atmosphere as the seasons changed there. Cassini also provided up-close observations of Saturn’s exotic storms and jet streams, and heard Saturn’s lightning, which cannot be detected from Earth. The Grand Finale orbits provided valuable data for understanding Saturn’s interior structure and magnetic dynamo, in addition to providing insight into material falling into the atmosphere from parts of the rings. Cassini’s Saturn science objectives were overseen by the Saturn Working Group (SWG). This group consisted of the scientists on the mission interested in studying the planet itself and phenomena which influenced it. The Saturn Atmospheric Modeling Working Group (SAMWG) was formed to specifically characterize Saturn’s uppermost atmosphere (thermosphere) and its variation with time, define the shape of Saturn’s 100 mbar and 1 bar pressure levels, and determine when the Saturn safely eclipsed Cassini from the Sun. Its membership consisted of experts in studying Saturn’s upper atmosphere and members of the engineering team. 2 VOLUME 1: MISSION OVERVIEW & SCIENCE OBJECTIVES AND RESULTS CONTENTS SATURN ........................................................................................................................................................................... 1 Executive -
Radiative Forcing of the Stratosphere of Jupiter, Part I: Atmospheric
*(Revised) Manuscript, clean version Click here to download (Revised) Manuscript, clean version: Manuscript.pdf Click here to view linked References 1 2 3 4 5 Radiative Forcing of the Stratosphere of Jupiter, Part I: 6 7 Atmospheric Cooling Rates from Voyager to Cassini 8 9 10 a, b a c d e 11 X. Zhang *, C.A. Nixon , R.L. Shia , R.A. West , P.G. J. Irwin , R.V. Yelle , M.A. 12 a,c a 13 Allen , Y.L. Yung 14 15 16 17 18 a Division of Geological and Planetary Sciences, California Institute of Technology, 19 20 Pasadena, CA, 91125, USA 21 b 22 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 23 c 24 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, 25 Pasadena, CA 91109, USA 26 d 27 Atmospheric, Oceanic, and Planetary Physics, University of Oxford, Clarendon 28 29 Laboratory, Parks Road, Oxford, OX1 3PU,UK 30 e 31 Department of Planetary Sciences, University of Arizona, Tucson, Arizona, USA 32 33 34 35 36 *Corresponding author at: Division of Geological and Planetary Sciences, California 37 38 Institute of Technology, Pasadena, CA, 91125, USA. 39 40 E-mail address: [email protected] (X. Zhang) 41 42 43 44 45 46 47 Submitted to: 48 49 Plan. Space Sci. (PSS) Special issue on Outer planets systems 50 51 52 53 54 55 56 57 58 59 60 61 62 63 1 64 65 1 2 3 4 Abstract 5 6 7 8 We developed a line-by-line heating and cooling rate model for the stratosphere of 9 10 Jupiter, based on two complete sets of global maps of temperature, C2H2 and C2H6, 11 12 retrieved from the Cassini and Voyager observations in the latitude and vertical plane, 13 with a careful error analysis. -
Exercise 3.0 the CELESTIAL HORIZON SYSTEM
Exercise 3.0 THE CELESTIAL HORIZON SYSTEM I. Introduction When we stand at most locations on the Earth, we have the distinct impression that the Earth is flat. This occurs because the curvature of the small area of the Earth usually visible is very slight. We call this “flat Earth” the Plane of the Horizon and divide it up into 4 quadrants, each containing 90o, by using the cardinal points of the compass. The latter are the North, South, East, and west points of the horizon. We describe things as being vertical or “straight up” if they line up with the direction of gravity at that location. It is easy for us to determine “straight up” because we have a built in mechanism for this in the inner ear (the semicircular canals). Because it seems so “natural”, we build a coordinate system on these ideas called the Horizon System. The Celestial Horizon System is one of the coordinate systems that astronomers find useful for locating objects in the sky. It is depicted in the Figure below. Figure 1. The above diagram is a skewed perspective, schematic diagram of the celestial sphere with circles drawn only for the half above the horizon. Circles on the far side, or western half, of the celestial sphere are drawn as dashed curves. All the reference circles of this system do not share in the rotation of the celestial sphere and, therefore, this coordinate system is fixed with respect to a given observer. The basis for the system is the direction of gravity. We can describe this as the line from the observer on the surface of the Earth through the center of the Earth. -
Capricorn (Astrology) - Wikipedia, the Free Encyclopedia
מַ זַל גְּדִ י http://www.morfix.co.il/en/Capricorn بُ ْر ُج ال َج ْدي http://www.arabdict.com/en/english-arabic/Capricorn برج جدی https://translate.google.com/#auto/fa/Capricorn Αιγόκερως Capricornus - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Capricornus h m s Capricornus Coordinates: 21 00 00 , −20° 00 ′ 00 ″ From Wikipedia, the free encyclopedia Capricornus /ˌkæprɨˈkɔrnəs/ is one of the constellations of the zodiac. Its name is Latin for "horned goat" or Capricornus "goat horn", and it is commonly represented in the form Constellation of a sea-goat: a mythical creature that is half goat, half fish. Its symbol is (Unicode ♑). Capricornus is one of the 88 modern constellations, and was also one of the 48 constellations listed by the 2nd century astronomer Ptolemy. Under its modern boundaries it is bordered by Aquila, Sagittarius, Microscopium, Piscis Austrinus, and Aquarius. The constellation is located in an area of sky called the Sea or the Water, consisting of many water-related constellations such as Aquarius, Pisces and Eridanus. It is the smallest constellation in the zodiac. List of stars in Capricornus Contents Abbreviation Cap Genitive Capricorni 1 Notable features Pronunciation /ˌkæprɨˈkɔrnəs/, genitive 1.1 Deep-sky objects /ˌkæprɨˈkɔrnaɪ/ 1.2 Stars 2 History and mythology Symbolism the Sea Goat 3 Visualizations Right ascension 20 h 06 m 46.4871 s–21 h 59 m 04.8693 s[1] 4 Equivalents Declination −8.4043999°–−27.6914144° [1] 5 Astrology 6 Namesakes Family Zodiac 7 Citations Area 414 sq. deg. (40th) 8 See also Main stars 9, 13,23 9 External links Bayer/Flamsteed 49 stars Notable features Stars with 5 planets Deep-sky objects Stars brighter 1 than 3.00 m Several galaxies and star clusters are contained within Stars within 3 Capricornus. -
3.- the Geographic Position of a Celestial Body
Chapter 3 Copyright © 1997-2004 Henning Umland All Rights Reserved Geographic Position and Time Geographic terms In celestial navigation, the earth is regarded as a sphere. Although this is an approximation, the geometry of the sphere is applied successfully, and the errors caused by the flattening of the earth are usually negligible (chapter 9). A circle on the surface of the earth whose plane passes through the center of the earth is called a great circle . Thus, a great circle has the greatest possible diameter of all circles on the surface of the earth. Any circle on the surface of the earth whose plane does not pass through the earth's center is called a small circle . The equator is the only great circle whose plane is perpendicular to the polar axis , the axis of rotation. Further, the equator is the only parallel of latitude being a great circle. Any other parallel of latitude is a small circle whose plane is parallel to the plane of the equator. A meridian is a great circle going through the geographic poles , the points where the polar axis intersects the earth's surface. The upper branch of a meridian is the half from pole to pole passing through a given point, e. g., the observer's position. The lower branch is the opposite half. The Greenwich meridian , the meridian passing through the center of the transit instrument at the Royal Greenwich Observatory , was adopted as the prime meridian at the International Meridian Conference in 1884. Its upper branch is the reference for measuring longitudes (0°...+180° east and 0°...–180° west), its lower branch (180°) is the basis for the International Dateline (Fig.