Astronomy: Space Systems
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Apparent Size of Celestial Objects
NATURE [April 7, 1870 daher wie schon fri.jher die Vor!esungen Uber die Warme, so of rectifying, we assume. :J'o me the Moon at an altit11de of auch jetzt die vorliegenden Vortrage Uber d~n Sc:hall unter 1~rer 45° is about (> i!lches in diameter ; when near the horizon, she is besonderen Aufsicht iibersetzen lasse~, und die :On1ckbogen e1µer about a foot. If I look through a telescope of small ruag11ifyjng genauen Durchsicht unterzogen, dam1t auch die deutsche J3ear power (say IO or 12 diameters), sQ as to leave a fair margin in beitung den englischen Werken ihres Freundes Tyndall nach the field, the Moon is still 6 inches in diameter, though her Form und Inhalt moglichst entsprache.-H. :fIEL!>iHOLTZ, G. visible area has really increased a hundred:fold. WIEDEMANN." . Can we go further than to say, as has often been said, that aH Prof. Tyndall's work, his account of Helmhqltz's Theory of magnitudi; is relative, and that nothing is great or small except Dissonance included, having passed through the hands of Helm by comparison? · · W. R. GROVE, holtz himself, not only without protest or correction, bnt with u5, Harley Street, April 4 the foregoing expression of opinion, it does not seem lihly that any serious dimag'e has been done.] · An After Pirm~. Jl;xperim1mt SUPPOSE in the experiment of an ellipsoid or spheroid, referred Apparent Size of Celestial Qpjecti:; to in my last letter, rolling between two parallel liorizontal ABOUT fifteen years ago I was looking at Venus through a planes, we were to scratch on the rolling body the two equal 40-inch telescope, Venus then being very near the Moon and similar and opposite closed curves (the polhods so-called), traced of a crescent form, the line across the middle or widest part upon it by the successive axes of instantaneou~ solutioll ; and of the crescent being about one-tenth of the planet's diameter. -
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. -
Introduction to Astronomy from Darkness to Blazing Glory
Introduction to Astronomy From Darkness to Blazing Glory Published by JAS Educational Publications Copyright Pending 2010 JAS Educational Publications All rights reserved. Including the right of reproduction in whole or in part in any form. Second Edition Author: Jeffrey Wright Scott Photographs and Diagrams: Credit NASA, Jet Propulsion Laboratory, USGS, NOAA, Aames Research Center JAS Educational Publications 2601 Oakdale Road, H2 P.O. Box 197 Modesto California 95355 1-888-586-6252 Website: http://.Introastro.com Printing by Minuteman Press, Berkley, California ISBN 978-0-9827200-0-4 1 Introduction to Astronomy From Darkness to Blazing Glory The moon Titan is in the forefront with the moon Tethys behind it. These are two of many of Saturn’s moons Credit: Cassini Imaging Team, ISS, JPL, ESA, NASA 2 Introduction to Astronomy Contents in Brief Chapter 1: Astronomy Basics: Pages 1 – 6 Workbook Pages 1 - 2 Chapter 2: Time: Pages 7 - 10 Workbook Pages 3 - 4 Chapter 3: Solar System Overview: Pages 11 - 14 Workbook Pages 5 - 8 Chapter 4: Our Sun: Pages 15 - 20 Workbook Pages 9 - 16 Chapter 5: The Terrestrial Planets: Page 21 - 39 Workbook Pages 17 - 36 Mercury: Pages 22 - 23 Venus: Pages 24 - 25 Earth: Pages 25 - 34 Mars: Pages 34 - 39 Chapter 6: Outer, Dwarf and Exoplanets Pages: 41-54 Workbook Pages 37 - 48 Jupiter: Pages 41 - 42 Saturn: Pages 42 - 44 Uranus: Pages 44 - 45 Neptune: Pages 45 - 46 Dwarf Planets, Plutoids and Exoplanets: Pages 47 -54 3 Chapter 7: The Moons: Pages: 55 - 66 Workbook Pages 49 - 56 Chapter 8: Rocks and Ice: -
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. -
Geodetic Position Computations
GEODETIC POSITION COMPUTATIONS E. J. KRAKIWSKY D. B. THOMSON February 1974 TECHNICALLECTURE NOTES REPORT NO.NO. 21739 PREFACE In order to make our extensive series of lecture notes more readily available, we have scanned the old master copies and produced electronic versions in Portable Document Format. The quality of the images varies depending on the quality of the originals. The images have not been converted to searchable text. GEODETIC POSITION COMPUTATIONS E.J. Krakiwsky D.B. Thomson Department of Geodesy and Geomatics Engineering University of New Brunswick P.O. Box 4400 Fredericton. N .B. Canada E3B5A3 February 197 4 Latest Reprinting December 1995 PREFACE The purpose of these notes is to give the theory and use of some methods of computing the geodetic positions of points on a reference ellipsoid and on the terrain. Justification for the first three sections o{ these lecture notes, which are concerned with the classical problem of "cCDputation of geodetic positions on the surface of an ellipsoid" is not easy to come by. It can onl.y be stated that the attempt has been to produce a self contained package , cont8.i.ning the complete development of same representative methods that exist in the literature. The last section is an introduction to three dimensional computation methods , and is offered as an alternative to the classical approach. Several problems, and their respective solutions, are presented. The approach t~en herein is to perform complete derivations, thus stqing awrq f'rcm the practice of giving a list of for11111lae to use in the solution of' a problem. -
Models for Earth and Maps
Earth Models and Maps James R. Clynch, Naval Postgraduate School, 2002 I. Earth Models Maps are just a model of the world, or a small part of it. This is true if the model is a globe of the entire world, a paper chart of a harbor or a digital database of streets in San Francisco. A model of the earth is needed to convert measurements made on the curved earth to maps or databases. Each model has advantages and disadvantages. Each is usually in error at some level of accuracy. Some of these error are due to the nature of the model, not the measurements used to make the model. Three are three common models of the earth, the spherical (or globe) model, the ellipsoidal model, and the real earth model. The spherical model is the form encountered in elementary discussions. It is quite good for some approximations. The world is approximately a sphere. The sphere is the shape that minimizes the potential energy of the gravitational attraction of all the little mass elements for each other. The direction of gravity is toward the center of the earth. This is how we define down. It is the direction that a string takes when a weight is at one end - that is a plumb bob. A spirit level will define the horizontal which is perpendicular to up-down. The ellipsoidal model is a better representation of the earth because the earth rotates. This generates other forces on the mass elements and distorts the shape. The minimum energy form is now an ellipse rotated about the polar axis. -
Lunar Motion Motion A
2 Lunar V. Lunar Motion Motion A. The Lunar Calendar Dr. Bill Pezzaglia B. Motion of Moon Updated 2012Oct30 C. Eclipses 3 1. Phases of Moon 4 A. The Lunar Calendar 1) Phases of the Moon 2) The Lunar Month 3) Calendars based on Moon b). Elongation Angle 5 b.2 Elongation Angle & Phase 6 Angle between moon and sun (measured eastward along ecliptic) Elongation Phase Configuration 0º New Conjunction 90º 1st Quarter Quadrature 180º Full Opposition 270º 3rd Quarter Quadrature 1 b.3 Elongation Angle & Phase 7 8 c). Aristarchus 275 BC Measures the elongation angle to be 87º when the moon is at first quarter. Using geometry he determines the sun is 19x further away than the moon. [Actually its 400x further !!] 9 Babylonians (3000 BC) note phases are 7 days apart 10 2. The Lunar Month They invent the 7 day “week” Start week on a) The “Week” “moon day” (Monday!) New Moon First Quarter b) Synodic Month (29.5 days) Time 0 Time 1 week c) Spring and Neap Tides Full Moon Third Quarter New Moon Time 2 weeks Time 3 weeks Time 4 weeks 11 b). Stone Circles 12 b). Synodic Month Stone circles often have 29 stones + 1 xtra one Full Moon to Full Moon off to side. Originally there were 30 “sarson The cycle of stone” in the outer ring of Stonehenge the Moon’s phases takes 29.53 days, or ~4 weeks Babylonians measure some months have 29 days (hollow), some have 30 (full). 2 13 c1). Tidal Forces 14 c). Tides This animation illustrates the origin of tidal forces. -
TIDAL THEORY By: Paul O’Hargan
TIDAL THEORY By: Paul O’Hargan (1Tidaltheory.doc, revision – 12/14/2000) INTRODUCTION The word "tides" is a generic term used to define the alternating rise and fall in sea level with respect to the land, produced, in part, by the gravitational attraction of the moon and sun. There are additional nonastronomical factors influencing local heights and times of tides such as configuration of the coastline, depth of the water, ocean-floor topography, and other hydrographic and meteorological influences. Knowledge of these heights and times is important in practical applications such as navigation, harbor construction, tidal datums for hydrography and for mean high water line survey procedures, the determination of base lines for fixing offshore territorial limits and for tide predictions. ORIGIN OF ASTRONOMICAL TIDE RAISING FORCES At the surface of the earth, the earth's force of gravitational attraction acts in a direction toward its center, and thus holds the ocean waters confined to this surface. However, the gravitational forces of the moon and sun also act externally upon the earth's ocean waters. These external forces are exerted as tide producing forces, called tractive forces. To all outward appearances, the moon revolves around the earth, but in actuality, the moon and earth revolve together around their common center of mass called the barycenter. The two astronomical bodies are held together by gravitational attraction, but are simultaneously kept apart by an equal and opposite centrifugal force. At the earth's surface an imbalance between these two forces results in the fact that there exists, on the side of the earth turned toward the moon, a net tide producing force which acts in the direction of the moon. -
Using the SFA Star Charts and Understanding the Equatorial Coordinate System
Using the SFA Star Charts and Understanding the Equatorial Coordinate System SFA Star Charts created by Dan Bruton of Stephen F. Austin State University Notes written by Don Carona of Texas A&M University Last Updated: August 17, 2020 The SFA Star Charts are four separate charts. Chart 1 is for the north celestial region and chart 4 is for the south celestial region. These notes refer to the equatorial charts, which are charts 2 & 3 combined to form one long chart. The star charts are based on the Equatorial Coordinate System, which consists of right ascension (RA), declination (DEC) and hour angle (HA). From the northern hemisphere, the equatorial charts can be used when facing south, east or west. At the bottom of the chart, you’ll notice a series of twenty-four numbers followed by the letter “h”, representing “hours”. These hour marks are right ascension (RA), which is the equivalent of celestial longitude. The same point on the 360 degree celestial sphere passes overhead every 24 hours, making each hour of right ascension equal to 1/24th of a circle, or 15 degrees. Each degree of sky, therefore, moves past a stationary point in four minutes. Each hour of right ascension moves past a stationary point in one hour. Every tick mark between the hour marks on the equatorial charts is equal to 5 minutes. Right ascension is noted in ( h ) hours, ( m ) minutes, and ( s ) seconds. The bright star, Antares, in the constellation Scorpius. is located at RA 16h 29m 30s. At the left and right edges of the chart, you will find numbers marked in degrees (°) and being either positive (+) or negative(-). -
Solar System KEY.Pdf
Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earth-centered (geocentric) and Sun-centered (heliocentric) models of our solar system? A) the Moon B) the Sun C) Venus D) Polaris 3. In which type of model are the Sun, other stars, and the Moon in orbit around the Earth? A) heliocentric model B) tetrahedral model C) concentric model D) geocentric model 4. The diagram below shows one model of a portion of the universe. What type of model does the diagram best demonstrate? A) a heliocentric model, in which celestial objects orbit Earth B) a heliocentric model, in which celestial objects orbit the Sun C) a geocentric model, in which celestial objects orbit Earth D) a geocentric model, in which celestial objects orbit the Sun 5. Which diagram represents a geocentric model? [Key: E = Earth, P = Planet, S = Sun] A) B) C) D) 6. Which statement best describes the geocentric model of our solar system? A) The Earth is located at the center of the model. B) All planets revolve around the Sun. C) The Sun is located at the center of the model. D) All planets except the Earth revolve around the Sun. 7. Which apparent motion can be explained by a geocentric model? A) deflection of the wind B) curved path of projectiles C) motion of a Foucault pendulum D) the sun's path through the sky 8. In the geocentric model (the Earth at the center of the universe), which motion would occur? A) The Earth would revolve around the Sun. -
Lecture 1: Introduction to Ocean Tides
Lecture 1: Introduction to ocean tides Myrl Hendershott 1 Introduction The phenomenon of oceanic tides has been observed and studied by humanity for centuries. Success in localized tidal prediction and in the general understanding of tidal propagation in ocean basins led to the belief that this was a well understood phenomenon and no longer of interest for scientific investigation. However, recent decades have seen a renewal of interest for this subject by the scientific community. The goal is now to understand the dissipation of tidal energy in the ocean. Research done in the seventies suggested that rather than being mostly dissipated on continental shelves and shallow seas, tidal energy could excite far traveling internal waves in the ocean. Through interaction with oceanic currents, topographic features or with other waves, these could transfer energy to smaller scales and contribute to oceanic mixing. This has been suggested as a possible driving mechanism for the thermohaline circulation. This first lecture is introductory and its aim is to review the tidal generating mechanisms and to arrive at a mathematical expression for the tide generating potential. 2 Tide Generating Forces Tidal oscillations are the response of the ocean and the Earth to the gravitational pull of celestial bodies other than the Earth. Because of their movement relative to the Earth, this gravitational pull changes in time, and because of the finite size of the Earth, it also varies in space over its surface. Fortunately for local tidal prediction, the temporal response of the ocean is very linear, allowing tidal records to be interpreted as the superposition of periodic components with frequencies associated with the movements of the celestial bodies exerting the force. -
12.002 Physics and Chemistry of the Earth and Terrestrial Planets Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 12.002 Physics and Chemistry of the Earth and Terrestrial Planets Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 55 Gravity Anomalies For a sphere with mass M, the gravitational potential field Vg ouside of the sphere is: MG V = " g r -11 3 -1 -2 where G is the universal gravitational constant (6.67300 × 10 m kg s ) and r is dis!ta nce from the center of the sphere. The gravitational field is related to the potential field by: MG r ˆ g = "#Vg = " 2 r r again provided that the field is measured outside of the sphere. ! Planetary Reference Gravity Field Because planets are not spheres, but rather slightly oblate spheroids (because of their rotation around the spin axis), the gravitational field is not quite that of a sphere. For an oblate spheroid, the magnitude of the gravitational field has terms proportional to the sign of the latitude, or: MG g = + Asin2 " + Bsin4 " r2 This is called the “reference gravity field”. If we want to look at gravity due to mass anom! alies within the crust and mantle, we need to first subtract off the reference gravity field from the observed gravity field to look at what is left over that is due to mass anomalies or dynamic processes that result in mass anomalies. On earth g at the surface is 9.81 m/s2, while the anomalies we want to look at are 4 or 5 orders of magnitude smaller.