Oblate Spheroid (See Figure 1), a Solid Formed When an Ellipse Is Rotated About Its Axis
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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. -
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: -
Geodesy Methods Over Time
Geodesy methods over time GISC3325 - Lecture 4 Astronomic Latitude/Longitude • Given knowledge of the positions of an astronomic body e.g. Sun or Polaris and our time we can determine our location in terms of astronomic latitude and longitude. US Meridian Triangulation This map shows the first project undertaken by the founding Superintendent of the Survey of the Coast Ferdinand Hassler. Triangulation • Method of indirect measurement. • Angles measured at all nodes. • Scaled provided by one or more precisely measured base lines. • First attributed to Gemma Frisius in the 16th century in the Netherlands. Early surveying instruments Left is a Quadrant for angle measurements, below is how baseline lengths were measured. A non-spherical Earth • Willebrod Snell van Royen (Snellius) did the first triangulation project for the purpose of determining the radius of the earth from measurement of a meridian arc. • Snellius was also credited with the law of refraction and incidence in optics. • He also devised the solution of the resection problem. At point P observations are made to known points A, B and C. We solve for P. Jean Picard’s Meridian Arc • Measured meridian arc through Paris between Malvoisine and Amiens using triangulation network. • First to use a telescope with cross hairs as part of the quadrant. • Value obtained used by Newton to verify his law of gravitation. Ellipsoid Earth Model • On an expedition J.D. Cassini discovered that a one-second pendulum regulated at Paris needed to be shortened to regain a one-second oscillation. • Pendulum measurements are effected by gravity! Newton • Newton used measurements of Picard and Halley and the laws of gravitation to postulate a rotational ellipsoid as the equilibrium figure for a homogeneous, fluid, rotating Earth. -
The Coriolis Effect in Meteorology
THE CORIOLIS EFFECT IN METEOROLOGY On this page I discuss the rotation-of-Earth-effect that is taken into account in Meteorology, where it is referred to as 'the Coriolis effect'. (For the rotation of Earth effect that applies in ballistics, see the following two Java simulations: Great circles and Ballistics). The rotating Earth A key consequence of the Earth's rotation is the deviation from perfectly spherical form: there is an equatorial bulge. The bulge is small; on Earth pictures taken from outer space you can't see it. It may seem unimportant but it's not: what matters for meteorology is an effect that arises from the Earth's rotation and Earth's oblateness together. A model: parabolic dish Thinking about motion over the Earth's surface is rather complicated, so I turn now to a model that is simpler but still presents the feature that gives rise to the Coriolis effect. Source: PAOC, MIT Courtesy of John Marshall The dish in the picture is used by students of Geophysical Fluid Dynamics for lab exercises. This dish was manufactured as follows: a flat platform with a rim was rotating at a very constant angular velocity (10 revolutions per minute), and a synthetic resin was poured onto the platform. The resin flowed out, covering the entire area. It had enough time to reach an equilibrium state before it started to set. The surface was sanded to a very smooth finish. Also, note the construction that is hanging over the dish. The vertical rod is not attached to the table but to the dish; when the dish rotates the rod rotates with it. -
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. -
The Evolution of Earth Gravitational Models Used in Astrodynamics
JEROME R. VETTER THE EVOLUTION OF EARTH GRAVITATIONAL MODELS USED IN ASTRODYNAMICS Earth gravitational models derived from the earliest ground-based tracking systems used for Sputnik and the Transit Navy Navigation Satellite System have evolved to models that use data from the Joint United States-French Ocean Topography Experiment Satellite (Topex/Poseidon) and the Global Positioning System of satellites. This article summarizes the history of the tracking and instrumentation systems used, discusses the limitations and constraints of these systems, and reviews past and current techniques for estimating gravity and processing large batches of diverse data types. Current models continue to be improved; the latest model improvements and plans for future systems are discussed. Contemporary gravitational models used within the astrodynamics community are described, and their performance is compared numerically. The use of these models for solid Earth geophysics, space geophysics, oceanography, geology, and related Earth science disciplines becomes particularly attractive as the statistical confidence of the models improves and as the models are validated over certain spatial resolutions of the geodetic spectrum. INTRODUCTION Before the development of satellite technology, the Earth orbit. Of these, five were still orbiting the Earth techniques used to observe the Earth's gravitational field when the satellites of the Transit Navy Navigational Sat were restricted to terrestrial gravimetry. Measurements of ellite System (NNSS) were launched starting in 1960. The gravity were adequate only over sparse areas of the Sputniks were all launched into near-critical orbit incli world. Moreover, because gravity profiles over the nations of about 65°. (The critical inclination is defined oceans were inadequate, the gravity field could not be as that inclination, 1= 63 °26', where gravitational pertur meaningfully estimated. -
World Geodetic System 1984
World Geodetic System 1984 Responsible Organization: National Geospatial-Intelligence Agency Abbreviated Frame Name: WGS 84 Associated TRS: WGS 84 Coverage of Frame: Global Type of Frame: 3-Dimensional Last Version: WGS 84 (G1674) Reference Epoch: 2005.0 Brief Description: WGS 84 is an Earth-centered, Earth-fixed terrestrial reference system and geodetic datum. WGS 84 is based on a consistent set of constants and model parameters that describe the Earth's size, shape, and gravity and geomagnetic fields. WGS 84 is the standard U.S. Department of Defense definition of a global reference system for geospatial information and is the reference system for the Global Positioning System (GPS). It is compatible with the International Terrestrial Reference System (ITRS). Definition of Frame • Origin: Earth’s center of mass being defined for the whole Earth including oceans and atmosphere • Axes: o Z-Axis = The direction of the IERS Reference Pole (IRP). This direction corresponds to the direction of the BIH Conventional Terrestrial Pole (CTP) (epoch 1984.0) with an uncertainty of 0.005″ o X-Axis = Intersection of the IERS Reference Meridian (IRM) and the plane passing through the origin and normal to the Z-axis. The IRM is coincident with the BIH Zero Meridian (epoch 1984.0) with an uncertainty of 0.005″ o Y-Axis = Completes a right-handed, Earth-Centered Earth-Fixed (ECEF) orthogonal coordinate system • Scale: Its scale is that of the local Earth frame, in the meaning of a relativistic theory of gravitation. Aligns with ITRS • Orientation: Given by the Bureau International de l’Heure (BIH) orientation of 1984.0 • Time Evolution: Its time evolution in orientation will create no residual global rotation with regards to the crust Coordinate System: Cartesian Coordinates (X, Y, Z). -
True Polar Wander: Linking Deep and Shallow Geodynamics to Hydro- and Bio-Spheric Hypotheses T
True Polar Wander: linking Deep and Shallow Geodynamics to Hydro- and Bio-Spheric Hypotheses T. D. Raub, Yale University, New Haven, CT, USA J. L. Kirschvink, California Institute of Technology, Pasadena, CA, USA D. A. D. Evans, Yale University, New Haven, CT, USA © 2007 Elsevier SV. All rights reserved. 5.14.1 Planetary Moment of Inertia and the Spin-Axis 565 5.14.2 Apparent Polar Wander (APW) = Plate motion +TPW 566 5.14.2.1 Different Information in Different Reference Frames 566 5.14.2.2 Type 0' TPW: Mass Redistribution at Clock to Millenial Timescales, of Inconsistent Sense 567 5.14.2.3 Type I TPW: Slow/Prolonged TPW 567 5.14.2.4 Type II TPW: Fast/Multiple/Oscillatory TPW: A Distinct Flavor of Inertial Interchange 569 5.14.2.5 Hypothesized Rapid or Prolonged TPW: Late Paleozoic-Mesozoic 569 5.14.2.6 Hypothesized Rapid or Prolonged TPW: 'Cryogenian'-Ediacaran-Cambrian-Early Paleozoic 571 5.14.2.7 Hypothesized Rapid or Prolonged TPW: Archean to Mesoproterozoic 572 5.14.3 Geodynamic and Geologic Effects and Inferences 572 5.14.3.1 Precision of TPW Magnitude and Rate Estimation 572 5.14.3.2 Physical Oceanographic Effects: Sea Level and Circulation 574 5.14.3.3 Chemical Oceanographic Effects: Carbon Oxidation and Burial 576 5..14.4 Critical Testing of Cryogenian-Cambrian TPW 579 5.14A1 Ediacaran-Cambrian TPW: 'Spinner Diagrams' in the TPW Reference Frame 579 5.14.4.2 Proof of Concept: Independent Reconstruction of Gondwanaland Using Spinner Diagrams 581 5.14.5 Summary: Major Unresolved Issues and Future Work 585 References 586 5.14.1 Planetary Moment of Inertia location ofEarth's daily rotation axis and/or by fluc and the Spin-Axis tuations in the spin rate ('length of day' anomalies). -
The History of Geodesy Told Through Maps
The History of Geodesy Told through Maps Prof. Dr. Rahmi Nurhan Çelik & Prof. Dr. Erol KÖKTÜRK 16 th May 2015 Sofia Missionaries in 5000 years With all due respect... 3rd FIG Young Surveyors European Meeting 1 SUMMARIZED CHRONOLOGY 3000 BC : While settling, people were needed who understand geometries for building villages and dividing lands into parts. It is known that Egyptian, Assyrian, Babylonian were realized such surveying techniques. 1700 BC : After floating of Nile river, land surveying were realized to set back to lost fields’ boundaries. (32 cm wide and 5.36 m long first text book “Papyrus Rhind” explain the geometric shapes like circle, triangle, trapezoids, etc. 550+ BC : Thereafter Greeks took important role in surveying. Names in that period are well known by almost everybody in the world. Pythagoras (570–495 BC), Plato (428– 348 BC), Aristotle (384-322 BC), Eratosthenes (275–194 BC), Ptolemy (83–161 BC) 500 BC : Pythagoras thought and proposed that earth is not like a disk, it is round as a sphere 450 BC : Herodotus (484-425 BC), make a World map 350 BC : Aristotle prove Pythagoras’s thesis. 230 BC : Eratosthenes, made a survey in Egypt using sun’s angle of elevation in Alexandria and Syene (now Aswan) in order to calculate Earth circumferences. As a result of that survey he calculated the Earth circumferences about 46.000 km Moreover he also make the map of known World, c. 194 BC. 3rd FIG Young Surveyors European Meeting 2 150 : Ptolemy (AD 90-168) argued that the earth was the center of the universe. -
Appendix a Glossary
BASICS OF RADIO ASTRONOMY Appendix A Glossary Absolute magnitude Apparent magnitude a star would have at a distance of 10 parsecs (32.6 LY). Absorption lines Dark lines superimposed on a continuous electromagnetic spectrum due to absorption of certain frequencies by the medium through which the radiation has passed. AM Amplitude modulation. Imposing a signal on transmitted energy by varying the intensity of the wave. Amplitude The maximum variation in strength of an electromagnetic wave in one wavelength. Ångstrom Unit of length equal to 10-10 m. Sometimes used to measure wavelengths of visible light. Now largely superseded by the nanometer (10-9 m). Aphelion The point in a body’s orbit (Earth’s, for example) around the sun where the orbiting body is farthest from the sun. Apogee The point in a body’s orbit (the moon’s, for example) around Earth where the orbiting body is farthest from Earth. Apparent magnitude Measure of the observed brightness received from a source. Astrometry Technique of precisely measuring any wobble in a star’s position that might be caused by planets orbiting the star and thus exerting a slight gravitational tug on it. Astronomical horizon The hypothetical interface between Earth and sky, as would be seen by the observer if the surrounding terrain were perfectly flat. Astronomical unit Mean Earth-to-sun distance, approximately 150,000,000 km. Atmospheric window Property of Earth’s atmosphere that allows only certain wave- lengths of electromagnetic energy to pass through, absorbing all other wavelengths. AU Abbreviation for astronomical unit. Azimuth In the horizon coordinate system, the horizontal angle from some arbitrary reference direction (north, usually) clockwise to the object circle. -
This Restless Globe
www.astrosociety.org/uitc No. 45 - Winter 1999 © 1999, Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, CA 94112. This Restless Globe A Look at the Motions of the Earth in Space and How They Are Changing by Donald V. Etz The Major Motions of the Earth How These Motions Are Changing The Orientation of the Earth in Space The Earth's Orbit Precession in Human History The Motions of the Earth and the Climate Conclusion Our restless globe and its companion. While heading out for The Greek philosopher Heraclitus of Ephesus, said 2500 years ago that the its rendezvous with Jupiter, a camera on NASA's Galileo perceptible world is always changing. spacecraft snapped this 1992 image of Earth and its Moon. The Heraclitus was not mainstream, of course. Among his contemporaries were terminator, or line between night and day, is clearly visible on the philosophers like Zeno of Elea, who used his famous paradoxes to argue that two worlds. Image courtesy of change and motion are logically impossible. And Aristotle, much admired in NASA. ancient Greece and Rome, and the ultimate authority in medieval Europe, declared "...the earth does not move..." We today know that Heraclitus was right, Aristotle was wrong, and Zeno...was a philosopher. Everything in the heavens moves, from the Earth on which we ride to the stars in the most distant galaxies. As James B. Kaler has pointed out in The Ever-Changing Sky: "The astronomer quickly learns that nothing is truly stationary. There are no fixed reference frames..." The Earth's motions in space establish our basic units of time measurement and the yearly cycle of the seasons.