DOCSLIB.ORG

Satellite Altimetry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Satellite Altimetry Introduction to Geodesy Alexander Braun Byrd Polar Research Center and Laboratory of Space Geodesy and Remote Sensing The Ohio State University, Columbus, OH, USA [email protected] Undergraduate course Dept. of Geomatics Engineering, University of Calgary << >> What is Geodesy? Geodesy (greek) - divide the Earth ) F.R. Helmert (1880) - \The science of measuring the size and shape ) of the Earth and of mapping of the Earth" Torge (1975) - added gravity and reference frame \Geodesy aims at ) determining the size and shape of the Earth globally as well as its intrinsic gravity field, also generated by other celestial bodies, and the International Reference Ellipsoid as global reference frame, all as function of time." << >> What is Geodesy? Determination of the size and shape of the Earth ) by measuring distance and angle >> coordinates ! Time dependency of distance and angle >> dynamics, reference ) frame caused by Earth rotation, polar motion, plate motions, geodynamics, ! tides Gravity field >> determines the geometry and drives the dynamical ) processes Earth mass distribution, external bodies, Earth and ocean tides, ! atmospheric mass variations GEOMETRY - DYNAMICS - GRAVITY OF THE EARTH << >> What are the objectives? Provide fundamental parameters for life on Earth and in space ) Figure of the Earth ) Gravity field ) Variations in time ) Provide reference frame and coordinates ) Provide map projections, coordinate transformations, and reference ) systems << >> What are the tools? Theodolite, levelling, compass, laser levels ) GPS - global positioning, clock ) Gravity field - gravimetry, airborne, terrestrial, space-borne ) Reference frame, coordinates, projections - mathematical description ) of the size and shape, or measurements, or analytical relationships sensors - GPS, altimetry, laser ranging, VLBI, DORIS, SAR ) << >> Who is using geodesy? engineering - navigation, transportation, GPS, civil engineering, ) monitoring of deformations, cadastral information, GIS geophysics and geology - mineral exploration, crustal and earthquake ) deformation, plate tectonics oceanography - sea level change, tides, ship routing, hydrography ) physics - linear collider, Synchrotron Radiation Facilities, no-gravity ) experiments \Geodetic sciences" uses geodesy for solving scientific problems \Geomatics engineering" uses geodesy for solving engineering problems. << >> Course title: Introduction to Geodesy ) Lectures: 3 times per week, 1 hour each, total: 39 hours ) Laboratory: 1 per week, 2-3 hours, total: 26-39 hours ) Pre-requisites ) AMAT217: Calculus for engineers and scientists ! ENGG233,ENGG335: Computing I + II ! AMAT309: Vector calculus ! High-school physics ! << >> Grading ) Final exam: 40% Labs: 30% Quiz: 20% Presentation: 10% Literature ) W. Torge, Geodesy, 2001, Paperback 416 pp, Walter de Gruyter, ISBN: 3110170728 Heiskanen, W.A. and H. Moritz, 1967: Physical Geodesy, W.H. Freeman, San Francisco, 364 pp J. A. Elithorp Jr and D. D. Findorff, Geodesy for Geomatics and Geographic Information System Professionals, paperback: 259 pages, ISBN: 1-59399-087-1 << >> Section Title lecture hours 1 What is geodesy? 1 2 Trigonometry and coordinate systems 4 3 Reference system and reference frame 4 4 Coordinate transformations and vertical datum 3 5 Gravity field 5 6 Geodynamics 3 7 Satellite geodesy 2 8 Gravity missions 2 9 Altimetry and SAR 2 10 VLBI, GPS, and satellite laser ranging 3 11 Basic applications in engineering 3 12 Course summary 1 13 Lectures used for quiz preparation/ repetition and student presentations 6 << >> Labs # Title 1 Trigonometry, coordinate systems, reference frame, transformations 2 Gravity field and geodynamics 3 Satellite geodesy and sensors 4 Selected geodetic problems << >> Quiz and Final Exam # Title 1 Quiz after lecture section 4 including Trigonometry, coordinate systems, reference frame, transformations 2 Final exam including entire course and lab material << >> Outline of the course 1-1 lecture: What is geodesy? ) History of Geodesy, famous geodesists, geodesy as a link between natural sciences and engineering. 2-4 Trigonometry and coordinate systems ) space-fixed, Earth fixed, non-geocentric, celestial, geocentric, topo- centric coordinate systems spherical and ellipsoidal coordinates 3-4 Reference system and reference frame ) IERS, celestial and terrestrial reference frame, WGS84, GRS80, height systems, geopotential numbers, orthometric heights, normal heights, spheroid, ellipsoid, rotational ellipsoid, geoid, vertical deflections << >> 4-3 Coordinate transformations and vertical datum ) dynamic height, orthometric and ellipsoidal height, map projections 5-5 Gravity field ) Newton, geopotential, centrifugal forces, Laplace and Poisson equation, spherical harmonic expansions, normal gravity, Brun's formula, gravity anomalies, Vening-Meinesz transformation, gravimetry, gradiometry, abs. and relative gravimetry, networks, Bouger gravity, isostasy, temporal gravity variations 6-3 Geodynamics ) motion in a celestial systems, motion in a terrestrial system, Earth rotation, precession and nutation, Earth deformations, Earth tides and ocean tides, tidal loading, plate tectonics, Earthquakes, driving forces of geodynamic processes, pole tides, length of day variations 7-2 Satellite geodesy ) << >> Satellite mission concept, orbit determination, sensor technology, what can we measure better from space and what not? 8-2 Gravity missions ) satellite orbitography, measuring gravity from space (distance, velocity and acceleration methods), CHAMP, GRACE, GOCE, current gravity field models, accuracy, resolution 9-2 Altimetry and SAR ) principles of altimetry, applications, SAR radar imagery, SAR interferometry, Digital elevation models, JASON-1, ENVISAT, ICESat, CryoSat, ALOS, RADARSAT-2 10-3 VLBI, GPS and satellite laser ranging ) radio-sources, Quasars, VLBI stations and principle of long- baseline interferometry, basics of GPS constellation and positioning, principles of DORIS and station distribution, satellite laser ranging, station coordinates and velocities, ITRF << >> 11-3 Applications of geodesy in engineering ) positioning, navigation, transportation, deformation monitoring, hydrography 12-1 Course summary ) 13-6 Lectures used for quiz preparation/repetition and student ) presentations << >> Example lecture: Satellite Altimetry << >> What is an altimeter? altus (latin) - height metron (greek) - to measure An altimeter is an instrument to measure height, altitude or elevation. Altimeters are based on two physical principles: Barometric altimeter - pressure difference ) Range altimeter using the distance-velocity-travel time relation ) << >> A barometric altimeter is a pressure sensor to detect the barometric pressure at instrument altitude. The difference of the barometric pressure and the pressure at sea level can be converted into the altitude. altitude = 1000 (SLP BP )) (1) ∗ − e:g: altitude = 1000 (30 in=Hg 28 in=Hg) = 2000 feet (2) ∗ − or in SI units - meters and Pascal: altitude(m) = 0:09 (m=P a) (SLP (P a) BP (P a)) (3) ∗ − << >> The range altimeter based on a distance-velocity-travel time relation is measuring the two-way travel time of a signal with a known velocity. The distance or the \range" can be derived: velocity TWT distance = ∗ (4) 2 << >> Where do we need to measure a distance? Autofocus in cameras - infrared light (10000 GHz) ) Navigation and positioning - GPS (1.575 Ghz, 1.227 GHz) ) Traffic control, speeding tickets - radar (1 MHz - 3 GHz) ) Aviation - barometric, GPS ) Engineering and construction - GPS, laser (400-800 nm) ) << >> Electromagnetic waves travel with the speed of light: v = 3 108 m/s ∗ << >> Satellite altimetry << >> Orbit determination Once we know the travel time and the velocity, we can derive the distance between satellite and Earth surface. To derive the topography, we need to know the position of the satellite at the time of the measurement, the orbit. Satellite Laser Ranging - SLR ) DORIS, PRARE ) GPS ) << >> SLR and DORIS network >>> Jason - Instruments movie << >> What changes the satellite orbit? Earth gravity field ) Third-body gravitational attraction from the Sun, Moon, other ) planets Atmospheric drag ) Direct solar radiation pressure ) Albedo radiation reflected from the Earth's surface ) >>> Orbit and gravity movie << >> << >> Mission Operational accuracy cycle/d altitude/km Skylab 1973 9 month 100 m 435 GEOS-3 1975-1978 1-2 m 30 days 840 SEASAT 1978 3 month 10 cm 762 GEOSAT 1986-90 5 cm 800 Topex/Poseidon 1992 - present < 5 cm 9.9 1337 ERS-1 1991 - 2000 5 cm 35, 163 780 ERS-2 1995 - 2003 5 cm 35 780 GFO-1 1998 - present 5 cm 800 Jason-1 Dec 2001 - pres. < 5 cm 9.9 1337 ENVISAT Mar 2002 - pres. < 5 cm 35 796 <<Cryosat Sep 2004 369 720 >> Laser altimetry missions MGS Mars 1996-2000 2-30 m 378 ICESat Earth Jan 2003 - present < 10 cm 8, 91 600 SELENE Moon Sep 2004 5 m 100 km << >> Altimetry data coverage Depending on the orbit characteristics, the satellite is flying in different patterns. Projected onto the Earth's surface, the flight lines are called tracks. Compromise of temporal and spatial resolution << >> Radar or Laser? Radar altimetry Laser altimetry - footprint 2-20 km - footprint 40-70 meters - vertical accuracy < 5cm - vertical accuracy < 10cm - weather independent - weather dependent, clouds - robust - energy consuming, not robust - long history, 18 years - short missions only - operates on most altimetry - operates on ICESat, MGS and missions - works over water and SELENE - works over water, ice ice and land << >> Applications Satellite altimetry has applications
Load more

Recommended publications
  • UCGE Reports Ionosphere Weighted Global Positioning System Carrier
    UCGE Reports Number 20155 Ionosphere Weighted Global Positioning System Carrier Phase Ambiguity Resolution (URL: http://www.geomatics.ucalgary.ca/links/GradTheses.html) Department of Geomatics Engineering By George Chia Liu December 2001 Calgary, Alberta, Canada THE UNIVERSITY OF CALGARY IONOSPHERE WEIGHTED GLOBAL POSITIONING SYSTEM CARRIER PHASE AMBIGUITY RESOLUTION by GEORGE CHIA LIU A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA OCTOBER, 2001 c GEORGE CHIA LIU 2001 Abstract Integer Ambiguity constraint is essential in precise GPS positioning. The perfor- mance and reliability of the ambiguity resolution process are being hampered by the current culmination (Y2000) of the eleven-year solar cycle. The traditional approach to mitigate the high ionospheric effect has been either to reduce the inter-station separation or to form ionosphere-free observables. Neither is satisfactory: the first restricts the operating range, and the second no longer possesses the ”integerness” of the ambiguities. A third generalized approach is introduced herein, whereby the zero ionosphere weight constraint, or pseudo-observables, with an appropriate weight is added to the Kalman Filter algorithm. The weight can be tightly fixed yielding the model equivalence of an independent L1/L2 dual-band model. At the other extreme, an infinite floated weight gives the equivalence of an ionosphere-free model, yet perserves the ambiguity integerness. A stochastically tuned, or weighted, model provides a compromise between the two ex- tremes. The reliability of ambiguity estimates relies on many factors, including an accurate functional model, a realistic stochastic model, and a subsequent efficient integer search algorithm.
    [Show full text]
  • Geodesy in the 21St Century
    Eos, Vol. 90, No. 18, 5 May 2009 VOLUME 90 NUMBER 18 5 MAY 2009 EOS, TRANSACTIONS, AMERICAN GEOPHYSICAL UNION PAGES 153–164 geophysical discoveries, the basic under- Geodesy in the 21st Century standing of earthquake mechanics known as the “elastic rebound theory” [Reid, 1910], PAGES 153–155 Geodesy and the Space Era was established by analyzing geodetic mea- surements before and after the 1906 San From flat Earth, to round Earth, to a rough Geodesy, like many scientific fields, is Francisco earthquakes. and oblate Earth, people’s understanding of technology driven. Over the centuries, it In 1957, the Soviet Union launched the the shape of our planet and its landscapes has developed as an engineering discipline artificial satellite Sputnik, ushering the world has changed dramatically over the course because of its practical applications. By the into the space era. During the first 5 decades of history. These advances in geodesy— early 1900s, scientists and cartographers of the space era, space geodetic technolo- the study of Earth’s size, shape, orientation, began to use triangulation and leveling mea- gies developed rapidly. The idea behind and gravitational field, and the variations surements to record surface deformation space geodetic measurements is simple: Dis- of these quantities over time—developed associated with earthquakes and volcanoes. tance or phase measurements conducted because of humans’ curiosity about the For example, one of the most important between Earth’s surface and objects in Earth and because of geodesy’s application to navigation, surveying, and mapping, all of which were very practical areas that ben- efited society.
    [Show full text]
  • Solar Radiation Pressure Models for Beidou-3 I2-S Satellite: Comparison and Augmentation
    remote sensing Article Solar Radiation Pressure Models for BeiDou-3 I2-S Satellite: Comparison and Augmentation Chen Wang 1, Jing Guo 1,2 ID , Qile Zhao 1,3,* and Jingnan Liu 1,3 1 GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China; [email protected] (C.W.); [email protected] (J.G.); [email protected] (J.L.) 2 School of Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, UK 3 Collaborative Innovation Center of Geospatial Technology, Wuhan University, 129 Luoyu Road, Wuhan 430079, China * Correspondence: [email protected]; Tel.: +86-027-6877-7227 Received: 22 December 2017; Accepted: 15 January 2018; Published: 16 January 2018 Abstract: As one of the most essential modeling aspects for precise orbit determination, solar radiation pressure (SRP) is the largest non-gravitational force acting on a navigation satellite. This study focuses on SRP modeling of the BeiDou-3 experimental satellite I2-S (PRN C32), for which an obvious modeling deficiency that is related to SRP was formerly identified. The satellite laser ranging (SLR) validation demonstrated that the orbit of BeiDou-3 I2-S determined with empirical 5-parameter Extended CODE (Center for Orbit Determination in Europe) Orbit Model (ECOM1) has the sun elongation angle (# angle) dependent systematic error, as well as a bias of approximately −16.9 cm. Similar performance has been identified for European Galileo and Japanese QZSS Michibiki satellite as well, and can be reduced with the extended ECOM model (ECOM2), or by using the a priori SRP model to augment ECOM1. In this study, the performances of the widely used SRP models for GNSS (Global Navigation Satellite System) satellites, i.e., ECOM1, ECOM2, and adjustable box-wing model have been compared and analyzed for BeiDou-3 I2-S satellite.
    [Show full text]
  • Geomatics Guidance Note 3
    Geomatics Guidance Note 3 Contract area description Revision history Version Date Amendments 5.1 December 2014 Revised to improve clarity. Heading changed to ‘Geomatics’. 4 April 2006 References to EPSG updated. 3 April 2002 Revised to conform to ISO19111 terminology. 2 November 1997 1 November 1995 First issued. 1. Introduction Contract Areas and Licence Block Boundaries have often been inadequately described by both licensing authorities and licence operators. Overlaps of and unlicensed slivers between adjacent licences may then occur. This has caused problems between operators and between licence authorities and operators at both the acquisition and the development phases of projects. This Guidance Note sets out a procedure for describing boundaries which, if followed for new contract areas world-wide, will alleviate the problems. This Guidance Note is intended to be useful to three specific groups: 1. Exploration managers and lawyers in hydrocarbon exploration companies who negotiate for licence acreage but who may have limited geodetic awareness 2. Geomatics professionals in hydrocarbon exploration and development companies, for whom the guidelines may serve as a useful summary of accepted best practice 3. Licensing authorities. The guidance is intended to apply to both onshore and offshore areas. This Guidance Note does not attempt to cover every aspect of licence boundary definition. In the interests of producing a concise document that may be as easily understood by the layman as well as the specialist, definitions which are adequate for most licences have been covered. Complex licence boundaries especially those following river features need specialist advice from both the survey and the legal professions and are beyond the scope of this Guidance Note.
    [Show full text]
  • PRINCIPLES and PRACTICES of GEOMATICS BE 3200 COURSE SYLLABUS Fall 2015
    PRINCIPLES AND PRACTICES OF GEOMATICS BE 3200 COURSE SYLLABUS Fall 2015 Meeting times: Lecture class meets promptly at 10:10-11:00 AM Mon/Wed in438 Brackett Hall and lab meets promptly at 12:30-3:20 PM Wed at designated sites Course Basics Geomatics encompass the disciplines of surveying, mapping, remote sensing, and geographic information systems. It’s a relatively new term used to describe the science and technology of dealing with earth measurement data that includes collection, sorting, management, planning and design, storage, and presentation of the data. In this class, geomatics is defined as being an integrated approach to the measurement, analysis, management, storage, and presentation of the descriptions and locations of spatial data. Goal: Designed as a "first course" in the principles of geomeasurement including leveling for earthwork, linear and area measurements (traversing), mapping, and GPS/GIS. Description: Basic surveying measurements and computations for engineering project control, mapping, and construction layout. Leveling, earthwork, area, and topographic measurements using levels, total stations, and GPS. Application of Mapping via GIS. 2 CT2: This course is a CT seminar in which you will not only study the course material but also develop your critical thinking skills. Prerequisite: MTHSC 106: Calculus of One Variable I. Textbook: Kavanagh, B. F. Surveying: Principles and Applications. Prentice Hall. 2010. Lab Notes: Purchase Lab notes at Campus Copy Shop [REQUIRED]. Materials: Textbook, Lab Notes (must be brought to lab), Field Book, 3H/4H Pencil, Small Scale, and Scientific Calculator. Attendance: Regular and punctual attendance at all classes and field work is the responsibility of each student.
    [Show full text]
  • Reference Systems for Surveying and Mapping Lecture Notes
    Delft University of Technology Reference Systems for Surveying and Mapping Lecture notes Hans van der Marel ii The front cover shows the NAP (Amsterdam Ordnance Datum) ”datum point” at the Stopera, Amsterdam (picture M.M.Minderhoud, Wikipedia/Michiel1972). H. van der Marel Lecture notes on Reference Systems for Surveying and Mapping: CTB3310 Surveying and Mapping CTB3425 Monitoring and Stability of Dikes and Embankments CIE4606 Geodesy and Remote Sensing CIE4614 Land Surveying and Civil Infrastructure February 2020 Publisher: Faculty of Civil Engineering and Geosciences Delft University of Technology P.O. Box 5048 Stevinweg 1 2628 CN Delft The Netherlands Copyright ©2014­2020 by H. van der Marel The content in these lecture notes, except for material credited to third parties, is licensed under a Creative Commons Attributions­NonCommercial­SharedAlike 4.0 International License (CC BY­NC­SA). Third party material is shared under its own license and attribution. The text has been type set using the MikTex 2.9 implementation of LATEX. Graphs and diagrams were produced, if not mentioned otherwise, with Matlab and Inkscape. Preface This reader on reference systems for surveying and mapping has been initially compiled for the course Surveying and Mapping (CTB3310) in the 3rd year of the BSc­program for Civil Engineering. The reader is aimed at students at the end of their BSc program or at the start of their MSc program, and is used in several courses at Delft University of Technology. With the advent of the Global Positioning System (GPS) technology in mobile (smart) phones and other navigational devices almost anyone, anywhere on Earth, and at any time, can determine a three–dimensional position accurate to a few meters.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Coordinate Systems in Geodesy
    COORDINATE SYSTEMS IN GEODESY E. J. KRAKIWSKY D. E. WELLS May 1971 TECHNICALLECTURE NOTES REPORT NO.NO. 21716 COORDINATE SYSTElVIS IN GEODESY E.J. Krakiwsky D.E. \Vells Department of Geodesy and Geomatics Engineering University of New Brunswick P.O. Box 4400 Fredericton, N .B. Canada E3B 5A3 May 1971 Latest Reprinting January 1998 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. TABLE OF CONTENTS page LIST OF ILLUSTRATIONS iv LIST OF TABLES . vi l. INTRODUCTION l 1.1 Poles~ Planes and -~es 4 1.2 Universal and Sidereal Time 6 1.3 Coordinate Systems in Geodesy . 7 2. TERRESTRIAL COORDINATE SYSTEMS 9 2.1 Terrestrial Geocentric Systems • . 9 2.1.1 Polar Motion and Irregular Rotation of the Earth • . • • . • • • • . 10 2.1.2 Average and Instantaneous Terrestrial Systems • 12 2.1. 3 Geodetic Systems • • • • • • • • • • . 1 17 2.2 Relationship between Cartesian and Curvilinear Coordinates • • • • • • • . • • 19 2.2.1 Cartesian and Curvilinear Coordinates of a Point on the Reference Ellipsoid • • • • • 19 2.2.2 The Position Vector in Terms of the Geodetic Latitude • • • • • • • • • • • • • • • • • • • 22 2.2.3 Th~ Position Vector in Terms of the Geocentric and Reduced Latitudes . • • • • • • • • • • • 27 2.2.4 Relationships between Geodetic, Geocentric and Reduced Latitudes • . • • • • • • • • • • 28 2.2.5 The Position Vector of a Point Above the Reference Ellipsoid . • • . • • • • • • . .• 28 2.2.6 Transformation from Average Terrestrial Cartesian to Geodetic Coordinates • 31 2.3 Geodetic Datums 33 2.3.1 Datum Position Parameters .
    [Show full text]
  • Satellite Geodesy: Foundations, Methods and Applications, Second Edition
    Satellite Geodesy: Foundations, Methods and Applications, Second Edition By Günter Seeber, 589 pages, 281 figures, 64 tables, ISBN: 3-11-017549-5, published by Walter de Gruyter GmbH & Co., Berlin, 2003 The first edition of this book came out in 1993, when it made an enormous contribution to the field. It brought together in one volume a vast amount Günter Seeber of information scattered throughout the geodetic literature on satellite mis­ Satellite Geodesy sions, observables, mathematical models and applications. In the inter­ 2nd Edition vening ten years the field has devel­ oped at an astonishing rate, and the new edition has been completely revised to take this into account. Apart from a review of the historical development of the field, the book is divided into three main sections. The first part is a general introduction to the fundamentals of the subject: refer­ ence frames; time systems; signal propagation; Keplerian models of satel­ de Gruyter lite motion; orbit perturbations; orbit determination; orbit types and constel­ lations. The second section, which contributes to the fields of terrestrial comprises the major part of the book, and marine physical and geometrical is a detailed description of the principal geodesy, navigation and geodynamics. techniques falling under the umbrella of satellite geodesy. Those covered The book is written in an accessible are: optical techniques; Doppler posi­ style, particularly given the technical tioning; Global Navigation Satellite nature of the content, and is therefore Systems (GNSS, incorporating GPS, useful to a wide community of readers. GLONASS and GALILEO), Satellite Every topic has extensive and up to Laser Ranging (SLR), satellite altime­ date references allowing for further try, gravity field missions, Very Long investigation where necessary.
    [Show full text]
  • 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.
    [Show full text]
  • Eratosthenes' Map of the Oecumene Re Vie W
    GEODESY AND CARTOGRAPHY ISSN 2029-6991 print / ISSN 2029-7009 online 2012 Volume 38(2): 81–85 doi:10.3846/20296991.2012.695332 REVIEW UDK 528.9 ERATOSTHENES’ MAP OF THE OECUMENE Viktoras Lukoševičius1, Tomas Duksa2 1Technology Faculty, Šiauliai University, Vilniaus g. 141, LT-76353 Šiauliai, Lithuania 2Lithuanian Cartographic Society, M. K. Čiurlionio g. 21/27, LT-03101 Vilnius, Lithuania E-mails: [email protected] (corresponding author); [email protected] Received 26 April 2012; accepted 21 June 2012 Abstract. Eratosthenes (circa 276 B.C.–194 B.C.) is considered a famous scientist of ancient Greece. He was a mathematician and geographer. Born in Cyrene, now Shahhat (Libya), he was appointed to teach the son of the Egyptian King Ptolemy III Euergetes. In 240 B.C., he became the third chief librarian the Great Library of Alexan- dria. Eratosthenes laid basics for mathematical geography. He was the first to calculate precisely in an original way the Earth meridian’s length between Syene and Alexandria. For this purpose he used perpendicular projection of the sun rays during summer solstice (06.22) near the town Syene, now Aswan. His estimation of the length of the Earth’s radius (6300 km) is close to present estimation (6371 km). He calculated that a year possesses 365.25 days. He also emphasized the significance of maps as the most important thing in geography. Eratosthenes was the first one to use the term “geographem” to describe the Earth. In this way he legitimized the term of geography. He also put into system geographical information from various sources in order to obtain a map of the world as precise as possible.
    [Show full text]