DOCSLIB.ORG

Guidance Note 7 Part 2

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Guidance Note 7 Part 2 IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – September 2019 To facilitate improvement, this document is subject to revision. The current version is available at www.epsg.org. Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas Revised - September 2019 Page 1 of 162 IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – September 2019 To facilitate improvement, this document is subject to revision. The current version is available at www.epsg.org. Table of Contents Preface ............................................................................................................................................................5 1 IMPLEMENTATION NOTES ................................................................................................................. 6 1.1 ELLIPSOID PARAMETERS ......................................................................................................................... 6 1.2 ARCTANGENT FUNCTION ......................................................................................................................... 6 1.3 ANGULAR UNITS ....................................................................................................................................... 7 1.4 LONGITUDE 'WRAP-AROUND' .................................................................................................................. 7 1.5 OFFSETS .................................................................................................................................................... 7 1.6 COORDINATE TRANSFORMATION DIRECTION ........................................................................................ 7 2 COORDINATE CONVERSIONS AND TRANSFORMATIONS - INTRODUCTION ..................... 8 2.1 BASIC CONCEPTS ...................................................................................................................................... 8 2.2 MAP PROJECTION METHODS ................................................................................................................... 9 2.3 MAP PROJECTION PARAMETERS .......................................................................................................... 10 3 MAP PROJECTION FORMULAS ........................................................................................................ 17 3.1 CONIC MAP PROJECTIONS .................................................................................................................... 17 3.1.1 LAMBERT CONIC CONFORMAL ............................................................................................................. 17 3.1.1.1 Lambert Conic Conformal (2SP)....................................................................................................... 19 3.1.1.2 Lambert Conic Conformal (1SP)....................................................................................................... 20 3.1.1.3 Lambert Conic Conformal (1SP West Orientated)............................................................................ 21 3.1.1.4 Lambert Conic Conformal (2SP Belgium) ........................................................................................ 22 3.1.1.5 Lambert Conic Conformal (2SP Michigan) ...................................................................................... 23 3.1.1.6 Lambert Conic Near-Conformal........................................................................................................ 24 3.1.2 KROVAK ............................................................................................................................................... 26 3.1.2.1 Krovak ............................................................................................................................................... 27 3.1.2.2 Krovak (North Orientated) ................................................................................................................ 30 3.1.2.3 Krovak Modified ............................................................................................................................... 31 3.1.2.4 Krovak Modified (North Orientated) ................................................................................................ 33 3.1.3 ALBERS EQUAL AREA .......................................................................................................................... 34 3.1.4 BONNE .................................................................................................................................................. 35 3.1.4.1 Bonne (South Orientated) .................................................................................................................. 36 3.1.5 AMERICAN POLYCONIC ........................................................................................................................ 36 3.2 CYLINDRICAL MAP PROJECTIONS ........................................................................................................ 37 3.2.1 MERCATOR ........................................................................................................................................... 37 3.2.1.1 Mercator (Spherical) .......................................................................................................................... 43 3.2.1.2 Popular Visualisation Pseudo-Mercator ("Web Mercator") .............................................................. 44 3.2.2 CASSINI-SOLDNER ................................................................................................................................ 45 3.2.2.1 Hyperbolic Cassini-Soldner .............................................................................................................. 47 3.2.3 TRANSVERSE MERCATOR ..................................................................................................................... 49 3.2.3.1 General Case...................................................................................................................................... 49 3.2.3.2 Transverse Mercator Zoned Grid System .......................................................................................... 56 3.2.3.3 Transverse Mercator (South Orientated) ........................................................................................... 57 3.2.4 OBLIQUE MERCATOR ........................................................................................................................... 59 3.2.4.1 Hotine Oblique Mercator ................................................................................................................... 60 3.2.4.2 Laborde Oblique Mercator ................................................................................................................ 64 Page 2 of 162 IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – September 2019 To facilitate improvement, this document is subject to revision. The current version is available at www.epsg.org. 3.2.5 EQUIDISTANT CYLINDRICAL ................................................................................................................ 66 3.2.5.1 Equidistant Cylindrical (Spherical) ................................................................................................... 68 3.2.5.2 Pseudo Plate Carrée ........................................................................................................................... 69 3.2.6 LAMBERT CYLINDRICAL EQUAL AREA ................................................................................................ 69 3.2.6.1 Lambert Cylindrical Equal Area (Spherical) ..................................................................................... 69 3.3 AZIMUTHAL MAP PROJECTIONS........................................................................................................... 70 3.3.1 STEREOGRAPHIC ................................................................................................................................... 70 3.3.1.1 Oblique and Equatorial Stereographic ............................................................................................... 70 3.3.1.2 Polar Stereographic ........................................................................................................................... 73 3.3.2 LAMBERT AZIMUTHAL EQUAL AREA ................................................................................................... 78 3.3.2.1 Lambert Azimuthal Equal Area (Spherical) ...................................................................................... 80 3.3.3 AZIMUTHAL EQUIDISTANT ................................................................................................................... 81 3.3.3.1 Modified Azimuthal Equidistant ....................................................................................................... 81 3.3.3.2 Guam Projection ................................................................................................................................ 82 3.3.4 PERSPECTIVES ...................................................................................................................................... 84 3.3.4.1 Intoduction ........................................................................................................................................ 84 3.3.4.2 Vertical Perspective ........................................................................................................................... 85 3.3.4.3 Vertical Perspective
Load more

Recommended publications
  • Map Projections--A Working Manual
    This is a reproduction of a library book that was digitized by Google as part of an ongoing effort to preserve the information in books and make it universally accessible. https://books.google.com 7 I- , t 7 < ?1 > I Map Projections — A Working Manual By JOHN P. SNYDER U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1395 _ i UNITED STATES GOVERNMENT PRINTING OFFIGE, WASHINGTON: 1987 no U.S. DEPARTMENT OF THE INTERIOR BRUCE BABBITT, Secretary U.S. GEOLOGICAL SURVEY Gordon P. Eaton, Director First printing 1987 Second printing 1989 Third printing 1994 Library of Congress Cataloging in Publication Data Snyder, John Parr, 1926— Map projections — a working manual. (U.S. Geological Survey professional paper ; 1395) Bibliography: p. Supt. of Docs. No.: I 19.16:1395 1. Map-projection — Handbooks, manuals, etc. I. Title. II. Series: Geological Survey professional paper : 1395. GA110.S577 1987 526.8 87-600250 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, DC 20402 PREFACE This publication is a major revision of USGS Bulletin 1532, which is titled Map Projections Used by the U.S. Geological Survey. Although several portions are essentially unchanged except for corrections and clarification, there is consider able revision in the early general discussion, and the scope of the book, originally limited to map projections used by the U.S. Geological Survey, now extends to include several other popular or useful projections. These and dozens of other projections are described with less detail in the forthcoming USGS publication An Album of Map Projections. As before, this study of map projections is intended to be useful to both the reader interested in the philosophy or history of the projections and the reader desiring the mathematics.
    [Show full text]
  • 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]
  • Implications for the Adoption of Global Reference Geodesic System SIRGAS2000 on the Large Scale Cadastral Cartography in Brazil
    Implications for the Adoption of Global Reference Geodesic System SIRGAS2000 on the Large Scale Cadastral Cartography in Brazil Vivian de Oliveira FERNANDES and Ruth Emilia NOGUEIRA, Brazil Key words: SIRGAS2000, SAD69, Global Geodesic System SUMMARY Since 2005 Brazil is going through a singular moment into Cartography. In January 2005, SIRGAS2000 began to be the geodetic official reference system for Geodesy and Cartography, with the concomitant use of SAD69. Since January 2015, only SIRGAS2000 will be official, and all cartographical products will have to be referenced into this Datum. The adoption of a geocentric reference system happens from the technological evolution that has favored an improvement of the Geodetic Reference System – SGR. Differently of a single alternative for the improvement of the SGR, the adoption of a new geocentric reference system is a basic necessity into the world-wide scenery to activities that depend on spatialized information. The technological advancements in the global positioning methods, specially in the satellite positioning systems. This change reaches more quickly the organs that need spatialized information in their infrastructure and planning activities, like town halls and services concessionaires like Telecommunications, Sanitation, Electric Energy among others, which need the real knowledge of the urban space: use and occupation of the soil, subsoil and air space, fiscal and housing technical register, generic plant of values, block plant, register reference plant, municipal master plan, among others that are derived from a cartographical basis of quality. Officially, were adopted these geodetic reference systems in Brazil: Córrego Alegre, Astro Datum Chuá, SAD69, and now SIRGAS2000. For legislation it is in transition for the SIRGAS2000.
    [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]
  • Ts 144 031 V12.3.0 (2015-07)
    ETSI TS 1144 031 V12.3.0 (201515-07) TECHNICAL SPECIFICATION Digital cellular telecocommunications system (Phahase 2+); Locatcation Services (LCS); Mobile Station (MS) - SeServing Mobile Location Centntre (SMLC) Radio Resosource LCS Protocol (RRLP) (3GPP TS 44.0.031 version 12.3.0 Release 12) R GLOBAL SYSTTEM FOR MOBILE COMMUNUNICATIONS 3GPP TS 44.031 version 12.3.0 Release 12 1 ETSI TS 144 031 V12.3.0 (2015-07) Reference RTS/TSGG-0244031vc30 Keywords GSM ETSI 650 Route des Lucioles F-06921 Sophia Antipolis Cedex - FRANCE Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16 Siret N° 348 623 562 00017 - NAF 742 C Association à but non lucratif enregistrée à la Sous-Préfecture de Grasse (06) N° 7803/88 Important notice The present document can be downloaded from: http://www.etsi.org/standards-search The present document may be made available in electronic versions and/or in print. The content of any electronic and/or print versions of the present document shall not be modified without the prior written authorization of ETSI. In case of any existing or perceived difference in contents between such versions and/or in print, the only prevailing document is the print of the Portable Document Format (PDF) version kept on a specific network drive within ETSI Secretariat. Users of the present document should be aware that the document may be subject to revision or change of status. Information on the current status of this and other ETSI documents is available at http://portal.etsi.org/tb/status/status.asp If you find errors in the present document, please send your comment to one of the following services: https://portal.etsi.org/People/CommiteeSupportStaff.aspx Copyright Notification No part may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm except as authorized by written permission of ETSI.
    [Show full text]
  • Arxiv:1811.01571V2 [Cs.CV] 24 Jan 2019 Many Traditional Cnns on 3D Data Simply Extend the 2D Convolutional Op- Erations to 3D, for Example, the Work of Wu Et Al
    SPNet: Deep 3D Object Classification and Retrieval using Stereographic Projection Mohsen Yavartanoo1[0000−0002−0109−1202], Eu Young Kim1[0000−0003−0528−6557], and Kyoung Mu Lee1[0000−0001−7210−1036] Department of ECE, ASRI, Seoul National University, Seoul, Korea https://cv.snu.ac.kr/ fmyavartanoo, shreka116, [email protected] Abstract. We propose an efficient Stereographic Projection Neural Net- work (SPNet) for learning representations of 3D objects. We first trans- form a 3D input volume into a 2D planar image using stereographic projection. We then present a shallow 2D convolutional neural network (CNN) to estimate the object category followed by view ensemble, which combines the responses from multiple views of the object to further en- hance the predictions. Specifically, the proposed approach consists of four stages: (1) Stereographic projection of a 3D object, (2) view-specific fea- ture learning, (3) view selection and (4) view ensemble. The proposed ap- proach performs comparably to the state-of-the-art methods while having substantially lower GPU memory as well as network parameters. Despite its lightness, the experiments on 3D object classification and shape re- trievals demonstrate the high performance of the proposed method. Keywords: 3D object classification · 3D object retrieval · Stereographic Projection · Convolutional Neural Network · View Ensemble · View Se- lection. 1 Introduction In recent years, success of deep learning methods, in particular, convolutional neural network (CNN), has urged rapid development in various computer vision applications such as image classification, object detection, and super-resolution. Along with the drastic advances in 2D computer vision, understanding 3D shapes and environment have also attracted great attention.
    [Show full text]
  • Unusual Map Projections Tobler 1999
    Unusual Map Projections Waldo Tobler Professor Emeritus Geography department University of California Santa Barbara, CA 93106-4060 http://www.geog.ucsb.edu/~tobler 1 Based on an invited presentation at the 1999 meeting of the Association of American Geographers in Hawaii. Copyright Waldo Tobler 2000 2 Subjects To Be Covered Partial List The earth’s surface Area cartograms Mercator’s projection Combined projections The earth on a globe Azimuthal enlargements Satellite tracking Special projections Mapping distances And some new ones 3 The Mapping Process Common Surfaces Used in cartography 4 The surface of the earth is two dimensional, which is why only (but also both) latitude and longitude are needed to pin down a location. Many authors refer to it as three dimensional. This is incorrect. All map projections preserve the two dimensionality of the surface. The Byte magazine cover from May 1979 shows how the graticule rides up and down over hill and dale. Yes, it is embedded in three dimensions, but the surface is a curved, closed, and bumpy, two dimensional surface. Map projections convert this to a flat two dimensional surface. 5 The Surface of the Earth Is Two-Dimensional 6 The easy way to demonstrate that Mercator’s projection cannot be obtained as a perspective transformation is to draw lines from the latitudes on the projection to their occurrence on a sphere, here represented by an adjoining circle. The rays will not intersect in a point. 7 Mercator’s Projection Is Not Perspective 8 It is sometimes asserted that one disadvantage of a globe is that one cannot see all of the entire earth at one time.
    [Show full text]
  • Development of 3D Datum Transformation Model Between Wgs 84 and Clarke 1880 for Cross Rivers State, Nigeria
    British Journal of Environmental Sciences Vol.7, No.2, pp. 70-86, May 2019 Published by European Centre for Research Training and Development UK (www.eajournals.org) DEVELOPMENT OF 3D DATUM TRANSFORMATION MODEL BETWEEN WGS 84 AND CLARKE 1880 FOR CROSS RIVERS STATE, NIGERIA Aniekan Eyoh1, Onuwa Okwuashi 2 and Akwaowo Ekpa3 Department of Geoinformatics & Surveying, Faculty of Environmental Studies, University of Uyo, Nigeria 1, 2 & 3 ABSTRACT: The need to have unified 3D datum transformation parameters for Nigeria for converting coordinates from Minna to WGS84 datum and vice-versa in order to overcome the ambiguity, inconsistency and non-conformity of existing traditional reference frames within national and international mapping system is long overdue. This study therefore develops the optimal transformation parameters between Clarke 1880 and WGS84 datums and vice-versa for Cross River State in Nigeria using the Molodensky-Badekas model. One hundred (100) first order 3D geodetic controls common in the Clarke 1880 and WGS84 datums were used for the study. Least squares solutions of the model was solved using MATLAB programming software. The datum shift parameters derived in the study were ΔX=99.388653795075243m ± 2.453509278, ΔY = 15.027733957346365m ± 2.450564809, ΔZ = -60.390012806020579m ± 2.450556881,α=-0.000000601338389±0.000004394,β=0.000021566705811 ± 0.00004133728, γ = 0.000034795781381 ± 0.00007348844, S(ppm) = 0.9999325233 ± 0.00003047930445. The results of the computation showed roughly good estimates of the datum shift parameters (dX, dY, dZ, K, RX , RY , RZ, K ) and standard deviation of the parameters. The computed residuals of the XYZ parameters were relatively good. The result of the test computation of the shift parameters using the entire 107 points were however not significantly different from those obtained with the 100 points, as the results showed good agreement between them.
    [Show full text]
  • Map Projections Paper 4 (Th.) UNIT : I ; TOPIC : 3 …Introduction
    FOR SEMESTER 3 GE Students , Geography Map Projections Paper 4 (Th.) UNIT : I ; TOPIC : 3 …Introduction Prepared and Compiled By Dr. Rajashree Dasgupta Assistant Professor Dept. of Geography Government Girls’ General Degree College 3/23/2020 1 Map Projections … The method by which we transform the earth’s spheroid (real world) to a flat surface (abstraction), either on paper or digitally Define the spatial relationship between locations on earth and their relative locations on a flat map Think about projecting a see- through globe onto a wall Dept. of Geography, GGGDC, 3/23/2020 Kolkata 2 Spatial Reference = Datum + Projection + Coordinate system Two basic locational systems: geometric or Cartesian (x, y, z) and geographic or gravitational (f, l, z) Mean sea level surface or geoid is approximated by an ellipsoid to define an earth datum which gives (f, l) and distance above geoid gives (z) 3/23/2020 Dept. of Geography, GGGDC, Kolkata 3 3/23/2020 Dept. of Geography, GGGDC, Kolkata 4 Classifications of Map Projections Criteria Parameter Classes/ Subclasses Extrinsic Datum Direct / Double/ Spherical Triple Surface Spheroidal Plane or Ist Order 2nd Order 3rd Order surface of I. Planar a. Tangent i. Normal projection II. Conical b. Secant ii. Transverse III. Cylindric c. Polysuperficial iii. Oblique al Method of Perspective Semi-perspective Non- Convention Projection perspective al Intrinsic Properties Azimuthal Equidistant Othomorphic Homologra phic Appearance Both parallels and meridians straight of parallels Parallels straight, meridians curve and Parallels curves, meridians straight meridians Both parallels and meridians curves Parallels concentric circles , meridians radiating st. lines Parallels concentric circles, meridians curves Geometric Rectangular Circular Elliptical Parabolic Shape 3/23/2020 Dept.
    [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]
  • 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]