DOCSLIB.ORG

Coordinate Systemssystems Coordinatecoordinate Systemssystems –– Keykey Conceptsconcepts

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

CoordinateCoordinate SystemsSystems CoordinateCoordinate SystemsSystems –– keykey conceptsconcepts ►►ProjectionsProjections andand CoordinateCoordinate SystemsSystems ►►DataData QualityQuality ►►MetaMeta DataData ProjectionsProjections andand CoordinateCoordinate Systems:Systems: GeographicGeographic CoordinateCoordinate SystemSystem ►►UsesUses 3D3D sphericalspherical surfacesurface toto definedefine locationslocations ►►OftenOften incorrectlyincorrectly calledcalled aa datumdatum ►►IncludesIncludes angularangular unitunit ofof measure,measure, primeprime meridianmeridian andand datumdatum ►►PointPoint referencedreferenced byby longitude/latitudelongitude/latitude ►►AnglesAngles measuredmeasured byby degreesdegrees ParallelsParallels –– LinesLines ofof LatitudeLatitude Latitude lines are parallel The equator defines the line of zero latitude Every degree of latitude is theoretically equal Parallels run east/west; measure distances north and south of equator MeridiansMeridians –– LinesLines ofof LongitudeLongitude Meridians converge at the poles Line of zero longitude is called the Prime Meridian Distance of 1° longitude decreases toward the poles Meridians run north/south; measure distance east & west of Prime Meridian GraticularGraticular NetworkNetwork Network of Lat/Long called a graticule Origin of graticule (0,0) where Equator and Prime Meridian intersect 4 geographic quadrants based on compass bearings from Origin Degrees,Degrees, Minutes,Minutes, SecondsSeconds (DMS)(DMS) ► PointPoint onon Earth’sEarth’s surfacesurface referencedreferenced byby Lat/LongLat/Long valuesvalues ► Lat/LongLat/Long basedbased onon 360°360° ► EachEach degreedegree hashas 6060 minutesminutes ► EachEach minuteminute hashas 6060 secondsseconds DecimalDecimal DegreesDegrees (DD)(DD) ►►SimilarSimilar toto DMSDMS ►►MinutesMinutes andand secondsseconds expressedexpressed asas decimaldecimal valuesvalues ►►ESRIESRI productsproducts requirerequire DDDD inin geodatasetsgeodatasets ConvertingConverting fromfrom DMSDMS toto DDDD 37°37° 36'36' 30"30" (DMS)(DMS) ►►DivideDivide eacheach valuevalue byby thethe numbernumber ofof minutesminutes oror secondsseconds inin aa degree:degree: 3636 minutesminutes == .60.60 degreesdegrees (36/60)(36/60) 3030 secondsseconds == .00833.00833 degreesdegrees (30/3600)(30/3600) ►► AddAdd upup thethe degreesdegrees toto getget thethe answer:answer: ►►37°37° ++ .60°.60° ++ .00833°.00833° == 37.6083337.60833 DDDD SpheresSpheres andand SpheroidsSpheroids Sphere Spheroid •Shape and size of GCS surface defined by sphere or spheroid. •Mathematical calculations easier on a sphere. •Sphere can be used for small-scale maps (< 1:5,000,000) •Spheroid gives better accuracy for large-scale maps (>1:1,000,000 MajorMajor andand MinorMinor AxesAxes ofof EllipseEllipse Minor Axis Major Axis Semiminor Axis Semimajor Axis Shape of ellipse defined by two radii. Longer radius: Semimajor Axis Shorter radius: Semiminor Axis Rotating spheroid around semiminor axis creates a spheroid SpheroidsSpheroids forfor AccurateAccurate MappingMapping ► EarthEarth hashas beenbeen surveyedsurveyed manymany timestimes ► SurveysSurveys resultresult inin manymany spheroidsspheroids ► SpheroidSpheroid chosenchosen toto fitfit oneone countrycountry ► BestBest fitfit forfor oneone regionsregions notnot samesame forfor anotheranother regionregion ► EarthEarth isis neitherneither perfectperfect spheresphere nornor spheroidspheroid ► ChangingChanging coordinatecoordinate system’ssystem’s spheroidspheroid changeschanges allall previouslypreviously measuredmeasured valuesvalues DatumsDatums ►►SpheroidsSpheroids approximateapproximate earth’searth’s shapeshape ►►DatumDatum definesdefines positionposition ofof spheroidspheroid relativerelative toto centercenter ofof thethe earthearth ►►DatumDatum definesdefines originorigin andand orientationorientation ofof lat/longlat/long lineslines ►►LocalLocal datumdatum alignsaligns spheroidspheroid toto fitfit surfacesurface inin aa particularparticular areaarea DatumDatum ComparisonsComparisons Local geographic Coordinate system Earth-centered geographic Coordinate system Earth’s surface Earth-centered datum Local datum NorthNorth AmericanAmerican DatumsDatums ► NAD27NAD27 –– uses Clarke 1866 spheroid Origin – Meade Ranch Kansas Manually calculated control points ► NAD83NAD83 Based on earth and satellite observations Uses GRS80 spheroid Origin is earth’s center of mass Previous control points shift as much as 500’ ProjectedProjected CoordinateCoordinate SystemsSystems ►►DefinedDefined onon flat,flat, 2D2D surfacesurface ►►HasHas constantconstant lengths,lengths, anglesangles andand areaarea ►►AlwaysAlways basedbased onon geographicgeographic coordinatecoordinate systemsystem ►►X,YX,Y coordinatescoordinates onon gridgrid WhatWhat isis aa MapMap Projection?Projection? ► TransformationTransformation ofof 3D3D surfacesurface toto 2D2D flatflat sheetsheet ► CausesCauses distortiondistortion inin thethe shape,shape, area,area, distancedistance oror directiondirection ofof datadata ► UsesUses mathematicalmathematical formulasformulas toto relaterelate sphericalspherical coordinatescoordinates toto planarplanar coordinatescoordinates ► DifferentDifferent projectionsprojections causecause differentdifferent distortionsdistortions ► MapMap projectionsprojections designeddesigned forfor specificspecific purposepurpose –– i.e.i.e. largelarge--scalescale datadata inin limitedlimited areaarea RelevanceRelevance toto GISGIS ► mapsmaps areare aa commoncommon sourcesource ofof inputinput datadata forfor aa GISGIS 1) often input maps will be in different projections, requiring transformation of one or all maps to make coordinates compatible 2) thus, mathematical functions of projections are needed in a GIS ► oftenoften GISGIS areare usedused forfor projectsprojects ofof globalglobal oror regionalregional scalesscales soso considerationconsideration ofof thethe effecteffect ofof thethe earth'searth's curvaturecurvature isis necessarynecessary ► monitormonitor screensscreens areare analogousanalogous toto aa flatflat sheetsheet ofof paperpaper 1) thus,thus, needneed toto provideprovide transformationstransformations fromfrom thethe curvedcurved surfacesurface toto thethe planeplane forfor displayingdisplaying datadata ConclusionConclusion ►►WhatWhat isis aa coordinatecoordinate system?system? AA coordinatecoordinate systemsystem isis aa gridgrid thatthat maymay bebe usedused toto definedefine wherewhere aa particularparticular locationlocation isis ►►ConnectionConnection betweenbetween projectionprojection andand coordinatecoordinate systemsystem TheThe projectionprojection definesdefines thethe coordinatecoordinate systemsystem byby definingdefining thethe 22--DD surfacesurface ofof thethe earthearth.
Recommended publications

  • AS/NZS ISO 6709:2011 ISO 6709:2008 ISO 6709:2008 Cor.1 (2009) AS/NZS ISO 6709:2011 AS/NZS ISO 6709:2011

    AS/NZS ISO 6709:2011 ISO 6709:2008 ISO 6709:2008 Cor.1 (2009) AS/NZS ISO 6709:2011AS/NZS ISO Australian/New Zealand Standard™ Standard representation of geographic point location by coordinates AS/NZS ISO 6709:2011 This Joint Australian/New Zealand Standard was prepared by Joint Technical Committee IT-004, Geographical Information/Geomatics. It was approved on behalf of the Council of Standards Australia on 15 November 2011 and on behalf of the Council of Standards New Zealand on 14 November 2011. This Standard was published on 23 December 2011. The following are represented on Committee IT-004: ANZLIC—The Spatial Information Council Australasian Fire and Emergency Service Authorities Council Australian Antarctic Division Australian Hydrographic Office Australian Map Circle CSIRO Exploration and Mining Department of Lands, NSW Department of Primary Industries and Water, Tas. Geoscience Australia Land Information New Zealand Mercury Project Solutions Office of Spatial Data Management The University of Melbourne Keeping Standards up-to-date Standards are living documents which reflect progress in science, technology and systems. To maintain their currency, all Standards are periodically reviewed, and new editions are published. Between editions, amendments may be issued. Standards may also be withdrawn. It is important that readers assure themselves they are using a current Standard, which should include any amendments which may have been published since the Standard was purchased. Detailed information about joint Australian/New Zealand Standards can be found by visiting the Standards Web Shop at www.saiglobal.com.au or Standards New Zealand web site at www.standards.co.nz and looking up the relevant Standard in the on-line catalogue.
  • International Standard

    International Standard

    International Standard INTERNATIONAL ORGANIZATION FOR STANDARDIZATlON.ME~YHAPO~HAR OPI-AHH3AWlR fl0 CTAH~APTM3Al&lM.ORGANISATION INTERNATIONALE DE NORMALISATION Standard representation of latitude, longitude and altitude for geographic Point locations Reprksen ta tion normalis6e des latitude, longitude et altitude pbur Ia localisa tion des poin ts gkographiques First edition - 1983-05-15i Teh STANDARD PREVIEW (standards.iteh.ai) ISO 6709:1983 https://standards.iteh.ai/catalog/standards/sist/40603644-5feb-4b20-87de- d0a2bddb21d5/iso-6709-1983 UDC 681.3.04 : 528.28 Ref. No. ISO 67094983 (E) Descriptors : data processing, information interchange, geographic coordinates, representation of data. Price based on 3 pages Foreword ISO (the International Organization for Standardization) is a worldwide federation of national Standards bodies (ISO member bedies). The work of developing International Standards is carried out through ISO technical committees. Every member body interested in a subject for which a technical committee has been authorized has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. Draft International Standards adopted by the technical committees are circulated to the member bodies for approval before their acceptance as International Standards by the ISO Council. International Standard ISO 6709 was developediTeh Sby TTechnicalAN DCommitteeAR DISO/TC PR 97,E VIEW Information processing s ystems, and was circulated to the member bodies in November 1981. (standards.iteh.ai) lt has been approved by the member bodies of the following IcountriesSO 6709 :1: 983 https://standards.iteh.ai/catalog/standards/sist/40603644-5feb-4b20-87de- Belgium France d0a2bddRomaniab21d5/is o-6709-1983 Canada Germany, F.
  • TYPHOONS and DEPRESSIONS OVER the FAR EAST Morning Observation, Sep Teinber 6, from Rasa Jima Island by BERNARDF

    TYPHOONS and DEPRESSIONS OVER the FAR EAST Morning Observation, Sep Teinber 6, from Rasa Jima Island by BERNARDF

    SEPTEMBER1940 MONTHLY WEATHER REVIEW 257 days west of the 180th meridian. In American coastal appear to be independent of the typhoon of August 28- waters fog was noted on 10 days each off Washington and September 5, are the following: The S. S. Steel Exporter California; on 4 days off Oregon; and on 3 days off Lower reported 0700 G. C. T. September 6, from latitude 20'18' California. N., longitude 129'30'E.) a pressure of 744.8 mm. (993.0 nib.) with west-northwest winds of force 9. Also, the TYPHOONS AND DEPRESSIONS OVER THE FAR EAST morning observation, Sep teinber 6, from Rasa Jima Island By BERNARDF. DOUCETTE, J. (one of the Nansei Island group) was 747.8 mm. (997.0 5. mb.) for pressure and east-northeast, force 4, for winds. [Weather Bureau, Manila, P. I.] Typhoon, September 11-19) 1940.-A depression, moving Typhoon, August %!-September 6,1940.-A low-pressure westerly, passed about 200 miles south of Guam and area far to the southeast of Guam moved west-northwest, quickly inclined to the north, intensifying to typhoon rapidly developing to typhoon intensity as it proceeded. strength, September 11 to 13. It was stationary, Sep- When the center reached the regions about 250 miles tember 13 and 14, about 150 miles west-northwest of west of Guam, the direction changed to the northwest, Guam, and then began a northwesterly and northerly and the storm continued along this course until it reached course to the ocean regions about 300 miles west of the the latitude of southern Formosa.
  • QUICK REFERENCE GUIDE Latitude, Longitude and Associated Metadata

    QUICK REFERENCE GUIDE Latitude, Longitude and Associated Metadata

    QUICK REFERENCE GUIDE Latitude, Longitude and Associated Metadata The Property Profile Form (PPF) requests the property name, address, city, state and zip. From these address fields, ACRES interfaces with Google Maps and extracts the latitude and longitude (lat/long) for the property location. ACRES sets the remaining property geographic information to default values. The data (known collectively as “metadata”) are required by EPA Data Standards. Should an ACRES user need to be update the metadata, the Edit Fields link on the PPF provides the ability to change the information. Before the metadata were populated by ACRES, the data were entered manually. There may still be the need to do so, for example some properties do not have a specific street address (e.g. a rural property located on a state highway) or an ACRES user may have an exact lat/long that is to be used. This Quick Reference Guide covers how to find latitude and longitude, define the metadata, fill out the associated fields in a Property Work Package, and convert latitude and longitude to decimal degree format. This explains how the metadata were determined prior to September 2011 (when the Google Maps interface was added to ACRES). Definitions Below are definitions of the six data elements for latitude and longitude data that are collected in a Property Work Package. The definitions below are based on text from the EPA Data Standard. Latitude: Is the measure of the angular distance on a meridian north or south of the equator. Latitudinal lines run horizontal around the earth in parallel concentric lines from the equator to each of the poles.
  • AIM: Latitude and Longitude

    AIM: Latitude and Longitude

    AIM: Latitude and Longitude Latitude lines run east/west but they measure north or south of the equator (0°) splitting the earth into the Northern Hemisphere and Southern Hemisphere. Latitude North Pole 90 80 Lines of 70 60 latitude are 50 numbered 40 30 from 0° at 20 Lines of [ 10 the equator latitude are 10 to 90° N.L. 20 numbered 30 at the North from 0° at 40 Pole. 50 the equator ] 60 to 90° S.L. 70 80 at the 90 South Pole. South Pole Latitude The North Pole is at 90° N 40° N is the 40° The equator is at 0° line of latitude north of the latitude. It is neither equator. north nor south. It is at the center 40° S is the 40° between line of latitude north and The South Pole is at 90° S south of the south. equator. Longitude Lines of longitude begin at the Prime Meridian. 60° W is the 60° E is the 60° line of 60° line of longitude west longitude of the Prime east of the W E Prime Meridian. Meridian. The Prime Meridian is located at 0°. It is neither east or west 180° N Longitude West Longitude West East Longitude North Pole W E PRIME MERIDIAN S Lines of longitude are numbered east from the Prime Meridian to the 180° line and west from the Prime Meridian to the 180° line. Prime Meridian The Prime Meridian (0°) and the 180° line split the earth into the Western Hemisphere and Eastern Hemisphere. Prime Meridian Western Eastern Hemisphere Hemisphere Places located east of the Prime Meridian have an east longitude (E) address.
  • Latitude/Longitude Data Standard

    Latitude/Longitude Data Standard

    LATITUDE/LONGITUDE DATA STANDARD Standard No.: EX000017.2 January 6, 2006 Approved on January 6, 2006 by the Exchange Network Leadership Council for use on the Environmental Information Exchange Network Approved on January 6, 2006 by the Chief Information Officer of the U. S. Environmental Protection Agency for use within U.S. EPA This consensus standard was developed in collaboration by State, Tribal, and U. S. EPA representatives under the guidance of the Exchange Network Leadership Council and its predecessor organization, the Environmental Data Standards Council. Latitude/Longitude Data Standard Std No.:EX000017.2 Foreword The Environmental Data Standards Council (EDSC) identifies, prioritizes, and pursues the creation of data standards for those areas where information exchange standards will provide the most value in achieving environmental results. The Council involves Tribes and Tribal Nations, state and federal agencies in the development of the standards and then provides the draft materials for general review. Business groups, non- governmental organizations, and other interested parties may then provide input and comment for Council consideration and standard finalization. Standards are available at http://www.epa.gov/datastandards. 1.0 INTRODUCTION The Latitude/Longitude Data Standard is a set of data elements that can be used for recording horizontal and vertical coordinates and associated metadata that define a point on the earth. The latitude/longitude data standard establishes the requirements for documenting latitude and longitude coordinates and related method, accuracy, and description data for all places used in data exchange transaction. Places include facilities, sites, monitoring stations, observation points, and other regulated or tracked features. 1.1 Scope The purpose of the standard is to provide a common set of data elements to specify a point by latitude/longitude.
  • Why Do We Use Latitude and Longitude? What Is the Equator?

    Why Do We Use Latitude and Longitude? What Is the Equator?

    Where in the World? This lesson teaches the concepts of latitude and longitude with relation to the globe. Grades: 4, 5, 6 Disciplines: Geography, Math Before starting the activity, make sure each student has access to a globe or a world map that contains latitude and longitude lines. Why Do We Use Latitude and Longitude? The Earth is divided into degrees of longitude and latitude which helps us measure location and time using a single standard. When used together, longitude and latitude define a specific location through geographical coordinates. These coordinates are what the Global Position System or GPS uses to provide an accurate locational relay. Longitude and latitude lines measure the distance from the Earth's Equator or central axis - running east to west - and the Prime Meridian in Greenwich, England - running north to south. What Is the Equator? The Equator is an imaginary line that runs around the center of the Earth from east to west. It is perpindicular to the Prime Meridan, the 0 degree line running from north to south that passes through Greenwich, England. There are equal distances from the Equator to the north pole, and also from the Equator to the south pole. The line uniformly divides the northern and southern hemispheres of the planet. Because of how the sun is situated above the Equator - it is primarily overhead - locations close to the Equator generally have high temperatures year round. In addition, they experience close to 12 hours of sunlight a day. Then, during the Autumn and Spring Equinoxes the sun is exactly overhead which results in 12-hour days and 12-hour nights.
  • AS/NZS ISO 6709:2008 Standard Representation of Latitude, Longitude

    AS/NZS ISO 6709:2008 Standard Representation of Latitude, Longitude

    AS/NZS ISO 6709:2008 ISO 6709:1983 AS/NZS ISO 6709:2008 Australian/New Zealand Standard™ Standard representation of latitude, longitude and altitude for geographic point locations AS/NZS ISO 6709:2008 This Joint Australian/New Zealand Standard was prepared by Joint Technical Committee IT-004, Geographical Information/Geomatics. It was approved on behalf of the Council of Standards Australia on 25 July 2008 and on behalf of the Council of Standards New Zealand on 21 July 2008. This Standard was published on 16 September 2008. The following are represented on Committee IT-004: ACT Planning and Land Authority ANZLIC - the Spatial Information Council Australian Antarctic Division Australian Bureau of Statistics Australian Hydrographic Office Australian Key Centre In Land Information Studies Australian Map Circle Australian Spatial Information Business Association CSIRO Exploration & Mining Department for Administrative and Information Services (SA) Department of Defence (Australia) Department of Lands NSW Department of Natural Resources and Water (Qld) Department of Planning and Infrastructure (NT) Department of Primary Industries and Water Tasmania Department of Sustainability and Environment (Victoria) Geoscience Australia InterGovernmental Committee on Surveying and Mapping Land Information New Zealand Office of Spatial Data Management Western Australian Land Information System Keeping Standards up-to-date Standards are living documents which reflect progress in science, technology and systems. To maintain their currency, all Standards are periodically reviewed, and new editions are published. Between editions, amendments may be issued. Standards may also be withdrawn. It is important that readers assure themselves they are using a current Standard, which should include any amendments which may have been published since the Standard was purchased.
  • The Longitude of the Mediterranean Throughout History: Facts, Myths and Surprises Luis Robles Macías

    The Longitude of the Mediterranean Throughout History: Facts, Myths and Surprises Luis Robles Macías

    The longitude of the Mediterranean throughout history: facts, myths and surprises Luis Robles Macías To cite this version: Luis Robles Macías. The longitude of the Mediterranean throughout history: facts, myths and sur- prises. E-Perimetron, National Centre for Maps and Cartographic Heritage, 2014, 9 (1), pp.1-29. hal-01528114 HAL Id: hal-01528114 https://hal.archives-ouvertes.fr/hal-01528114 Submitted on 27 May 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. e-Perimetron, Vol. 9, No. 1, 2014 [1-29] www.e-perimetron.org | ISSN 1790-3769 Luis A. Robles Macías* The longitude of the Mediterranean throughout history: facts, myths and surprises Keywords: History of longitude; cartographic errors; comparative studies of maps; tables of geographical coordinates; old maps of the Mediterranean Summary: Our survey of pre-1750 cartographic works reveals a rich and complex evolution of the longitude of the Mediterranean (LongMed). While confirming several previously docu- mented trends − e.g. the adoption of erroneous Ptolemaic longitudes by 15th and 16th-century European cartographers, or the striking accuracy of Arabic-language tables of coordinates−, we have observed accurate LongMed values largely unnoticed by historians in 16th-century maps and noted that widely diverging LongMed values coexisted up to 1750, sometimes even within the works of one same author.
  • Prime Meridian ×

    Prime Meridian ×

    This website would like to remind you: Your browser (Apple Safari 4) is out of date. Update your browser for more × security, comfort and the best experience on this site. Encyclopedic Entry prime meridian For the complete encyclopedic entry with media resources, visit: http://education.nationalgeographic.com/encyclopedia/prime-meridian/ The prime meridian is the line of 0 longitude, the starting point for measuring distance both east and west around the Earth. The prime meridian is arbitrary, meaning it could be chosen to be anywhere. Any line of longitude (a meridian) can serve as the 0 longitude line. However, there is an international agreement that the meridian that runs through Greenwich, England, is considered the official prime meridian. Governments did not always agree that the Greenwich meridian was the prime meridian, making navigation over long distances very difficult. Different countries published maps and charts with longitude based on the meridian passing through their capital city. France would publish maps with 0 longitude running through Paris. Cartographers in China would publish maps with 0 longitude running through Beijing. Even different parts of the same country published materials based on local meridians. Finally, at an international convention called by U.S. President Chester Arthur in 1884, representatives from 25 countries agreed to pick a single, standard meridian. They chose the meridian passing through the Royal Observatory in Greenwich, England. The Greenwich Meridian became the international standard for the prime meridian. UTC The prime meridian also sets Coordinated Universal Time (UTC). UTC never changes for daylight savings or anything else. Just as the prime meridian is the standard for longitude, UTC is the standard for time.
  • GMT and Longitude by Lunar Distance: Two Methods Compared from a Practitioner’S Point of View

    GMT and Longitude by Lunar Distance: Two Methods Compared from a Practitioner’S Point of View

    THE JOURNAL OF NAVIGATION (2019), 72, 1660–1664. c The Royal Institute of Navigation 2019 doi:10.1017/S0373463319000341 FORUM GMT and Longitude by Lunar Distance: Two Methods Compared From a Practitioner’s Point of View Eric Romelczyk (E-mail: [email protected]) This article discusses the technique of observing lunar distance - that is, angular distance between the moon and another celestial body - to establish universal time and longitude, from a practitioner’s point of view. The article presents a brief overview of the principles underlying the lunar distance observation and its use in celestial navigation. A discussion follows of two different methods for finding universal time by observing lunar distance, Dr. Wendel Brunner’s calculator-based method and the specialised inspection tables created by Bruce Stark. The article compares the two methods against each other for ease of use and accuracy. The author concludes that either method will provide satisfactory results, but that the technique of observing lunar dis- tance is unlikely to regain relevance in the modern-day practice of navigation and is primarily useful as a skill-building exercise in making sextant observations. KEYWORDS 1. Navigation. 2. History. 3. Nautical. 4. Time. Submitted: 8 August 2018. Accepted: 14 April 2019. First published online: 2 May 2019. 1. INTRODUCTION. 1.1. History of the lunar distance method. For centuries of seafaring history, a method for accurately measuring time to the degree of precision necessary to establish the navigator’s longitude was out of reach for practical purposes. It had been understood since the mid-16th century that the navigator’s longitude could be established either by reference to the moon’s angular distance from other celestial bodies - the “lunar distance”, measured by careful sextant observations - or by reference to a timepiece of sufficient accuracy.
  • Spherical Coordinate Systems

    Spherical Coordinate Systems

    Spherical Coordinate Systems Exploring Space Through Math Pre-Calculus let's examine the Earth in 3-dimensional space. The Earth is a large spherical object. In order to find a location on the surface, The Global Pos~ioning System grid is used. The Earth is conventionally broken up into 4 parts called hemispheres. The North and South hemispheres are separated by the equator. The East and West hemispheres are separated by the Prime Meridian. The Geographic Coordinate System grid utilizes a series of horizontal and vertical lines. The horizontal lines are called latitude lines. The equator is the center line of latitude. Each line is measured in degrees to the North or South of the equator. Since there are 360 degrees in a circle, each hemisphere is 180 degrees. The vertical lines are called longitude lines. The Prime Meridian is the center line of longitude. Each hemisphere either East or West from the center line is 180 degrees. These lines form a grid or mapping system for the surface of the Earth, This is how latitude and longitude lines are represented on a flat map called a Mercator Projection. Lat~ude , l ong~ude , and elevalion allows us to uniquely identify a location on Earth but, how do we identify the pos~ion of another point or object above Earth's surface relative to that I? NASA uses a spherical Coordinate system called the Topodetic coordinate system. Consider the position of the space shuttle . The first variable used for position is called the azimuth. Azimuth is the horizontal angle Az of the location on the Earth, measured clockwise from a - line pointing due north.