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Coordinate systems to specify locations on the surface of the Earth have been used for centuries In western geodesy the equator, the Tropics of Cancer and Capricorn, and lines of latitude and longitude were used to locate positions on the Earth Eastern cartographers used other rectangular grid systems as early as 270 CE (common/Christian Era, or AD 270, Anno Domini), and various units of length and angular distance have been used over history The meter is related to both linear and angular distance, having been defined in the late eighteenth century as one-ten-millionth of the distance from the pole to the equator
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Latitude, Longitude, and Altitude System The most commonly used coordinate system today is the latitude, longitude, and altitude system The prime meridian and the equator are the reference planes used to define latitude and longitude The geodetic latitude (there are many other defined latitudes) of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid In other words, latitude measures how far north or south of the equator a place is located The equator is situated at 0 , the North Pole at 90 north (or simply 90 , since a positive latitude number implies north), and the South Pole at 90 south (or 90 ) Latitude measurements range from 0 to 90 The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane Longitude measures how far east or west of the prime meridian a place is located The prime meridian runs through Greenwich, England Longitude is measured in terms of east, implied by a positive number, or west, implied by a negative number Longitude measurements range from 0 to 180 The geographical coordinates (latitude and longitude) are typically expressed in the sexagesimal form (ie, degrees, minutes, and seconds) Sexagesimal is a numeral system with 60 as the base; it originated with the ancient Sumerians in the 2000s BCE, was transmitted to the Babylonians, and is still used, in modified form, for measuring time, angles, and geographic coordinates The geodetic height at a point is the distance from the reference ellipsoid to the point in a direction normal to the ellipsoid Altitude is measured with reference to mean sea level (MSL), and height is measured with reference to the soil or ground level In this application, altitudes are known as above mean sea level (AMSL) and heights as above ground level (AGL) It is essential to show the vertical or altimetric reference datum (or VRD) with the altitude, because altitudes change when the vertical datum changes Sometimes the coordinates can be shown in universal transverse mercator (UTM) format or in values expressing north or east, for example When the positioning coordinates are obtained from topographical charts, they are normally expressed in UTM format
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It is important to remember that some GPS receivers are not able to display latitude and longitude readings in decimal degrees If one of these receivers is being used, it should be set to read in degrees and decimal minutes and then convert the latitude and longitude readings to decimal degrees
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Converting from degrees and decimal minutes to decimal degrees:
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1 degree = 60 minutes = 3,600 seconds Reading in decimal degrees = degrees + decimal minutes/(60 minutes/ degree)
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Example 1:
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A latitude reading is given as 15 3903' N Latitude in decimal degrees = 15 + 3903'/(60'/deg) = 15 + 06505 = 156505 N
Example 2:
1 = 60' = 3,600" 56 26' 45" N = 56 + 26'/60 + 45"/3600 = 56 + 043333 + 00125 = 5644583 N
Example 3:
88 245568 = 88 + 0245568(60)' = 88 14734' 88 14734' = 88 14' + 0734(60) " = 88 14' 4404"
The following is a lengthy but fairly simple formula for the distance calculation (in miles) between two coordinates on Earth It assumes that the actual shape of the Earth (called ellipsoid ) can be neglected and therefore uses mathematical solutions for a sphere Note that the coordinates are given in decimal degrees and have to be converted into radians before using the formula The conversion formula looks like this: Coordinates Radians = Coordinates DecimalDegrees
180
(624)
The Earth s equatorial radius, or semi-major axis, is the distance from its center to the equator and equals 6,3781370 km ( 3,963191 mi) The equatorial radius is often used to compare Earth with other planets The formula to calculate distance between sites: d = 3, 963191 arccos sin( LAT1 ) sin( LAT2 ) + cos( LAT1 ) cos( LAT2 ) cos( LONG2 LONG1 ) (625)
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