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Azimuth
An AZIMUTH (/ˈæzɪməθ/ ( listen )) (from the pl. form of the Arabic noun "السَّمْت" as-samt, meaning "the direction") is an angular measurement in a spherical coordinate system . The vector from an observer (origin ) to a point of interest is projected perpendicularly onto a reference plane ; the angle between the projected vector and a reference vector on the reference plane is called the azimuth. An example is the position of a star in the sky. The star is the point of interest, the reference plane is the horizon or the surface of the sea , and the reference vector points north . The azimuth is the angle between the north vector and the perpendicular projection of the star down onto the horizon. Azimuth
Azimuth
is usually measured in degrees (°). The concept is used in navigation , astronomy , engineering , mapping , mining and artillery
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Spatial Reference System
A SPATIAL REFERENCE SYSTEM (SRS) or COORDINATE REFERENCE SYSTEM (CRS) is a coordinate-based local, regional or global system used to locate geographical entities. A spatial reference system defines a specific map projection , as well as transformations between different spatial reference systems. Spatial reference systems are defined by the OGC 's Simple feature access using well-known text , and support has been implemented by several standards-based geographic information systems . Spatial reference systems can be referred to using a SRID
SRID
integer , including EPSG codes defined by the International Association of Oil and Gas Producers . It is specified in ISO 19111:2007 Geographic information—Spatial referencing by coordinates, also published as OGC Abstract Specification, Topic 2: Spatial referencing by coordinate
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Celestial Equator
The CELESTIAL EQUATOR is a great circle on the imaginary celestial sphere , in the same plane as the Earth
Earth
's equator . In other words, it is a projection of the terrestrial equator out into space. As a result of the Earth's axial tilt , the celestial equator is inclined by 23.4° with respect to the ecliptic plane . An observer standing on the Earth's equator visualizes the celestial equator as a semicircle passing directly overhead through the zenith . As the observer moves north (or south), the celestial equator tilts towards the opposite horizon. The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus the observer always sees the ends of the semicircle disappear over the horizon exactly due east and due west, regardless of the observer's position on Earth
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Radian
The RADIAN is the standard unit of angular measure, used in many areas of mathematics . The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees (expansion at  A072097 ). The unit was formerly an SI supplementary unit , but this category was abolished in 1995 and the radian is now considered an SI derived unit . Separately, the SI unit of solid angle measurement is the steradian . The radian is represented by the symbol RAD. An alternative symbol is c, the superscript letter c, for "circular measure", or the letter r, but both of those symbols are infrequently used as it can be easily mistaken for a degree symbol (°) or a radius (r). So for example, a value of 1.2 radians could be written as 1.2 rad, 1.2 r, 1.2rad, or 1.2c
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Right Ascension
RIGHT ASCENSION (abbreviated RA; symbol α) is the angular distance measured eastward along the celestial equator from the vernal equinox to the hour circle of the point in question. When combined with declination , these astronomical coordinates specify the direction of a point on the celestial sphere in the equatorial coordinate system . RIGHT ASCENSION and declination as seen on the inside of the celestial sphere . The primary direction of the system is the vernal equinox , the ascending node of the ecliptic (red) on the celestial equator (blue). Right ascension
Right ascension
is measured eastward along the celestial equator from the primary direction. An old term, right ascension (Latin, ascensio recta ) refers to the ascension, or the point on the celestial equator which rises with any celestial object, as seen from the Earth
Earth
's equator , where the celestial equator intersects the horizon at a right angle
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Angular Mil
A MILLIRADIAN, often called a MIL or MRAD, is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Mils are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel (up, down, left or right). Mils are also used for comparing shot groupings , or to compare the difficulty of hitting different sized shooting targets at different distances. When using a scope with both mil adjustment and a reticle with mil markings (called a mil/mil scope), the shooter can use the reticle as a "ruler" to count the number of mils a shot was off target which directly translates to the sight adjustment needed to hit the target with a follow up shot. Optics with mil markings in the reticle can also be used to make a range estimation of a known size target, or vice versa to determine a target size if the distance is known, a practice called "milling"
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Meridian (geography)
A (GEOGRAPHICAL) MERIDIAN (or LINE OF LONGITUDE) is the half of an imaginary great circle on the Earth's surface, terminated by the North Pole and the South Pole
South Pole
, connecting points of equal longitude . The position of a point along the meridian is given by its latitude indicating how many degrees north or south of the Equator the point is. Each meridian is perpendicular to all circles of latitude . Each is also the same length, being half of a great circle on the Earth's surface and therefore measuring 20,003.93 km (12,429.9 miles). CONTENTS * 1 Etymology * 2 Geographic * 3 Magnetic * 4 See also * 5 References * 6 External links ETYMOLOGYThe term "meridian" comes from the Latin meridies, meaning "midday"; the sun crosses a given meridian midway between the times of sunrise and sunset on that meridian. The same Latin stem gives rise to the terms a.m. (ante meridiem) and p.m
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True North
TRUE NORTH (geodetic north) is the direction along the earth's surface towards the geographic North Pole
North Pole
. True geodetic north differs from magnetic north (the direction a compass points toward the magnetic north pole), and from grid north (the direction northwards along the grid lines of a map projection ). Geodetic true north also differs very slightly from astronomical true north (typically by a few arcseconds ) because the local gravity may not point at the exact rotational axis of the earth. The direction of astronomical true north is marked in the skies by the north celestial pole . This is within about 1 degree of the position of Polaris
Polaris
, so that the star appears to trace a tiny circle in the sky each day. Due to the axial precession of the Earth, true north rotates in an arc with respect to the stars that takes approximately 25,000 years to complete
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Grad (angle)
The GRADIAN is a unit of measurement of an angle , equivalent to 1/400 of a turn , 9/10 of a degree , or π/200 of a radian . It is also known as GON (from Greek γωνία/gōnía for angle), GRAD, or GRADE. In continental Europe
Europe
, the French term centigrade was in use for one hundredth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale. CONTENTS * 1 History * 2 Benefits * 3 Use in surveying * 4 Conversion * 5 See also * 6 References * 7 External links HISTORYThe unit originated in connection with the French Revolution in France
France
as the grade, along with the metric system , hence it is occasionally referred to as a "metric degree"
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Atan2
In a variety of computer languages , the functionality of the multi-valued inverse tangent is provided under the function names of atan2 ( y , x ) {displaystyle operatorname {atan2} (y,x)} or arctan2 ( y , x ) {displaystyle operatorname {arctan2} (y,x)} . This function takes two arguments y and x, not both equal to zero, representing the coordinates of an arbitrary point ( x , y ) {displaystyle (x,y)} in the X/Y-plane, excluding the origin. The ratio y / x {displaystyle y/x} is interpreted as the tangent of an angle , {displaystyle theta ,} spanned by the X-axis and the ray from the origin to this point. The returned angle in radian is generally confined to the interval ( , ] {displaystyle (-pi ,pi ]} and positive for y > 0 {displaystyle y>0} (upper half-plane)
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Declination
In astronomy , DECLINATION (abbreviated DEC; symbol δ) is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system , the other being hour angle . Declination's angle is measured north or south of the celestial equator , along the hour circle passing through the point in question. Right ascension
Right ascension
and DECLINATION as seen on the inside of the celestial sphere . The primary direction of the system is the vernal equinox , the ascending node of the ecliptic (red) on the celestial equator (blue). Declination
Declination
is measured northward or southward from the celestial equator , along the hour circle passing through the point in question. The root of the word declination (Latin, declinatio) means "a bending away" or "a bending down". It comes from the same root as the words incline ("bend toward") and recline ("bend backward")
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Hour Angle
In astronomy and celestial navigation , the HOUR ANGLE is one of the coordinates used in the equatorial coordinate system to give the direction of a point on the celestial sphere . The hour angle of a point is the angle between two planes: one containing the Earth\'s axis and the zenith (the meridian plane), and the other containing the Earth\'s axis and the given point (the hour circle passing through the point). As seen from above the Earth
Earth
's north pole , a star's local hour angle (LHA) for an observer near New York (red dot). Also depicted are the star's right ascension and Greenwich hour angle (GHA), the local mean sidereal time (LMST) and Greenwich mean sidereal time (GMST). The symbol ʏ identifies the vernal equinox direction. The angle may be expressed as negative east of the meridian plane and positive west of the meridian plane, or as positive westward from 0° to 360°
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Oblate Spheroid
A SPHEROID, or ELLIPSOID OF REVOLUTION, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters . If the ellipse is rotated about its major axis, the result is a PROLATE (elongated) spheroid, shaped like an American football or rugby ball. If the ellipse is rotated about its minor axis, the result is an OBLATE (flattened) spheroid, shaped like a lentil . If the generating ellipse is a circle, the result is a sphere . A spheroid has circular symmetry . Because of the combined effects of gravity and rotation , the shape of the Earth
Earth
, and of all planets , is not quite a sphere but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography the Earth
Earth
is often approximated by an oblate spheroid instead of a sphere
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World Geodetic System
The WORLD GEODETIC SYSTEM (WGS) is a standard for use in cartography , geodesy , and navigation including GPS
GPS
. It comprises a standard coordinate system for the Earth
Earth
, a standard spheroidal reference surface (the datum or reference ellipsoid ) for raw altitude data, and a gravitational equipotential surface (the geoid ) that defines the nominal sea level. The latest revision is WGS 84 (also known as WGS 1984, EPSG:4326), established in 1984 and last revised in 2004. Earlier schemes included WGS 72, WGS 66, and WGS 60. WGS 84 is the reference coordinate system used by the Global Positioning System
Global Positioning System

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Culmination
In astronomy , the CULMINATION of a planet , star , or constellation is its transit over an observer's meridian . During a sidereal day , an astronomical object crosses the meridian twice: once at its UPPER CULMINATION, when it is (approximately) at its highest point as seen from the earth, and once at its LOWER CULMINATION, its (approximately) lowest point. Often, culmination is used to mean upper culmination. The altitude of an object in degrees at its upper culmination is equal to (90 − L + D), where L is the observer's latitude and D is the object's declination . CONTENTS * 1 Cases * 2 Period * 3 Sun * 4 Polaris
Polaris
* 5 See also * 6 References CASESThe three cases are dependent on the observer's latitude and the declination of the celestial body : * The object is above the horizon even at its lower culmination; i.e. if declination + latitude > 90° (i.e
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Geodesic
In differential geometry , a GEODESIC (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/ ) is a generalization of the notion of a "straight line " to "curved spaces ". The term "geodesic" comes from geodesy , the science of measuring the size and shape of Earth
Earth
; in the original sense, a geodesic was the shortest route between two points on the Earth's surface , namely, a segment of a great circle . The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory , one might consider a geodesic between two vertices /nodes of a graph . In the presence of an affine connection , a geodes