query: what do we call the celestial coordinate that is similar to the earths longitude coordinate

pos: Declination Earth. (An ellipsoid is an approximation to sea level that is mathematically manageable). For the moon this discrepancy can reach 0.003 degrees; the Sun and planets are hundreds of times more distant and for them the discrepancy is proportionately smaller (and for the stars is immeasurable). 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. The

pos: Celestial sphere poles, using right ascension and declination. The ecliptic coordinate system specifies positions relative to the ecliptic (Earth's orbit), using ecliptic longitude and latitude. Besides the equatorial and ecliptic systems, some other celestial coordinate systems, like the galactic coordinate system, are more appropriate for particular purposes. The ancients assumed the literal truth of stars attached to a celestial sphere, revolving about the Earth in one day, and a fixed Earth. The Eudoxan planetary model, on which the Aristotelian and Ptolemaic models were based, was the first geometric explanation for the "wandering" of the classical planets. The outer most of these "crystal

pos: Zodiac coordinate system, which measures astronomical positions by right ascension and declination rather than the ecliptic-based definitions of celestial longitude and celestial latitude. The word "zodiac" is also used in reference to the zodiacal cloud of dust grains that move among the planets, and the zodiacal light that originates from their scattering of sunlight. In Unicode, the symbols of zodiac signs are encoded in block "Miscellaneous Symbols": In Unicode 6.0 the sign for Ophiuchus has been added, too: Zodiac The zodiac is an area of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the

pos: Latitude averages out. Astronomical latitude is not to be confused with declination, the coordinate astronomers use in a similar way to specify the angular position of stars north/south of the celestial equator (see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to specify the angular position of stars north/south of the ecliptic (see ecliptic coordinates). Latitude In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle (defined below) which ranges from 0° at the Equator to 90° (North or South) at the poles. Lines of

pos: Equatorial coordinate system object. The vernal equinox point is one of the two where the ecliptic intersects the celestial equator. Analogous to terrestrial longitude, right ascension is usually measured in sidereal hours, minutes and seconds instead of degrees, a result of the method of measuring right ascensions by timing the passage of objects across the meridian as the Earth rotates. There are = 15° in one hour of right ascension, and 24 of right ascension around the entire celestial equator. When used together, right ascension and declination are usually abbreviated RA/Dec. Alternatively to right ascension, hour angle (abbreviated HA or LHA, "local hour

pos: Spherical astronomy astrometry. The primary elements of spherical astronomy are coordinate systems and time. The coordinates of objects on the sky are listed using the equatorial coordinate system, which is based on the projection of Earth's equator onto the celestial sphere. The position of an object in this system is given in terms of right ascension (α) and declination (δ). The latitude and local time can then be used to derive the position of the object in the horizontal coordinate system, consisting of the altitude and azimuth. The coordinates of celestial objects such as stars and galaxies are tabulated in a star

pos: Polar distance (astronomy) Polar distance (astronomy) In the celestial equatorial coordinate system Σ(α, δ) in astronomy, polar distance (PD) is an angular distance of a celestial object on its meridian measured from the celestial pole, similar to the way declination (dec, δ) is measured from the celestial equator. Polar distance (PD) = 90° ± δ Polar distances are expressed in degrees and cannot exceed 90° in magnitude. An object on the celestial equator has a PD of 90°. Polar distance is not affected by the precession of the equinoxes. If the polar distance of the Sun is equal to the observer's latitude, the

pos: Polar distance (astronomy) shadow path of a gnomon's tip on a sundial will be a parabola; at higher latitudes it will be an ellipse and lower, a hyperbola. Polar distance (astronomy) In the celestial equatorial coordinate system Σ(α, δ) in astronomy, polar distance (PD) is an angular distance of a celestial object on its meridian measured from the celestial pole, similar to the way declination (dec, δ) is measured from the celestial equator. Polar distance (PD) = 90° ± δ Polar distances are expressed in degrees and cannot exceed 90° in magnitude. An object on the celestial equator has a PD of 90°.

pos: Galactic coordinate system based on a galactic north pole at RA , dec +28° (in the B1900.0 epoch convention) and a 0° longitude at the point where the galactic plane and equatorial plane intersected. In 1958, the International Astronomical Union (IAU) defined the galactic coordinate system in reference to radio observations of galactic neutral hydrogen through the hydrogen line, changing the definition of the Galactic longitude by 32° and the latitude by 1.5°. In the equatorial coordinate system, for equinox and equator of 1950.0, the north galactic pole is defined at right ascension , declination +27.4°, in the constellation Coma Berenices, with a

pos: Hour angle is paired with the declination to fully specify the location of a point on the celestial sphere in the equatorial coordinate system. The local hour angle (LHA) of an object in the observer's sky is where LHA is the local hour angle of the object, LST is the local sidereal time, formula_3 is the object's right ascension, GST is Greenwich sidereal time and formula_4 is the observer's longitude (positive east from the prime meridian). These angles can be measured in time (24 hours to a circle) or in degrees (360 degrees to a circle)— one or the other, not both.

pos: Archaeoastronomy in its historical environment. To calculate what astronomical features a structure faced a coordinate system is needed. The stars provide such a system. If you were to go outside on a clear night you would observe the stars spinning around the celestial pole. This point is +90° if you are watching the North Celestial Pole or −90° if you are observing the Southern Celestial Pole. The concentric circles the stars trace out are lines of celestial latitude, known as "declination". The arc connecting the points on the horizon due East and due West (if the horizon is flat) and all

pos: Equinox zero. Its latitude will not be exactly zero, since Earth is not exactly in the plane of the ecliptic. Its declination will not be exactly zero either. (The ecliptic is defined by the barycenter of Earth and the Moon combined.) The modern definition of equinox is the instants when the Sun's apparent geocentric longitude is 0° (northward equinox) or 180° (southward equinox). See the adjacent diagram. Because of the precession of the Earth's axis, the position of the vernal point on the celestial sphere changes over time, and the equatorial and the ecliptic coordinate systems change accordingly. Thus when specifying

pos: Vega The minus sign indicates a relative motion toward the Earth. Motion transverse to the line of sight causes the position of Vega to shift with respect to the more distant background stars. Careful measurement of the star's position allows this angular movement, known as proper motion, to be calculated. Vega's proper motion is (mas) per year in right ascension—the celestial equivalent of longitude—and in declination, which is equivalent to a change in latitude. The net proper motion of Vega is 327.78 mas/y, which results in angular movement of a degree every 11,000 years. In the Galactic coordinate system, the space

neg: Celestial sphere bases of the reference systems. These include the Earth's equator, axis, and orbit. At their intersections with the celestial sphere, these form the celestial equator, the north and south celestial poles, and the ecliptic, respectively. As the celestial sphere is considered arbitrary or infinite in radius, all observers see the celestial equator, celestial poles, and ecliptic at the same place against the background stars. From these bases, directions toward objects in the sky can be quantified by constructing celestial coordinate systems. Similar to geographic longitude and latitude, the equatorial coordinate system specifies positions relative to the celestial equator and celestial

neg: Galactic coordinate system Galactic coordinate system The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane. Longitude (symbol ) measures the angular distance of an object eastward along the galactic equator from the galactic center. Analogous to terrestrial longitude, galactic longitude is usually measured

neg: Geographic coordinate system up formula_15. In an airplane, most objects of interest are below the aircraft, so it is sensible to define down as a positive number. The NED coordinates allow this as an alternative to the ENU. By convention, the north axis is labeled formula_16, the east formula_17 and the down formula_18. To avoid confusion between formula_13 and formula_16, etc. in this article we will restrict the local coordinate frame to ENU. Similar coordinate systems are defined for other celestial bodies such as: Geographic coordinate system A geographic coordinate system is a coordinate system that enables every location on Earth to be

neg: Celestial coordinate system of the Sun). The system is primarily used for computing the positions of planets and other solar system bodies, as well as defining their orbital elements. The galactic coordinate system uses the approximate plane of our galaxy as its fundamental plane. The solar system is still the center of the coordinate system, and the zero point is defined as the direction towards the galactic center. Galactic latitude resembles the elevation above the galactic plane and galactic longitude determines direction relative to the center of the galaxy. The supergalactic coordinate system corresponds to a fundamental plane that contains a higher than

neg: Spherical coordinate system systems following other conventions are used outside mathematics. In a geographical coordinate system positions are measured in latitude, longitude and height or altitude. There are a number of different celestial coordinate systems based on different fundamental planes and with different terms for the various coordinates. The spherical coordinate systems used in mathematics normally use radians rather than degrees and measure the azimuthal angle counterclockwise from the -axis to the -axis rather than clockwise from north (0°) to east (+90°) like the horizontal coordinate system. The polar angle is often replaced by the "elevation angle" measured from the reference plane. Elevation

neg: Spherical coordinate system the mean radius of the planet's reference surface, which is approximately for Earth. However, modern geographical coordinate systems are quite complex, and the positions implied by these simple formulae may be wrong by several kilometers. The precise standard meanings of latitude, longitude and altitude are currently defined by the World Geodetic System (WGS), and take into account the flattening of the Earth at the poles (about ) and many other details. In astronomy there are a series of spherical coordinate systems that measure the elevation angle from different fundamental planes. These reference planes are the observer's horizon, the celestial equator

neg: Celestial coordinate system Celestial coordinate system In astronomy, a celestial coordinate system (or celestial reference system) is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on. Coordinate systems can specify an object's position in three-dimensional space or plot merely its direction on a celestial sphere, if the object's distance is unknown or trivial. The coordinate systems are implemented in either spherical or rectangular coordinates. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth. These differ in their choice of fundamental plane, which divides the celestial sphere

neg: Celestial coordinate system into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, are simply the cartesian equivalent of the spherical coordinates, with the same fundamental () plane and primary (-axis) direction. Each coordinate system is named after its choice of fundamental plane. The following table lists the common coordinate systems in use by the astronomical community. The fundamental plane divides the celestial sphere into two equal hemispheres and defines the baseline for the latitudinal coordinates, similar to the equator in the geographic coordinate system. The poles are located at ±90° from the fundamental plane. The primary direction is the

neg: Tensors in curvilinear coordinates to formula_4. Let us denote this transformation by formula_28. We will represent the transformation from the coordinate system with coordinate variables formula_3 to the coordinate system with coordinates formula_4 as: formula_31 If the transformation formula_16 is bijective then we call the image of the transformation,namely formula_3, a set of admissible coordinates for formula_4. If formula_16 is linear the coordinate system formula_3 will be called an affine coordinate system ,otherwise formula_3 is called a curvilinear coordinate system As we now see that the Coordinates formula_3 and formula_4 are functions of each other, we can take the derivative of the coordinate variable

neg: Celestial coordinate system another equinox, they must be precessed to their place at J2000.0 before applying these formulae. These equations convert to equatorial coordinates referred to B2000.0. Celestial coordinate system In astronomy, a celestial coordinate system (or celestial reference system) is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on. Coordinate systems can specify an object's position in three-dimensional space or plot merely its direction on a celestial sphere, if the object's distance is unknown or trivial. The coordinate systems are implemented in either spherical or rectangular coordinates. Spherical coordinates, projected on the celestial sphere, are analogous

neg: Horizontal coordinate system Horizontal coordinate system The horizontal coordinate system, also known as topocentric coordinate system, is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. Coordinates of an object in the sky are expressed in terms of altitude (or elevation) angle and azimuth. This celestial coordinate system divides the sky into two hemispheres: the upper hemisphere, where objects above the horizon are visible, and the lower hemisphere, where objects below the horizon cannot be seen, since the Earth obstructs views of them. The great circle separating the hemispheres is called the celestial horizon, which is defined as

neg: Galactic anticenter +28° 56'. Galactic anticenter The galactic anticenter is a direction in space directly opposite to the Galactic Center, as viewed from Earth. This direction corresponds to a point on the celestial sphere. From the perspective of an observer on Earth, the galactic anticenter is located in the constellation Auriga, and Beta Tauri is the bright star that appears nearest this point. In terms of the galactic coordinate system, the Galactic Center (in Sagittarius) corresponds to a longitude of 0°, while the anticenter is located exactly at 180°. In the equatorial coordinate system, the anticenter is found at roughly RA 05h

neg: Galactic anticenter Galactic anticenter The galactic anticenter is a direction in space directly opposite to the Galactic Center, as viewed from Earth. This direction corresponds to a point on the celestial sphere. From the perspective of an observer on Earth, the galactic anticenter is located in the constellation Auriga, and Beta Tauri is the bright star that appears nearest this point. In terms of the galactic coordinate system, the Galactic Center (in Sagittarius) corresponds to a longitude of 0°, while the anticenter is located exactly at 180°. In the equatorial coordinate system, the anticenter is found at roughly RA 05h 46m, dec

neg: Expansion of the universe coordinates — for example, the latitude and longitude. Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example latitude and longitude, or X-Y-Z Cartesian coordinates. Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too. On the curved surface of the Earth, we can see this effect in

neg: Schwarzschild metric solution as Schwarzschild, using a simpler, more direct derivation. In the early years of general relativity there was a lot of confusion about the nature of the singularities found in the Schwarzschild and other solutions of the Einstein field equations. In Schwarzschild's original paper, he put what we now call the event horizon at the origin of his coordinate system. In this paper he also introduced what is now known as the Schwarzschild radial coordinate ( in the equations above), as an auxiliary variable. In his equations, Schwarzschild was using a different radial coordinate that was zero at the Schwarzschild

neg: Equatorial coordinate system the origin is removed to the center of the Sun. It is commonly used in planetary orbit calculation. The three astronomical rectangular coordinate systems are related by Equatorial coordinate system The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox, and a right-handed convention. The origin at the

neg: Equatorial coordinate system Equatorial coordinate system The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox, and a right-handed convention. The origin at the center of Earth means the coordinates are "geocentric", that is, as seen from the centre of Earth as if it were transparent. The fundamental plane and the

neg: Longitude of Mars (since about 2002) is to use planetocentric coordinates. The meridian of Mars is located at Airy-0 crater. Tidally-locked bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere. However, libration due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an analemma. Longitude Longitude (, ), is a geographic coordinate that specifies the

neg: Coordinate singularity of the coordinate system chosen, which is singular at the poles. A different coordinate system would eliminate the apparent discontinuity, e.g. by replacing the latitude/longitude representation with an -vector representation. Stephen Hawking aptly summed this up, when once asking the question, "What lies north of the North Pole?". Coordinate singularity A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame. An example is the apparent (longitudinal) singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0

neg: Barycentric celestial reference system Barycentric celestial reference system The barycentric celestial reference system (BCRS) is a coordinate system used in astrometry to specify the location and motions of astronomical objects. It was created in 2000 by the International Astronomical Union (IAU) to be the global standard reference system for objects located outside the gravitational vicinity of Earth: planets, moons, and other Solar System bodies, stars and other objects in the Milky Way galaxy, and extra-galactic objects. The geocentric celestial reference system (GCRS), also created by the IAU in 2000, is a similar standard coordinate system used to specify the location and motions of near-earth

neg: Coordinate singularity Coordinate singularity A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame. An example is the apparent (longitudinal) singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (i.e., jumping from longitude 0 to longitude 180 degrees). In fact, longitude is not uniquely defined at the poles. This discontinuity, however, is only apparent; it is an artifact

neg: Ingo Swann the geographical features of the Earth and their approximate latitude and longitude. (It is Swann who suggests these Coordinate Remote Viewing tests, not the experimenters. He is in control.) "Or it was possible that we were inadvertently cueing the subject (Swann), since we as experimenters knew what the answers were." Soon Targ and Puthoff performed more experiments with Swann and the controls were tightened to eliminate the possibility of error. This time Swann was given the latitude and longitude of ten targets, in the end there would be ten runs, for a total of 100. "Only" the evaluations of the

neg: Ecliptic coordinate system as an epoch, when giving a position in ecliptic coordinates. The three most commonly used are: A position in the ecliptic coordinate system is thus typically specified "true equinox and ecliptic of date", "mean equinox and ecliptic of J2000.0", or similar. Note that there is no "mean ecliptic", as the ecliptic is not subject to small periodic oscillations. From antiquity through the 18th century, ecliptic longitude was commonly measured using twelve zodiacal signs, each of 30° longitude, a practice that continues in modern astrology. The signs approximately corresponded to the constellations crossed by the ecliptic. Longitudes were specified in signs,

neg: Horizontal coordinate system perfectly smooth Earth without an atmosphere. In practice, the "apparent" horizon has a slight negative altitude due to the curvature of Earth, the value of which gets more negative as the observer ascends higher above sea level. In addition, atmospheric refraction causes celestial objects very close to the horizon to appear about half a degree higher than they would if there were no atmosphere. Horizontal coordinate system The horizontal coordinate system, also known as topocentric coordinate system, is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. Coordinates of an object in the sky are

neg: Zodiac celestial coordinate system, or more specifically an ecliptic coordinate system, which takes the ecliptic as the origin of latitude and the Sun's position at vernal equinox as the origin of longitude. The English word ' derives from ', the Latinized form of the Ancient Greek "zōidiakòs kýklos" (), meaning "cycle or circle of little animals". "Zōidion" () is the diminutive of "zōion" (, "animal"). The name reflects the prominence of animals (and mythological hybrids) among the twelve signs. The zodiac was in use by the Roman era, based on concepts inherited by Hellenistic astronomy from Babylonian astronomy of the Chaldean

neg: Geohash translate to actual distance, see Haversine formula. Example of non-linearity for latitude-longitude system: Note that these limitations are not due to geohashing, and not due to latitude-longitude coordinates, but due to the difficulty of mapping coordinates on a sphere (non linear and with wrapping of values, similar to modulo arithmetic) to two dimensional coordinates and the difficulty of exploring a two dimensional space uniformly. The first is related to Geographical coordinate system and Map projection, and the other to Hilbert curve and z-order curve. Once a coordinate system is found that represents points linearly in distance and wraps up at

neg: Equinox island depicted in the middle of the ocean; the green arrows give cardinal directions. The following special cases are depicted: The March equinox occurs about when the Sun appears to cross the celestial equator northward. In the Northern Hemisphere, the term "vernal point" is used for the time of this occurrence and for the precise direction in space where the Sun exists at that time. This point is the origin of some celestial coordinate systems, which are usually rooted to an astronomical epoch since it gradually varies (precesses) over time: Strictly speaking, at the equinox, the Sun's ecliptic longitude is

neg: Celestial coordinate system a negative value for , it can be rendered positive by simply adding 360°. Again, in solving the equation for , use of the two-argument arctangent that accounts for the quadrant is recommended. Thus, again consistent with the convention of azimuth being measured from the south and opening positive to the west, where These equations are for converting equatorial coordinates to Galactic coordinates. formula_10 are the equatorial coordinates of the North Galactic Pole and formula_11 is the Galactic longitude of the North Celestial Pole. Referred to J2000.0 the values of these quantities are: If the equatorial coordinates are referred to

neg: Galactic coordinate system adopted by the IAU, the galactic coordinates of Sgr A* are latitude south, longitude . Since as defined the galactic coordinate system does not rotate with time, Sgr A* is actually decreasing in longitude at the rate of galactic rotation at the sun, , approximately 5.7 milliarcseconds per year (see Oort constants). In some applications use is made of rectangular coordinates based on galactic longitude and latitude and distance. In some work regarding the distant past or future the galactic coordinate system is taken as rotating so that the -axis always goes to the centre of the galaxy. There are

neg: Equinox (celestial coordinates) Solar System, only a few of the classical orbital elements are affected by a switch of equinox: the longitude of the ascending node and (to a much lesser extent) the inclination. If another set of orbital elements are used, such as the position and velocity vectors for a particular epoch, all components can be affected by a switch of equinox. Equinox is often confused with epoch, with the difference between the two being that the equinox addresses changes in the coordinate system, while the epoch addresses changes in the position of the celestial body itself. The currently used standard equinox

neg: Transport of structure we can consider "X" as a smooth manifold as well. That is, let formula_10 be a homeomorphism; we must define coordinate charts on "X", which we will do by "pulling back" coordinate charts on "M" through formula_6. Recall that a coordinate chart on formula_12 is an open set "U" together with an injective map for some "n"; to get such a chart on "X", we let Furthermore, it is required that the charts cover "M", we must check that the transported charts cover "X", which follows immediately from the fact that formula_6 is a bijection. Finally, since "M" is a

neg: Axes conventions called rolling, rotation about the "Y"-axis is called pitching, and rotation about the "Z"-axis is called yawing. For satellites orbiting the earth it is normal to use the Equatorial coordinate system. The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, the projections of the Earth's north and south geographic poles become the north and south celestial poles, respectively. Deep space satellites use other Celestial coordinate system, like the Ecliptic coordinate system. If the goal is to keep the shuttle during its orbits in a constant attitude with respect to the sky, e.g. in

neg: Coordinate space vector space. It is not necessary that every "n"-tuple from the cartesian product of the coordinate sets maps to an element of the space, nor is it necessary that every element have a unique set of coordinates. For example, a geographic coordinate system might assign coordinates of latitude and longitude to locations on the surface of the Earth, but here it will be necessary either to constrain the allowed coordinate pairs or to allow distinct sets of coordinates for the same points. Coordinate space In mathematics, a coordinate space is a space in which an ordered list of coordinates, each

neg: Location well defined in varies by context. London, for instance, has a legal boundary, but this is unlikely to completely match with general usage. An area within a town, such as Covent Garden in London, also almost always has some ambiguity as to its extent. An absolute location is designated using a specific pairing of latitude and longitude in a Cartesian coordinate grid — for example, a Spherical coordinate system or an ellipsoid-based system such as the World Geodetic System — or similar methods. For instance, the position of Lake Maracaibo in Venezuela can be expressed approximately in the WGS84 coordinate

neg: Celestial coordinate system It is based on the position of stars relative to an observer's ideal horizon. The "equatorial" coordinate system is centered at Earth's center, but fixed relative to the celestial poles and the vernal equinox. The coordinates are based on the location of stars relative to Earth's equator if it were projected out to an infinite distance. The equatorial describes the sky as seen from the solar system, and modern star maps almost exclusively use equatorial coordinates. The "equatorial" system is the normal coordinate system for most professional and many amateur astronomers having an equatorial mount that follows the movement of

neg: Ecliptic coordinate system Ecliptic coordinate system The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits of Solar System objects. Because most planets (except Mercury) and many small Solar System bodies have orbits with slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (northward) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates. The celestial equator and the ecliptic are slowly moving due to

neg: Geographic coordinate system Geographic coordinate system A geographic coordinate system is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined 3D Cartesian vector. A common choice of coordinates is latitude, longitude and elevation. To specify a location on a plane requires a map projection. The invention of a geographic coordinate system is generally credited to Eratosthenes

neg: Geographic coordinate system metric-based cartesian grid laid out on a conformally projected surface to locate positions on the surface of the Earth. The UTM system is not a single map projection but a series of sixty, each covering 6-degree bands of longitude. The UPS system is used for the polar regions, which are not covered by the UTM system. During medieval times, the stereographic coordinate system was used for navigation purposes. The stereographic coordinate system was superseded by the latitude-longitude system. Although no longer used in navigation, the stereographic coordinate system is still used in modern times to describe crystallographic orientations in the

neg: ECEF as the origin. The plane of reference can be aligned with the Earth's celestial equator, the ecliptic, or the Milky Way's galactic equator. These 3D celestial coordinate systems add actual distance as the Z axis to the equatorial, ecliptic, and galactic coordinate systems used in spherical astronomy. The distances involved are so great compared to the relative velocities of the stars, that for most purposes, the time component can be neglected. ECEF ECEF (acronym for "earth-centered, earth-fixed"), also known as ECR (initialism for "earth-centered rotational"), is a geographic and Cartesian coordinate system and is sometimes known as a "conventional terrestrial"

neg: Schwarzschild coordinates is that the "constant time coordinate surfaces" formula_8 form a family of (isometric) "spatial hyperslices". (This is not true for example in the Boyer–Lindquist chart for the exterior region of the Kerr vacuum, where the timelike coordinate vector is not hypersurface orthogonal.) In the Schwarzschild chart, the surfaces formula_9 appear as round spheres (when we plot loci in polar spherical fashion), and from the form of the line element, we see that the metric restricted to any of these surfaces is That is, these "nested coordinate spheres" do in fact represent geometric spheres with That is, they are "geometric round

neg: Light-cone coordinates Light-cone coordinates In special relativity, light-cone coordinates is a special coordinate system where two of the coordinates, x and x are null coordinates and all the other coordinates are spatial. Call them formula_1. Assume we are working with a (d,1) Lorentzian signature. Instead of the standard coordinate system (using Einstein notation) with formula_3 we have with formula_5, formula_6 and formula_7. Both x and x can act as "time" coordinates. One nice thing about light cone coordinates is that the causal structure is partially included into the coordinate system itself. A boost in the tx plane shows up as formula_8, formula_9,

neg: Universal Transverse Mercator coordinate system First let's compute some intermediate values: The final formulae are: Universal Transverse Mercator coordinate system The Universal Transverse Mercator (UTM) conformal projection uses a 2-dimensional Cartesian coordinate system to give locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, i.e. it is used to identify locations on the Earth independently of vertical position. However, it differs from that method in several respects. The UTM system is not a single map projection. The system instead divides the Earth into sixty zones, each being a six-degree band of longitude, and

neg: Universal Transverse Mercator coordinate system Universal Transverse Mercator coordinate system The Universal Transverse Mercator (UTM) conformal projection uses a 2-dimensional Cartesian coordinate system to give locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, i.e. it is used to identify locations on the Earth independently of vertical position. However, it differs from that method in several respects. The UTM system is not a single map projection. The system instead divides the Earth into sixty zones, each being a six-degree band of longitude, and uses a secant transverse Mercator projection in each zone. Most

neg: Synergetics (Fuller) that sense. An energy event is always special case. Whenever we have experienced energy, we have special case. The physicist's first definition of physical is that it is an experience that is extracorporeally, remotely, instrumentally apprehensible. Metaphysical includes all the experiences that are excluded by the definition of physical. Metaphysical is always generalized principle.(1075.11) Tetrahedral mensuration also involved substituting what Fuller called the "isotropic vector matrix" (IVM) for the standard XYZ coordinate system, as his principal conceptual backdrop for special case physicality: The synergetics coordinate system -- in contradistinction to the XYZ coordinate system -- is linearly referenced to the

neg: Isotropic coordinates hyperslices. The surfaces formula_9 appear as round spheres (when we plot loci in polar spherical fashion), and from the form of the line element, we see that the metric restricted to any of these surfaces is That is, these "nested coordinate spheres" do in fact represent geometric spheres, but the appearance of formula_11 rather than formula_12 shows that the radial coordinate does not correspond to area in the same way as for spheres in ordinary euclidean space. Compare Schwarzschild coordinates, where the radial coordinate does have its natural interpretation in terms of the nested spheres. The loci formula_13 mark the

neg: Spherical coordinate system the convention that in these cases the arbitrary coordinates are zero. To plot a dot from its spherical coordinates , where is inclination, move units from the origin in the zenith direction, rotate by about the origin towards the azimuth reference direction, and rotate by about the zenith in the proper direction. The geographic coordinate system uses the azimuth and elevation of the spherical coordinate system to express locations on Earth, calling them respectively longitude and latitude. Just as the two-dimensional Cartesian coordinate system is useful on the plane, a two-dimensional spherical coordinate system is useful on the surface of

neg: Tetrad formalism changing from one coordinate tetrad basis to another). Switching between multiple coordinate charts is necessary because, except in trivial cases, it is not possible for a single coordinate chart to cover the entire manifold. Changing to and between general tetrads is much similar and equally necessary (except for parallelizable manifolds). Any tensor can locally be written in terms of this coordinate tetrad or a general (co)tetrad. For example, the metric tensor formula_20 can be expressed as: (here we use the Einstein summation convention). Likewise, the metric can be expressed with respect to an arbitrary (co)tetrad as We can translate from

neg: Zodiac constellations can be traced even further back, to Bronze Age (First Babylonian dynasty) sources, including Gemini "The Twins", from MAŠ.TAB.BA.GAL.GAL "The Great Twins", and Cancer "The Crab", from AL.LUL "The Crayfish", among others. Around the end of the 5th century BC, Babylonian astronomers divided the ecliptic into twelve equal "signs", by analogy to twelve schematic months of thirty days each. Each sign contained thirty degrees of celestial longitude, thus creating the first known celestial coordinate system. Unlike modern astronomers, who place the beginning of the sign of Aries at the place of the Sun at the vernal equinox; Babylonian astronomers

neg: Singularity (mathematics) different frame. An example is the apparent singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (in the case of the example, jumping from longitude 0 to longitude 180 degrees). This discontinuity, however, is only apparent; it is an artifact of the coordinate system chosen, which is singular at the poles. A different coordinate system would eliminate the apparent discontinuity, e.g. by replacing the latitude/longitude representation with an -vector representation.

neg: Vaidya metric formula_3 by formula_4 and Eq(1) could be transformed into the "retarded(/outgoing) Schwarzschild metric" formula_5 or, we could instead employ the "advanced(/ingoing)" null coordinate formula_6 by formula_7 so Eq(1) becomes the "advanced(/ingoing) Schwarzschild metric" formula_8 Eq(3) and Eq(5), as static and spherically symmetric solutions, are valid for both ordinary celestial objects with finite radii and singular objects such as black holes. It turns out that, it is still physically reasonable if one extends the mass parameter formula_9 in Eqs(3) and Eq(5) from a constant to functions of the corresponding null coordinate, formula_10 and formula_11 respectively, thus formula_12 formula_13 The extended metrics

neg: Khmer language main clause. The various types of clauses in Khmer include the coordinate clause, the relative clause and the subordinate clause. Word order in clauses is the same for that of the basic sentences described above. Coordinate clauses do not necessarily have to be marked; they can simply follow one another. When explicitly marked, they are joined by words similar to English conjunctions such as ("and") and ("and then") or by clause-final conjunction-like adverbs and , both of which can mean "also" or "and also"; disjunction is indicated by ("or"). Relative clauses can be introduced by ("that") but, similar to coordinate

neg: Quaternions and spatial rotation quaternions will yield a unit quaternion. Also, the space of unit quaternions is "flat" in any infinitesimal neighborhood of a given unit quaternion. We can parameterize the surface of a sphere with two coordinates, such as latitude and longitude. But latitude and longitude are ill-behaved (degenerate) at the north and south poles, though the poles are not intrinsically different from any other points on the sphere. At the poles (latitudes +90° and −90°), the longitude becomes meaningless. It can be shown that no two-parameter coordinate system can avoid such degeneracy. We can avoid such problems by embedding the sphere in

neg: Geometry processing and "v" coordinate functions. The wobbliness and distortion apparent in the mass springs methods are due to high variations in the "u" and "v" coordinate functions. With this approach, the objective function becomes the Dirichlet energy on "u" and "v:" formula_57 There are a few other things to consider. We would like to minimize the angle distortion to preserve orthogonality. That means we would like formula_58. In addition, we would also like the mapping to have proportionally similar sized regions as the original. This results to setting the Jacobian of the "u" and "v" coordinate functions to 1. formula_59 Putting

neg: Coordinate conditions Coordinate conditions In general relativity, the laws of physics can be expressed in a generally covariant form. In other words, the description of the world as given by the laws of physics does not depend on our choice of coordinate systems. However, it is often useful to fix upon a particular coordinate system, in order to solve actual problems or make actual predictions. A coordinate condition selects such coordinate system(s). The Einstein field equations do not determine the metric uniquely, even if one knows what the metric tensor equals everywhere at an initial time. This situation is analogous to the

neg: Epoch (astronomy) or date of reference but also in their relations to other conditions of reference, such as coordinate systems specified by "equinox", or "equinox and equator", or "equinox and ecliptic" – when these are needed for fully specifying astronomical data of the considered type. When the data are dependent for their values on a particular coordinate system, the date of that coordinate system needs to be specified directly or indirectly. Celestial coordinate systems most commonly used in astronomy are equatorial coordinates and ecliptic coordinates. These are defined relative to the (moving) vernal equinox position, which itself is determined by the orientations

neg: Ecliptic coordinate system fundamental plane on the ecliptic plane, and the -axis toward the vernal equinox. The coordinates have a right-handed convention, that is, if one extends their right thumb upward, it simulates the -axis, their extended index finger the -axis, and the curl of the other fingers points generally in the direction of the -axis. These rectangular coordinates are related to the corresponding spherical coordinates by where is the obliquity of the ecliptic. Ecliptic coordinate system The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits of Solar System objects. Because most planets (except

neg: Well-known text a longitude axis. The coordinate system is related to Earth by the WGS84 geodetic datum: The WKT format can describe not only geographic coordinate reference systems, but also geocentric, projected, vertical, temporal and engineering ones (for example a coordinate reference system attached to a boat). The standard describes how to combine those coordinate reference systems together. A software capable to read coordinate reference systems in WKT 2 format can also read many (but not all) equivalent systems in WKT 1 format. Some caveats exist, notably the removal of the codice_10 element which is replaced by the codice_11 element. Another caveat

neg: Celestial coordinate system starting point of the longitudinal coordinates. The origin is the zero distance point, the "center of the celestial sphere", although the definition of celestial sphere is ambiguous about the definition of its center point. The "horizontal", or altitude-azimuth, system is based on the position of the observer on Earth, which revolves around its own axis once per sidereal day (23 hours, 56 minutes and 4.091 seconds) in relation to the star background. The positioning of a celestial object by the horizontal system varies with time, but is a useful coordinate system for locating and tracking objects for observers on Earth.

neg: Random coordinate descent coordinates, but to blocks of coordinates. Assume that we have space formula_37. This space has 5 coordinate directions, concretely formula_38 in which Random Coordinate Descent Method can move. However, one can group some coordinate directions into blocks and we can have instead of those 5 coordinate directions 3 block coordinate directions (see image). Random coordinate descent Randomized (Block) Coordinate Descent Method is an optimization algorithm popularized by Nesterov (2010) and Richtárik and Takáč (2011). The first analysis of this method, when applied to the problem of minimizing a smooth convex function, was performed by Nesterov (2010). In Nesterov's analysis the

neg: Computer-supported collaboration in improving work output? What words do workers come to work already understanding, what do they misunderstand, and how can we get them using the same words to mean the same thing? Study of content management, enterprise taxonomy and the other core instructional capital of the learning organization has become increasingly important due to ISO standards and the use of continuous improvement methods. Natural language and application commands tend to converge over time, becoming reflexive user interfaces. Where are the workers? Do we care? How do we coordinate them? How do we hire them, fire them, help them find the

neg: Chronometric singularity of time" to asking "what's north of the north pole". Chronometric singularity A chronometric singularity (also called a temporal or horological singularity) is a point at which time cannot be measured or described. An example involves a time at a coordinate singularity, e.g.a geographical pole. Since time on Earth is measured through longitudes, and no unique longitude exists at a pole, time is not defined uniquely at this point. There is a clear connection with coordinate singularities, as can be seen from this example. In relativity, similar singularities can be found in the case of Schwarzschild coordinates. Stephen Hawking once

neg: State Plane Coordinate System coordinate system to specify locations rather than a more complex spherical coordinate system (the geographic coordinate system of latitude and longitude). By using the Cartesian coordinate system's simple XY coordinates, "plane surveying" methods can be used, speeding up and simplifying calculations. Second, the system is highly accurate within each zone (error less than 1:10,000). Outside a specific state plane zone accuracy rapidly declines, thus the system is not useful for regional or national mapping. Most state plane zones are based on either a transverse Mercator projection or a Lambert conformal conic projection. The choice between the two map projections is

neg: Barycentric celestial reference system Solar System, its barycenter. This stable point for gravity helps to minimize relativistic effects from any observational frames of reference within the Solar System. The orientation of the BCRS coordinate system coincides with that of the International Celestial Reference System (ICRS). Both are centered at the barycenter of the Solar System, and both "point" in the same direction. That is, their axes are aligned with that of the International Celestial Reference Frame (ICRF), which was adopted as a standard by the IAU two years earlier (1998). The motivation of the ICRF is to define what "direction" means in space, by

neg: Derivations of the Lorentz transformations which we get Analogously, considering the motion of the origin of the frame "K", we get from which we get Combining these two gives and the transformation matrix has simplified, Now let us consider the group postulate "inverse element". There are two ways we can go from the "K"′ coordinate system to the "K" coordinate system. The first is to apply the inverse of the transform matrix to the "K"′ coordinates: The second is, considering that the "K"′ coordinate system is moving at a velocity "v" relative to the "K" coordinate system, the "K" coordinate system must be moving at

neg: Chronometric singularity Chronometric singularity A chronometric singularity (also called a temporal or horological singularity) is a point at which time cannot be measured or described. An example involves a time at a coordinate singularity, e.g.a geographical pole. Since time on Earth is measured through longitudes, and no unique longitude exists at a pole, time is not defined uniquely at this point. There is a clear connection with coordinate singularities, as can be seen from this example. In relativity, similar singularities can be found in the case of Schwarzschild coordinates. Stephen Hawking once compared by a talk-show guest's question about "before the beginning

neg: Coordinate descent do so are distributed across computer networks. Coordinate descent Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks. A line search along the coordinate direction can be performed at the current iterate to determine the appropriate step size. Coordinate descent is applicable in both differentiable and derivative-free contexts. Coordinate descent is based on the idea that

neg: Harmonic coordinate condition coordinate "x" is not actually a scalar, this is not a tensor equation. That is, it is not generally invariant. But coordinate conditions must not be generally invariant because they are supposed to pick out (only work for) certain coordinate systems and not others. Since the partial derivative of a coordinate is the Kronecker delta, we get: And thus, dropping the minus sign, we get the harmonic coordinate condition (also known as the de Donder gauge after Théophile de Donder): This condition is especially useful when working with gravitational waves. Consider the covariant derivative of the density of the reciprocal

neg: Spacetime formula_7 in space and by formula_8 in the formula_9-coordinate is: The constant formula_12, the speed of light, converts the units used to measure time (seconds) into units used to measure distance (meters). Note on nomenclature: Although for brevity, one frequently sees interval expressions expressed without deltas, including in most of the following discussion, it should be understood that in general, formula_13 means formula_7, etc. We are always concerned with "differences" of spatial or temporal coordinate values belonging to two events, and since there is no preferred origin, single coordinate values have no essential meaning. The equation above is similar to

neg: Equatorial coordinate system without a distance coordinate. The direction of sufficiently distant objects is the same for all observers, and it is convenient to specify this direction with the same coordinates for all. In contrast, in the horizontal coordinate system, a star's position differs from observer to observer based on their positions on the Earth's surface, and is continuously changing with the Earth's rotation. Telescopes equipped with equatorial mounts and setting circles employ the equatorial coordinate system to find objects. Setting circles in conjunction with a star chart or ephemeris allow the telescope to be easily pointed at known objects on the celestial

neg: Geographic coordinate conversion geodetic datums. Both geographic coordinate conversion and transformation will be considered in this article. This article assumes readers are already familiar with the content in the articles geographic coordinate system and geodetic datum. Informally, specifying a geographic location usually means giving the location's latitude and longitude. The numerical values for latitude and longitude can occur in a number of different formats: There are 60 minutes in a degree and 60 seconds in a minute. Therefore, to convert from a degrees minutes seconds format to a decimal degrees format, one may use the formula To convert back from decimal degree format

neg: Astrological sign longitude). Beyond the celestial bodies, other astrological points that are dependent on geographical location and time (namely, the Ascendant, the Midheaven, the Vertex and the houses' cusps) are also referenced within this ecliptic coordinate system. Various approaches to measuring and dividing the sky are currently used by differing systems of astrology, although the tradition of the Zodiac's names and symbols remain consistent. Western astrology measures from Equinox and Solstice points (points relating to equal, longest and shortest days of the tropical year), while Jyotiṣa or Vedic astrology measures along the equatorial plane (sidereal year). Precession results in Western astrology's zodiacal

neg: Four-force the concept of coordinate transformations between different coordinate systems. Assume that we know the correct expression for force in a coordinate system at which the particle is momentarily at rest. Then we can perform a transformation to another system to get the corresponding expression of force. In special relativity the transformation will be a Lorentz transformation between coordinate systems moving with a relative constant velocity whereas in general relativity it will be a general coordinate transformation. Consider the four-force formula_19 acting on a particle of mass formula_20 which is momentarily at rest in a coordinate system. The relativistic force formula_21

neg: First Point of Aries First Point of Aries The First Point of Aries, also known as the Cusp of Aries, is the location of the vernal equinox, used as a reference point in celestial coordinate systems; in diagrams using such coordinate systems, it is often indicated with the symbol ♈. Named for the constellation of Aries, it is one of the two points on the celestial sphere at which the celestial equator crosses the ecliptic, the other being the First Point of Libra, located exactly 180° from it. Due to precession of the equinoxes, currently, the position of the Sun on the March equinox

neg: First Point of Aries first point of Aries remains aligned with the Aries constellation. First Point of Aries The First Point of Aries, also known as the Cusp of Aries, is the location of the vernal equinox, used as a reference point in celestial coordinate systems; in diagrams using such coordinate systems, it is often indicated with the symbol ♈. Named for the constellation of Aries, it is one of the two points on the celestial sphere at which the celestial equator crosses the ecliptic, the other being the First Point of Libra, located exactly 180° from it. Due to precession of the equinoxes,

neg: Perifocal coordinate system Perifocal coordinate system The perifocal coordinate (PQW) system is a frame of reference for an orbit. The frame is centered at the focus of the orbit, i.e. the celestial body about which the orbit is centered. The unit vectors formula_1 and formula_2 lie in the plane of the orbit. formula_1 is directed towards the periapsis of the orbit and formula_2 has a true anomaly (formula_5) of 90 degrees past the periapsis. The third unit vector formula_6 is the angular momentum vector and is directed orthogonal to the orbital plane such that: And, since formula_6 is the angular momentum vector, it

neg: Local coordinates Local coordinates Local coordinates are measurement indices into a "local coordinate system" or a "local coordinate space". A simple example is using house numbers to locate a house on a street; the street is a local coordinate system within a larger system composed of city townships, states, countries, etc. Local systems exist for convenience. Continuing the geographic example, one could use latitude and longitude for all terrestrial locations, but unless one has a highly precise GPS device, this is impractical. In computer graphics and computer animation, local coordinate spaces are also useful for their ability to model independently transformable aspects

neg: Stone–Čech compactification "X". In fact, this closure is the Stone–Čech compactification. To verify this, we just need to verify that the closure satisfies the appropriate universal property. We do this first for "K" = [0, 1], where the desired extension of "f:" "X" → [0, 1] is just the projection onto the "f" coordinate in [0, 1]. In order to then get this for general compact Hausdorff "K" we use the above to note that "K" can be embedded in some cube, extend each of the coordinate functions and then take the product of these extensions. The special property of the unit

neg: Cartesian coordinate system out as a reference orientation, so the X-axis takes the orientation from geocenter out to [ 0 degrees longitude, 0 degrees latitude ]. Note that with 3 dimensions, and two perpendicular axes orientations pinned down for X and Z, the Y-axis is determined by the first two choices. In order to obey the right-hand rule, the Y-axis must point out from the geocenter to [ 90 degrees longitude, 0 degrees latitude ]. So what are the geocentric coordinates of the Empire State Building in New York City? Using [ longitude = −73.985656, latitude = 40.748433 ], Earth radius = 40,000/2π,

neg: Geographic coordinate system involves converting the spherical coordinates into Cartesian coordinates and applying a seven parameter transformation (translation, three-dimensional rotation), and converting back. In popular GIS software, data projected in latitude/longitude is often represented as a 'Geographic Coordinate System'. For example, data in latitude/longitude if the datum is the North American Datum of 1983 is denoted by 'GCS North American 1983'. The "latitude" (abbreviation: Lat., φ, or phi) of a point on Earth's surface is the angle between the equatorial plane and the straight line that passes through that point and through (or close to) the center of the Earth. Lines joining points

neg: Latitude "ξ", "μ", "χ", "θ"]. The geodetic latitude, or any of the auxiliary latitudes defined on the reference ellipsoid, constitutes with longitude a two-dimensional coordinate system on that ellipsoid. To define the position of an arbitrary point it is necessary to extend such a coordinate system into three dimensions. Three latitudes are used in this way: the geodetic, geocentric and parametric latitudes are used in geodetic coordinates, spherical polar coordinates and ellipsoidal coordinates respectively. At an arbitrary point consider the line which is normal to the reference ellipsoid. The geodetic coordinates are the latitude and longitude of the point on the

neg: Celestial coordinate system average number of local galaxies in the sky as seen from Earth. Conversions between the various coordinate systems are given. See the notes before using these equations. The classical equations, derived from spherical trigonometry, for the longitudinal coordinate are presented to the right of a bracket; simply dividing the first equation by the second gives the convenient tangent equation seen on the left. The rotation matrix equivalent is given beneath each case. This division is ambiguous because tan has a period of 180° () whereas cos and sin have periods of 360° (2). Note that azimuth () is measured from

neg: Universal Transverse Mercator coordinate system the Universal Transverse Mercator/Universal Polar Stereographic (UTM/UPS) coordinate system, which is a global (or universal) system of grid-based maps. The transverse Mercator projection is a variant of the Mercator projection, which was originally developed by the Flemish geographer and cartographer Gerardus Mercator, in 1570. This projection is conformal, which means it preserves angles and therefore shapes across small regions. However, it distorts distance and area. The UTM system divides the Earth into 60 zones, each 6° of longitude in width. Zone 1 covers longitude 180° to 174° W; zone numbering increases eastward to zone 60, which covers longitude 174°E to

neg: Spherical coordinate system that many loudspeakers tend toward omnidirectionality at lower frequencies. The spherical coordinate system is also commonly used in 3D game development to rotate the camera around the player's position. To a first approximation, the geographic coordinate system uses elevation angle (latitude) in degrees north of the equator plane, in the range , instead of inclination. Latitude is either geocentric latitude, measured at the Earth's center and designated variously by or geodetic latitude, measured by the observer's local vertical, and commonly designated . The azimuth angle (longitude), commonly denoted by , is measured in degrees east or west from some conventional

neg: Geographic coordinate conversion to degrees minutes seconds format, where the notation formula_3 means take the integer part of formula_4 and is called a floor function. A coordinate system conversion is a conversion from one coordinate system to another, with both coordinate systems based on the same geodetic datum. Common conversion tasks include conversion between geodetic and ECEF coordinates and conversion from one type of map projection to another. Geodetic coordinates (latitude formula_5, longitude formula_6, height formula_7) can be converted into ECEF coordinates using the following equation: where and formula_10 and formula_11 are the equatorial radius (semi-major axis) and the polar radius (semi-minor axis),

neg: Borel–Kolmogorov paradox on the sphere is equivalent to choosing the longitude "λ" uniformly from "[-π,π]" and choosing the latitude "φ" from "[-π/2,π/2]" with density formula_1. Then we can look at two different great circles: One distribution is uniform on the circle, the other is not. Yet both seem to be referring to the same great circle in different coordinate systems. In case (1) above, the conditional probability that the longitude λ lies in a set "E" given that φ = 0 can be written "P"(λ ∈ "E" | φ = 0). Elementary probability theory suggests this can be computed as "P"(λ ∈

neg: State Plane Coordinate System The panhandle of Alaska, whose maximum dimension is on a diagonal, uses an Oblique Mercator projection, which minimizes the combined error in the X and Y directions. In 1933, the North Carolina Department of Transportation asked the Coast and Geodetic Survey to assist in creating a comprehensive method for converting curvilinear coordinates (latitude and longitude) to a user-friendly, 2-dimensional Cartesian coordinate system. This request developed into the State Plane Coordinate System (SPCS), which is now the most widely used expression of coordinate information in local and regional surveying and mapping applications in the United States and its territories (Doyle, "Professional

neg: Digital Universe Atlas It therefore improves understanding of the surroundings of the solar system in terms of observer-neutral celestial coordinate systems—systems that are neither geocentric nor heliocentric—such as the galactic coordinate system and supergalactic coordinate system. The Digital Universe Atlas has spun off a commercial-grade planetarium platform from SCISS called Uniview that was featured in the White House star party on October 7, 2009. The Atlas database and Partiview interface is compatible with professional planetarium software such as Evans & Sutherland's Digistar and Sky-Skan's DigitalSky 2. Digital Universe Atlas Digital Universe Atlas is a free open source software planetarium application, available under the

neg: Hammer projection the intermediate variable The longitude and latitudes can then be calculated by where "λ" is the longitude from the central meridian and "φ" is the latitude. Visually, the Aitoff and Hammer projections are very similar. The Hammer has seen more use because of its equal-area property. The Mollweide projection is another equal-area projection of similar aspect, though with straight parallels of latitude, unlike the Hammer's curved parallels. William A. Briesemeister presented a variant of the Hammer in 1953. In this version, the central meridian is set to 10°E, the coordinate system is rotated to bring the 45°N parallel to the