Colatitude
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Colatitude
In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. Here Southern latitudes are defined to be negative, and as a result the colatitude is a non-negative quantity, ranging from zero at the North pole to 180° at the South pole. The colatitude corresponds to the conventional 3D polar angle in spherical coordinates, as opposed to the latitude as used in cartography. Examples Latitude and colatitude sum up to 90°. Astronomical use The colatitude is most useful in astronomy because it refers to the zenith distance of the celestial poles. For example, at latitude 42°N, Polaris (approximately on the North celestial pole) has an altitude of 42°, so the distance from the zenith (overhead point) to Polaris is . Adding the declination of a star to the observer's colatitude gives the maximum latitude of that star (its angle from the horizon at culmination or upper transit). For ex ...
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Latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or ''parallels'', run east–west as circles parallel to the equator. Latitude and ''longitude'' are used together as a coordinate pair to specify a location on the surface of the Earth. On its own, the term "latitude" normally refers to the ''geodetic latitude'' as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or ''normal'') to the ellipsoidal surface from the point, and the plane of the equator. Background Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface is modeled by the geoid, a surface which approximates the mean sea level over the ocean ...
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Spherical Coordinate System
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measured from a fixed zenith direction, and the ''azimuthal angle'' of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called '' colatitude'', ''zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will us ...
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Celestial Coordinate System
Astronomical coordinate systems are organized arrangements for specifying positions of satellites, planets, stars, galaxies, and other celestial objects relative to physical reference points available to a situated observer (e.g. the true horizon and north cardinal direction to an observer situated on the Earth's surface). Coordinate systems in astronomy 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. 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 into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, have the same fundamental () plane and primary (-axis) direction, such as a rotation axis. Each coordinate system is named after its choice of fundamental ...
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Schwarzschild Metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916, and around the same time independently by Johannes Droste, who published his more complete and modern-looking discussion four months after Schwarzschild. According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum. A Schwar ...
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Juneau
The City and Borough of Juneau, more commonly known simply as Juneau ( ; tli, Dzánti K'ihéeni ), is the capital city of the state of Alaska. Located in the Gastineau Channel and the Alaskan panhandle, it is a unified municipality and the second- largest city in the United States by area. Juneau was named the capital of Alaska in 1906, when the government of what was then the District of Alaska was moved from Sitka as dictated by the U.S. Congress in 1900. The municipality unified on July 1, 1970, when the city of Juneau merged with the city of Douglas and the surrounding Greater Juneau Borough to form the current municipality, which is larger by area than both Rhode Island and Delaware. Downtown Juneau () is nestled at the base of Mount Juneau and across the channel from Douglas Island. As of the 2020 census, the City and Borough had a population of 32,255, making it the third-most populous city in Alaska after Anchorage and Fairbanks. Juneau experiences a daily influx o ...
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Perth, Western Australia
Perth is the capital and largest city of the Australian state of Western Australia. It is the fourth most populous city in Australia and Oceania, with a population of 2.1 million (80% of the state) living in Greater Perth in 2020. Perth is part of the South West Land Division of Western Australia, with most of the metropolitan area on the Swan Coastal Plain between the Indian Ocean and the Darling Scarp. The city has expanded outward from the original British settlements on the Swan River, upon which the city's central business district and port of Fremantle are situated. Perth is located on the traditional lands of the Whadjuk Noongar people, where Aboriginal Australians have lived for at least 45,000 years. Captain James Stirling founded Perth in 1829 as the administrative centre of the Swan River Colony. It was named after the city of Perth in Scotland, due to the influence of Stirling's patron Sir George Murray, who had connections with the area. It gained city stat ...
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Circumpolar Star
A circumpolar star is a star that, as viewed from a given latitude on Earth, never sets below the horizon due to its apparent proximity to one of the celestial poles. Circumpolar stars are therefore visible from said location toward the nearest pole for the entire night on every night of the year (and would be continuously visible throughout the day too, were they not overwhelmed by the Sun's glare). Others are called ''seasonal'' stars. All circumpolar stars lie within a circumpolar circle whose size is determined by the observer's latitude. Specifically, the angular measure of the radius of this circle equals the observer's latitude. The closer the observer is to the North or South Pole, the larger the circumpolar circle is. Before the definition of the Arctic was formalized as the region north of the Arctic Circle which experiences the Midnight sun, it more broadly meant those places where the 'bear' constellations (Ursa Major, the Great Bear, and Ursa Minor, the Little Bear ...
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Alpha Centauri
Alpha Centauri ( Latinized from α Centauri and often abbreviated Alpha Cen or α Cen) is a triple star system in the constellation of Centaurus. It consists of 3 stars: Alpha Centauri A (officially Rigil Kentaurus), Alpha Centauri B (officially Toliman) and Alpha Centauri C (officially Proxima Centauri). Proxima Centauri is also the closest star to the Sun at 4.2465 light-years (1.3020 pc). Alpha Centauri A and B are Sun-like stars ( Class G and K, respectively), and together they form the binary star system Alpha Centauri AB. To the naked eye, the two main components appear to be a single star with an apparent magnitude of −0.27. It is the brightest star in the constellation and the third-brightest in the night sky, outshone only by Sirius and Canopus. Alpha Centauri A has 1.1 times the mass and 1.5 times the luminosity of the Sun, while Alpha Centauri B is smaller and cooler, at 0.9 times the Sun's mass and less than 0.5 times its luminosity. The pair or ...
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Culmination
In observational astronomy, culmination is the passage of a celestial object (such as the Sun, the Moon, a planet, a star, constellation or a deep-sky object) across the observer's local meridian. These events were also known as meridian transits, used in timekeeping and navigation, and measured precisely using a transit telescope. During each day, every celestial object appears to move along a circular path on the celestial sphere due to the Earth's rotation creating two moments when it crosses the meridian. Except at the geographic poles, any celestial object passing through the meridian has an upper culmination, when it reaches its highest point above the horizon, and nearly twelve hours later, is followed by a lower culmination, when it reaches its lowest point. The time of ''culmination'' (when the object culminates) is often used to mean upper culmination. An object's altitude (''A'') in degrees at its upper culmination is equal to 90 minus the observer's latitude (''L'') ...
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Horizon
The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether it intersects the relevant body's surface or not. The ''true horizon'' is a theoretical line, which can only be observed to any degree of accuracy when it lies along a relatively smooth surface such as that of Earth's oceans. At many locations, this line is obscured by terrain, and on Earth it can also be obscured by life forms such as trees and/or human constructs such as buildings. The resulting intersection of such obstructions with the sky is called the ''visible horizon''. On Earth, when looking at a sea from a shore, the part of the sea closest to the horizon is called the offing. Pronounced, "Hor-I-zon". The true horizon surrounds the observer and it is typically assumed to be a circle, drawn on the surface of a perfectly spherica ...
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Zenith
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" point on the celestial sphere. Origin The word "zenith" derives from an inaccurate reading of the Arabic expression (), meaning "direction of the head" or "path above the head", by Medieval Latin scribes in the Middle Ages (during the 14th century), possibly through Old Spanish. It was reduced to "samt" ("direction") and miswritten as "senit"/"cenit", the "m" being misread as "ni". Through the Old French "cenith", "zenith" first appeared in the 17th century. Relevance and use The term ''zenith'' sometimes means the highest point, way, or level reached by a celestial body on its daily apparent path around a given point of observation. This sense of the word is often used to describe the position of the Sun ("The sun reached its zenit ...
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Polaris
Polaris is a star in the northern circumpolar constellation of Ursa Minor. It is designated α Ursae Minoris ( Latinized to ''Alpha Ursae Minoris'') and is commonly called the North Star or Pole Star. With an apparent magnitude that fluctuates around 1.98, it is the brightest star in the constellation and is readily visible to the naked eye at night. The position of the star lies less than 1° away from the north celestial pole, making it the current northern pole star. The stable position of the star in the Northern Sky makes it useful for navigation. As the closest Cepheid variable its distance is used as part of the cosmic distance ladder. The revised ''Hipparcos'' stellar parallax gives a distance to Polaris of about , while the successor mission ''Gaia'' gives a distance of about . Calculations by other methods vary widely. Although appearing to the naked eye as a single point of light, Polaris is a triple star system, composed of the primary, a yellow super ...
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