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Vertical Circle
In spherical geometry, a vertical circle is a great circle on the celestial sphere that is perpendicular to the horizon. Therefore, it contains the vertical direction, passing through the zenith and the nadir. There is a vertical circle for any given azimuth, where azimuth is the angle measured east from the north on the celestial horizon. The vertical circle which is in the east–west direction is called the prime vertical. The vertical circle which is on the north–south direction is called the local celestial meridian (LCM), or principal vertical. Vertical circles are part of the horizontal coordinate system The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and ''azimuth''. Therefore, the horizontal coord .... See also * Vertical circle (instrument) References {{DEFAULTSORT:Vertical Circle Astronomical coordinate system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Geometry
300px, A sphere with a spherical triangle on it. Spherical geometry or spherics () is the geometry of the two-dimensional surface of a sphere or the -dimensional surface of higher dimensional spheres. Long studied for its practical applications to astronomy, navigation, and geodesy, spherical geometry and the metrical tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important differences. The sphere can be studied either ''extrinsically'' as a surface embedded in 3-dimensional Euclidean space (part of the study of solid geometry), or ''intrinsically'' using methods that only involve the surface itself without reference to any surrounding space. Principles In plane (Euclidean) geometry, the basic concepts are points and (straight) lines. In spherical geometry, the basic concepts are points and great circles. However, two great circles on a plane intersect in two antipodal points, unlike coplan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Great Circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Discussion Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space. For any pair of distinct non- antipodal points on the sphere, there is a unique great circle passing through both. (Every great circle through any point also passes through its antipodal point, so there are infinitely many great circles through two antipodal points.) The shorter of the two great-circle arcs between two distinct points on the sphere is called the ''minor arc'', and is the shortest surface-path between them. Its arc length is the great-circle distance between the points (the intrinsic distance on a sphere), and is proportional to the measure of the central angle formed by the two points and the center of the sphere. A great circle is the largest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celestial Sphere
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location. The celestial sphere is a conceptual tool used in spherical astronomy to specify the position of an object in the sky without consideration of its linear distance from the observer. The celestial equator divides the celestial sphere into northern and southern hemispheres. Description Because astronomical objects are at such remote distances, casual observation of the sky offers no information on their actual distances. All celestial objects seem equally far away, as if fixed onto the inside of a sphere with a large but unknown radius, which appears to rotate westwa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horizon
The horizon is the apparent curve 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 curve 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 sph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertical Direction
In astronomy, geography, and related sciences and contexts, a ''Direction (geometry, geography), direction'' or ''plane (geometry), plane'' passing by a given point is said to be vertical if it contains the local gravity direction at that point. Conversely, a direction, plane, or surface is said to be horizontal (or ''leveled'') if it is everywhere perpendicular to the vertical direction. In general, something that is vertical can be drawn from up to down (or down to up), such as the y-axis in the Cartesian coordinate system. Historical definition The word ''horizontal'' is derived from the Latin , which derives from the Greek , meaning 'separating' or 'marking a boundary'. The word ''vertical'' is derived from the late Latin ', which is from the same root as ''vertex'', meaning 'highest point' or more literally the 'turning point' such as in a whirlpool. Girard Desargues defined the vertical to be perpendicular to the horizon in his 1636 book ''Perspective''. Geophysical defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zenith
The zenith (, ) is the imaginary point on the celestial sphere directly "above" a particular location. "Above" means in the vertical direction (Vertical and horizontal, plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" point on the celestial sphere. The direction opposite of the zenith is the nadir. Origin The word ''zenith'' derives from an inaccurate reading of the Arabic language, 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 culmination, highest point, way, or level reached by a celestial body on its daily apparent path around a given poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nadir (astronomy)
The nadir is the direction pointing directly ''below'' a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface. The direction opposite of the nadir is the zenith. Etymology Although it entered English via other European languages, the word “nadir” is ultimately an Arabic loanword. It comes from the Arabic word “nazir”, meaning “opposite to”. More specifically, it originated from the Arabic phrase “nazir as-samt”, meaning “ heopposite direction”. Hebrew (whether ancient or modern) is a related language to Arabic, as they are both Semitic languages. Hebrew also has a word “nadir” (נדיר), but with a somewhat different meaning: it is an adjective meaning “rare”. However, the same word also has a specialized usage to match its meaning in other languages like English. Definitions Space science Since the concept of ''being below'' is itself somewhat vague, scientists define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Azimuth
An azimuth (; from ) is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system. Mathematically, the relative position vector from an observer ( origin) to a point of interest is projected perpendicularly onto a reference plane (the horizontal plane); the angle between the projected vector and a reference vector on the reference plane is called the azimuth. When used as a celestial coordinate, the azimuth is the horizontal direction of a star or other astronomical object in the sky. The star is the point of interest, the reference plane is the local area (e.g. a circular area with a 5 km radius at sea level) around an observer on Earth's surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane. Azimuth is usually measured in degrees (°), in the positive range 0° to 360° or in the signed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Vertical
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meridian (astronomy)
In astronomy, the meridian is the great circle passing through the celestial poles, as well as the zenith and nadir of an observer's location. Consequently, it contains also the north and south points on the horizon, and it is perpendicular to the celestial equator and horizon. Meridians, celestial and geographical, are determined by the pencil of planes passing through the Earth's rotation axis. For a location ''not'' on this axis, there is a unique meridian plane in this axial-pencil through that location. The intersection of this plane with Earth's surface defines two '' geographical meridians'' (either one east and one west of the prime meridian, or else the prime meridian itself and its anti-meridian), and the intersection of the plane with the celestial sphere is the celestial meridian for that location and time. There are several ways to divide the meridian into semicircles. In one approach, the observer's upper meridian extends from a celestial pole and passes t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horizontal Coordinate System
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and ''azimuth''. Therefore, the horizontal coordinate system is sometimes called the az/el system, the alt/az system, or the alt-azimuth system, among others. In an altazimuth mount of a telescope, the instrument's two axes follow altitude and azimuth. Definition This celestial coordinate system divides the sky into two hemispheres: The upper hemisphere, where objects are above the horizon and are visible, and the lower hemisphere, where objects are below the horizon and 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 the great circle on the celestial sphere whose plane is normal to the local gravity vector (the vertical direction). In practice, the horizon can be define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertical Circle (instrument)
The vertical circle is an optical instrument used to measure angles in astronomy, which name is derived from the mathematical concept of the vertical circle from spherical geometry. It is a device for measuring astronomical angles, which can be rotated in altitude and azimuth. It consists of a telescope (in astronomical geodesy occasionally also with a reflecting telescope), which is mounted on a horizontal tilting axis and is supported by a stable altazimuth mount. It is similar in design to the meridian circle, but the latter only has a horizontal tilting axis without the means to change azimuth. The angular movements around the tilting and standing axes are measured with large, finely divided circles and a reading microscope.{{cite book , last=Chauvenet , first=William , author-link=William Chauvenet , date=1863 , title=A Manual of Spherical and Practical Astronomy , volume=II: Theory and use of astronomical instruments , url=https://books.google.com/books?id=AVI8pz41ia8C&pg=PA31 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
