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Great Circle Route
Great-circle navigation or orthodromic navigation (related to orthodromic course; from the Greek ''ορθóς'', right angle, and ''δρóμος'', path) is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such routes yield the shortest distance between two points on the globe. Course The great circle path may be found using spherical trigonometry; this is the spherical version of the '' inverse geodetic problem''. If a navigator begins at ''P''1 = (φ1,λ1) and plans to travel the great circle to a point at point ''P''2 = (φ2,λ2) (see Fig. 1, φ is the latitude, positive northward, and λ is the longitude, positive eastward), the initial and final courses α1 and α2 are given by formulas for solving a spherical triangle :\begin \tan\alpha_1&=\frac,\\ \tan\alpha_2&=\frac,\\ \end where λ12 = λ2 − λ1In the article on great-circle distances, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth Radius
Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, denoted ''a'') to a minimum of nearly (polar radius, denoted ''b''). A ''nominal Earth radius'' is sometimes used as a unit of measurement in astronomy and geophysics, which is recommended by the International Astronomical Union to be the equatorial value. A globally-average value is usually considered to be with a 0.3% variability (±10 km) for the following reasons. The International Union of Geodesy and Geophysics (IUGG) provides three reference values: the ''mean radius'' (R) of three radii measured at two equator points and a pole; the ''authalic radius'', which is the radius of a sphere with the same surface area (R); and the ''volumetric radius'', which is the radius of a sphere having the same volume as the ellipsoid (R). All three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shanghai
Shanghai (; , , Standard Mandarin pronunciation: ) is one of the four direct-administered municipalities of the People's Republic of China (PRC). The city is located on the southern estuary of the Yangtze River, with the Huangpu River flowing through it. With a population of 24.89 million as of 2021, Shanghai is the most populous urban area in China with 39,300,000 inhabitants living in the Shanghai metropolitan area, the second most populous city proper in the world (after Chongqing) and the only city in East Asia with a GDP greater than its corresponding capital. Shanghai ranks second among the administrative divisions of Mainland China in human development index (after Beijing). As of 2018, the Greater Shanghai metropolitan area was estimated to produce a gross metropolitan product ( nominal) of nearly 9.1 trillion RMB ($1.33 trillion), exceeding that of Mexico with GDP of $1.22 trillion, the 15th largest in the world. Shanghai is one of the world's major centers for f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valparaíso
Valparaíso (; ) is a major city, seaport, naval base, and educational centre in the commune of Valparaíso, Chile. "Greater Valparaíso" is the second largest metropolitan area in the country. Valparaíso is located about northwest of Santiago by road and is one of the Pacific Ocean's most important seaports. Valparaíso is the capital of Chile's second most populated administrative region and has been the headquarters for the Chilean Navy since 1817 and the seat of the Chilean National Congress since 1990. Valparaíso played an important geopolitical role in the second half of the 19th century when it served as a major stopover for ships traveling between the Atlantic and Pacific oceans by crossing the Straits of Magellan. Valparaíso experienced rapid growth during its golden age, as a magnet for European immigrants, when the city was known by international sailors as "Little San Francisco" and "The Jewel of the Pacific". Notable inheritances from its golden age include Lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Great Ellipse
150px, A spheroid A great ellipse is an ellipse passing through two points on a spheroid and having the same center as that of the spheroid. Equivalently, it is an ellipse on the surface of a spheroid and centered on the origin, or the curve formed by intersecting the spheroid by a plane through its center. For points that are separated by less than about a quarter of the circumference of the earth, about 10\,000\,\mathrm, the length of the great ellipse connecting the points is close (within one part in 500,000) to the geodesic distance. The great ellipse therefore is sometimes proposed as a suitable route for marine navigation. The great ellipse is special case of an earth section path. Introduction Assume that the spheroid, an ellipsoid of revolution, has an equatorial radius a and polar semi-axis b. Define the flattening f=(a-b)/a, the eccentricity e=\sqrt, and the second eccentricity e'=e/(1-f). Consider two points: A at (geographic) latitude \phi_1 and longitude \l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhumb Line
In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north. Introduction The effect of following a rhumb line course on the surface of a globe was first discussed by the Portuguese mathematician Pedro Nunes in 1537, in his ''Treatise in Defense of the Marine Chart'', with further mathematical development by Thomas Harriot in the 1590s. A rhumb line can be contrasted with a great circle, which is the path of shortest distance between two points on the surface of a sphere. On a great circle, the bearing to the destination point does not remain constant. If one were to drive a car along a great circle one would hold the steering wheel fixed, but to follow a rhumb line one would have to turn the wheel, turning it more sharply as the poles are approached. In other words, a great circle is locally "straight" with zero geodesic curvature, whereas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesics On An Ellipsoid
The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an ''oblate ellipsoid'', a slightly flattened sphere. A ''geodesic'' is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry . If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. Finally, if the ellipsoid is further perturbed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphere Geodesic 2sigma
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the centre of the sphere, and is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings. Basic terminology As mentioned earlier is the sph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook ''Spherical trigonometry for the use of colleges and Schools''. Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods. P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Azimuth
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. 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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Node
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes. Planes of reference Common planes of reference include the following: * For a geocentric orbit, Earth's equatorial plane. In this case, non-inclined orbits are called ''equatorial''. * For a heliocentric orbit, the ecliptic or invariable plane. In this case, non-inclined orbits are called ''ecliptic''. * For an orbit outside the Solar System, the plane through the primary perpendicular to a line through the observer and the primary (called the ''plane of the sky''). Node distinction If a reference direction from one side of the plane of reference to the other is defined, the two nodes can be distinguished. For geocentric and heliocentric orbits, the ascending node (or north node) is where the orbiting object moves north through the plane of reference, and the descending nod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Way-point
A waypoint is an intermediate point or place on a route or line of travel, a stopping point or point at which course is changed, the first use of the term tracing to 1880. In modern terms, it most often refers to coordinates which specify one's position on the globe at the end of each "leg" (stage) of an air flight or sea passage, the generation and checking of which are generally done computationally (with a computer or other programmed device). Hence, the term connotes a reference point in physical space, most often associated with navigation, especially in the sea or air—e.g., in the case of sea navigation, a longitudinal and latitudinal coordinate or a GPS point in open water, a location near a known mapped shoal or other entity in a body of water, a point a fixed distance off of a geographical entity such as a lighthouse or harbour entrance, etc. When such a point corresponds to an element of physical geography on land, it can be referred to as a landmark. In air navigation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
