|
Geodetic Coordinates
Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a '' reference ellipsoid''. They include geodetic latitude (north/south) , ''longitude'' (east/west) , and ellipsoidal height (also known as geodetic height). The triad is also known as Earth ellipsoidal coordinates (not to be confused with '' ellipsoidal-harmonic coordinates''). Definitions Longitude measures the rotational angle between the zero meridian and the measured point. By convention for the Earth, Moon and Sun, it is expressed in degrees ranging from −180° to +180°. For other bodies a range of 0° to 360° is used. For this purpose, it is necessary to identify a ''zero meridian'', which for Earth is usually the Prime Meridian. For other bodies a fixed surface feature is usually referenced, which for Mars is the meridian passing through the crater Airy-0. It is possible for many different coordinate systems to be defined upon the same reference ellipsoid. Geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signed Distance
In mathematics and its applications, the signed distance function or signed distance field (SDF) is the orthogonal distance of a given point ''x'' to the boundary of a set Ω in a metric space (such as the surface of a geometric shape), with the sign determined by whether or not ''x'' is in the interior of Ω. The function has positive values at points ''x'' inside Ω, it decreases in value as ''x'' approaches the boundary of Ω where the signed distance function is zero, and it takes negative values outside of Ω. However, the alternative convention is also sometimes taken instead (i.e., negative inside Ω and positive outside). The concept also sometimes goes by the name oriented distance function/field. Definition Let be a subset of a metric space with metric , and \partial\Omega be its boundary. The distance between a point of and the subset \partial\Omega of is defined as usual as : d(x, \partial \Omega) = \inf_d(x, y), where \inf denotes the infimum. The ''sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinate System
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are * the radial distance along the line connecting the point to a fixed point called the origin; * the polar angle between this radial line and a given ''polar axis''; and * the azimuthal angle , which is the angle of rotation of the radial line around the polar axis. (See graphic regarding the "physics convention".) Once the radius is fixed, the three coordinates (''r'', ''θ'', ''φ''), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle) is called the ''reference plane'' (sometimes '' fundamental plane''). Terminology The radial distance from the fixed point of origin is also called the ''radius'', or ''radial line'', or ''radial coor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth's 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 (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted ''a'') of about to a minimum (polar radius, denoted ''b'') of nearly . 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 values are about . Other ways to define and measure the Earth's radius involve either the spheroid's radius of curvature or the actual topography. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Earth
Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Ancient Greek philosophy, Greek philosophers. In the 3rd century BC, History of geodesy#Hellenic world, Hellenistic astronomy established the figure of the Earth, roughly spherical shape of Earth as a physical fact and calculated the Earth's circumference. This knowledge was gradually adopted throughout the Old World during late antiquity, Late Antiquity and the Middle Ages, displacing earlier beliefs in a flat earth.Adoption by China via European science: and A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation (1519–1522). The realization that the figure of the Earth is more accurately described as an Earth ellipsoid, ellipsoid dates to the 17th century, as described by Isa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth Ellipsoid
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the ''equatorial axis'' () and the ''polar axis'' (); their radial difference is slightly more than 21 km, or 0.335% of (which is not quite 6,400 km). Many methods exist for determination of the axes of an Earth ellipsoid, ranging from meridian arcs up to modern satellite geodesy or the analysis and interconnection of continental geodetic networks. Amongst the different set of data used in national surveys are several of special importance: the Bessel ellipsoid of 1841, the international Hayfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interplanetary Spaceflight
Interplanetary spaceflight or interplanetary travel is spaceflight (Human spaceflight, crewed or Uncrewed spacecraft, uncrewed) between bodies within a single planetary system. Spaceflights become interplanetary by accelerating spacecrafts beyond orbital speed, reaching escape velocity relative to Earth at 11.2 km/s, entering heliocentric orbit, possibly accelerating further, often by performing gravity assist Flyby (spaceflight), flybys at Earth and other planets. Most of today's spaceflight remains Earth bound, with much less being interplanetary, all of which performed by uncrewed spacecrafts, and only just a few spaceflights having accelerated beyond, to system escape velocity, eventually performing interstellar spaceflight. Uncrewed space probes have flown to all the observed planets in the Solar System as well as to dwarf planets Pluto and Ceres (dwarf planet), Ceres, and several asteroids. Orbiters and landers return more information than fly-by missions. Crewed flights ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equatorial Bulge
An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere. On Earth The planet Earth has a rather slight equatorial bulge; its equatorial diameter is about greater than its polar diameter, with a difference of about of the equatorial diameter. If Earth were scaled down to a globe with an equatorial diameter of , that difference would be only . While too small to notice visually, that difference is still more than twice the largest deviations of the actual surface from the ellipsoid, including the tallest mountains and deepest oceanic trenches. Earth's rotation also affects the sea level, the imaginary surface used as a reference frame from which to measure altitudes. This surface coincides with the mean water surface level in oceans, and is extrapolated over land by taking into account the loc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Altitude
A geocentric orbit, Earth-centered orbit, or Earth orbit involves any object orbiting Earth, such as the Moon or artificial satellites. In 1997, NASA estimated there were approximately 2,465 artificial satellite payloads orbiting Earth and 6,216 pieces of space debris as tracked by the Goddard Space Flight Center. More than 16,291 objects previously launched have undergone orbital decay and entered Earth's atmosphere. A spacecraft enters orbit when its centripetal acceleration due to gravity is less than or equal to the centrifugal acceleration due to the horizontal component of its velocity. For a low Earth orbit, this velocity is about ; by contrast, the fastest crewed airplane speed ever achieved (excluding speeds achieved by deorbiting spacecraft) was in 1967 by the North American X-15. The energy required to reach Earth orbital velocity at an altitude of is about 36 MJ/kg, which is six times the energy needed merely to climb to the corresponding altitude. Sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Mechanics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Astrodynamics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun). History Until th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthometric Height
The orthometric height (symbol ''H'') is the vertical distance along the plumb line from a point of interest to a reference surface known as the ''geoid'', the vertical datum that approximates mean sea level. Orthometric height is one of the scientific formalizations of a layman's " height above sea level", along with other types of heights in Geodesy. In the US, the current NAVD88 datum is tied to a defined elevation at one point rather than to any location's exact mean sea level. Orthometric heights are usually used in the US for engineering work, although dynamic height may be chosen for large-scale hydrological purposes. Heights for measured points are shown on National Geodetic Survey data sheets, data that was gathered over many decades by precise spirit leveling over thousands of miles. Alternatives to orthometric height include dynamic height and normal height, and various countries may choose to operate with those definitions instead of orthometric. They may also ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geocentric Altitude
In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, and planets all orbit Earth. The geocentric model was the predominant description of the cosmos in many European ancient civilizations, such as those of Aristotle in Classical Greece and Ptolemy in Roman Egypt, as well as during the Islamic Golden Age. Two observations supported the idea that Earth was the center of the Universe. First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. The stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographic poles of Earth. Second, Earth seems to be unmoving from the perspective of an earthbound observer; i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
