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Prolate Cyclogon Generated By An Equilateral Triangle
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spheroids
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The ball (gridiron football), American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M's, M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation of the Earth, rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattening, flattened in the direction of its axis of rotation. For that reason, in cartography and geod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figure Of The Earth
Figure of the Earth is a Jargon, term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A Spherical Earth, sphere is a well-known historical approximation of the figure of the Earth that is satisfactory for many purposes. Several models with greater accuracy (including Earth ellipsoid, ellipsoid) have been developed so that Geographic coordinate system, coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns. Motivation Earth's Topography, topographic surface is apparent with its variety of land forms and water areas. This topographic surface is generally the concern of topographers, Hydrography, hydrographers, and Geophysics, geophysicists. While it is the surface on which Earth measurements are made, mathematically modeling it while taking the irregularities into account would be extremely compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Axis
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids. Formal treatment Formally the rotational symmetry is symmetry with respect to some or all rotations in ''m''-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of ''E''+(''m'') (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is hom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter De Gruyter
Walter de Gruyter GmbH, known as De Gruyter (), is a German scholarly publishing house specializing in academic literature. History The roots of the company go back to 1749 when Frederick the Great granted the Königliche Realschule in Berlin the royal privilege to open a bookstore and "to publish good and useful books". In 1800, the store was taken over by Georg Reimer (1776–1842), operating as the ''Reimer'sche Buchhandlung'' from 1817, while the school’s press eventually became the ''Georg Reimer Verlag''. From 1816, Reimer used the representative Sacken'sche Palace on Berlin's Wilhelmstraße for his family and the publishing house, whereby the wings contained his print shop and press. The building became a meeting point for Berlin salon life and later served as the official residence of the president of Germany. Born in Ruhrort in 1862, Walter de Gruyter took a position with Reimer Verlag in 1894. By 1897, at the age of 35, he had become sole proprietor of the h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geopotential Model
In geophysics and physical geodesy, a geopotential model is the theoretical analysis of measuring and calculating the effects of Earth's gravitational field (the geopotential). Newton's law Newton's law of universal gravitation states that the gravitational force ''F'' acting between two point masses ''m''1 and ''m''2 with centre of mass separation ''r'' is given by :\mathbf = - G \frac\mathbf where ''G'' is the gravitational constant and r̂ is the radial unit vector. For a non-pointlike object of continuous mass distribution, each mass element ''dm'' can be treated as mass distributed over a small volume, so the volume integral over the extent of object 2 gives: with corresponding gravitational potential where ρ = ρ(''x'', ''y'', ''z'') is the mass density at the volume element and of the direction from the volume element to point mass 1. u is the gravitational potential energy per unit mass. The case of a homogeneous sphere In the special case of a sphere with a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth's Gravity
The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm g=\, \mathit\, . In SI units this acceleration is expressed in metres per second squared (in symbols, m/ s2 or m·s−2) or equivalently in newtons per kilogram (N/kg or N·kg−1). Near Earth's surface, the gravity acceleration is approximately , which means that, ignoring the effects of air resistance, the speed of an object falling freely will increase by about per second every second. This quantity is sometimes referred to informally as ''little '' (in contrast, the gravitational constant is referred to as ''big ''). The precise strength of Earth's gravity varies depending on location. The nominal "average" value at Earth's surface, known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
