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Topic: Spheroid

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Ellipsoid

Oblate

Ellipse

Geoid

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Spherical Earth

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Reference ellipsoid

Precession of the equinoxes

Super ellipse

Physical geodesy

Tidal locking

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	Spheroid - Wikipedia, the free encyclopedia
		In mathematics, a spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes.
		A prolate spheroid has a semi-minor axis shorter than the semi-major axis (a > b); an oblate spheroid has a semi-minor axis longer than the semi-major axis (a < b) and can resemble a disk.
		The sphere is a special case of the spheroid in which the generating ellipse is a circle.
	en.wikipedia.org /wiki/Spheroid (191 words)

	PlanetMath: spheroid (Site not responding. Last check: 2007-11-07)
		A spheroid or ellipsoid of revolution is an ellipsoid such that two of the axes are equal in length.
		Also, the term oblate is used to describe spheriods in which the two axes of equal length are longer than the third (think of a doorknob) whilst the term prolate is used to describe spheriods for which the two equally long axes are shorter than the third axis (think of a cigar).
		This is version 2 of spheroid, born on 2005-01-12, modified 2005-01-12.
	planetmath.org /encyclopedia/Spheroid.html (141 words)

	SPHEROID - LoveToKnow Article on SPHEROID (Site not responding. Last check: 2007-11-07)
		The figure of the earth is frequently referred to as an oblate spheroid; this, however, is hardly correct, for the geoid has three unequal axes.
		The Cartesian equation to a spheroid assumes the forms xi/ai~~~.(y2_j~.zi)/bf=1, for the prolate, and (x2+zf)lal+yl/b1 = 1, for the oblate, the origin being the centre and the co-ordinate axes the axes of the original ellipse, x2la?+yilb1 = I, and the line perpendicular to the plane containing them.
		If drops of a liquid be placed on a highly heated surface, for example, the top of a stove, the liquid forms a number of tremulous globules which continually circulate internally.
	19.1911encyclopedia.org /S/SP/SPHEROID.htm (330 words)

	Spheroid Cultures for Cancer Research and Treatment
		Spheroid models are sphere-shaped cell colonies that permit growth and function studies of diverse normal and malignant tissues.
		Spheroids may be used for studies of viability, clonogenicity, LD5O, and metastatic potential under a variety of experimental conditions.
		Functional analysis of spheroids reveals that their secretory and metabolic activity is similar to that of the tumors or organs from which the spheroids derive.
	www.curedisease.com /Perspectives/vol_2_1990/Spheroid.html (1674 words)

	Spheroid - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes.
		A spheroid can also be characterised as an ellipsoid having two equal, as represented by the equation
		A prolate spheroid has one semiaxis longer than the other two, (a > b); an oblate spheroid has two equal semiaxes that are longer than the third one(a < b) and can resemble a disk.
	www.sanjuancapistrano.us /project/wikipedia/index.php/Spheroid (212 words)

	Fluent NEWS - Spring 2005 - The Prolate Spheroid Separates Turbulence Models
		Contours of the normalized invariant of the deformation tensor in a cross-flow plane toward the rear of the spheroid; the RSTM-2 model was used with an incidence angle of 20°
		On a cross section of the spheroid, about 2/3 of the length from the leading edge with a 20° incidence angle, the normalized invariant shows that the flow is largely shear-dominated throughout the boundary layer, and predominantly rotational near the core of the stream-wise vortices on the leeward side.
		For slender bodies like prolate spheroids, there is a nonlinear increase of lift with incidence angle, due to the low pressure near the cores of vortices that is impressed upon the nearby body surface.
	www.fluent.com /about/news/newsletters/05v14i1/a4.htm (1227 words)

	Spheroid Geometry
		Compared to a sphere, an oblate spheroid is flattened at the poles.
		The earth's flattening is quite small, about 1 part in 300, and navigation errors induced by assuming the earth is spherical, for the most part, do not exceed this, and so for many purposes a spherical approximation may be entirely adequate.
		However, the latitude used in navigation and geodesy is the geodetic or astronomical latitude, which is defined to be the angle between the northerly horizon at P and the polar axis.
	williams.best.vwh.net /ellipsoid/node1.html (300 words)

	Oblate - Wikipedia, the free encyclopedia
		An oblate spheroid is an ellipsoid having a shorter axis and two equal longer axes.
		The oblate spheroid is interesting because it is the approximate shape of many planets and celestial bodies, including the Earth.
		It is therefore the geometric figure most used for defining reference ellipsoids, upon which cartographic and geodetic systems are based.
	en.wikipedia.org /wiki/Oblate_spheroid (129 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The ability to control and manipulate the formation of spheroids from pluripotent cells and other types of cells that are derived directly, or indirectly from human tissue, as well as the interactions between the spheroids and between the spheroid-forming cells (i.
		Although a preferred embodiment of the invention is with ES cells, the invention is not limited to ES cell derived cells and tissues.
		For example, in one aspect of the invention, aggregation of spheroid-forming cells, such as ES cells, sufficient to induce spheroid or EB formation is permitted, and aggregation between cells within a spheroid or EB is permitted.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=03/04626.030306&ELEMENT_SET=DECL (10791 words)

	Spheroid space large work & living area & volume 1G gravity pictures (Site not responding. Last check: 2007-11-07)
		The Oblate Spheroid or flatten around the axis sphere shape was arrived at because the ring shape would not supply any real open air volume or enough surface area for that open feeling needed for ideal living condition.
		These spheroid space stations are to be made from steel from the asteroid belt and for the most part will not found in any closer than Mars.
		This is building that will circle the spheroid serving as a sealable save area during the rest of the construction and after construction of the spheroid.
	www.space-where-i-want-to-be.120host.net /sphere.html (1255 words)

	Phosphorous metabolites and steady-state energetics of transformed fibroblasts during three-dimensional growth -- ...
		Spheroids were initiated and cultured essentially as documented previously (37).
		The perfusion chamber was equipped with an integrated container for standard solutions, a temperature sensor, a medium input with the perfusion stream mixing the spheroid suspension, a medium output (1), and an overflow medium output (2).
		MR1 and Rat1-T1 spheroids are characterized by a decrease in mitochondrial
	ajpcell.physiology.org /cgi/content/full/283/4/C1287 (6413 words)

	SOPAC : Spheroid
		A triaxial spheroid could have been used but this representation does not bring a better accuracy in comparison to the level of complexity of the geometric figure.
		A spheroid is characterised by its semi-major axis a, and its degree of flattening f.
		This was all the theory about the spheroid, and placing it as close as possible as from the true representation of the earth.
	www.sopac.org /tiki/tiki-index.php?page=Spheroid (1299 words)

	Structure: Axisymmetric: Maclaurin Spheroids
		As luck would have it, however, the gravitational potential at the surface of and inside an homogeneous spheroid is expressible in terms of analytical functions.
		If the spheroid is uniformly rotating, this behavior conspires nicely with the behavior of the centrifugal acceleration -- which also will be a linear function of
		the polar radius of a uniform-density object whose surface is defined precisely by an oblate spheroid.
	www.phys.lsu.edu /astro/H_Book.current/Applications/Structure/Axisymmetric/Maclaurin.shtml (1309 words)

	GIS Tips - The Ellipsoid! Part I (Site not responding. Last check: 2007-11-07)
		Those involved in these efforts came to realize that the earth was not a true sphere, but a spheroid.
		My dictionary defines a spheroid as a "sphere like" object, implying that anything close to, but not exactly, a sphere is a spheroid.
		Spheroid, therefore, is a rather general term which leaves a lot of room for subjective interpretation.
	www.mentorsoftwareinc.com /CC/gistips/TIPS0998.HTM (1255 words)

	CSPICE Routines: RECGEO_C
		This spheroid is a volume of revolution: its horizontal cross sections are circular.
		The shape of the spheroid is defined by an equatorial radius `re' and a polar radius `rp'.
		For a point P on the reference spheroid, this is the angle between the XY plane and the outward normal vector at P. For a point P not on the reference spheroid, the geodetic latitude is that of the closest point to P on the spheroid.
	www.gps.caltech.edu /~marsdata/cspice/recgeo_c.html (615 words)

	Spheroid Reservoir BAL
		We have recently developed a novel device, the Spheroid Reservoir Bioartificial Liver, which is being evaluated in a preclinical model of liver failure with the ultimate goal of bedside treatment of patients in liver failure.
		Schematic of the Spheroid Reservoir Bioartificial Liver under in vitro condition (left) or at the bedside of a patient in liver failure.
		The Spheroid Reservoir Bioartificial Liver is current under investigation in preclinical trials of fulminant liver failure.
	mayoresearch.mayo.edu /mayo/research/nyberg_lab/projects.cfm (227 words)

	The SeisSoft Company - Projection and Datum FAQ (Site not responding. Last check: 2007-11-07)
		That spheroid, derived from satellite measurements of the Earth, is GRS80, and the datums that match it are NAD83 and WGS84.
		It is enough to say that in mathematics, a spheroid is a type of ellipsoid, one that is made by rotating an ellipse, in the third dimension, around either its long (semimajor) or short (semiminor) axis.
		It's probably easiest to remember that a spheroid is an Earth model, a datum is the practical application of the model.
	www.connect.net /jbanta/FAQ.html (2309 words)

	Projections used for datasets
		NAD83 is based on the GRS80 spheroid, derived from satellite geodesy, whereas NAD27 uses the Clarke 1866 spheroid.
		The USGS and other agencies are in the process of moving from the Clarke 1866 spheroid to a new spheroid derived from satellite geodesy (GRS80, whose axes match those of the Defense Mapping Agency's WGS84 spheroid to within a few millimeters), with a corresponding change in North American Datum from NAD27 to NAD83.
		For UTM, the value of the northing, which is computed as the distance from the equator along the surface of the approximating spheroid, is increased by an additonal 150 to 250 meters because the GRS80 spheroid is somewhat larger than the Clarke 1866 spheroid.
	dbwww.essc.psu.edu /geotree/notes/projections.html (2221 words)

	Fusor and/or General Fusion Theory - Prolate spheroid (Site not responding. Last check: 2007-11-07)
		It seems like many of the ions would tend to form a more or less collimated "beam", oscillating along the major axis of the spheroid.
		This might increase the chances of 'head on' ion-ion collisions - due to a higher population of ions heading in the opposite direction to collide with.
		It might also be useful to leave out the central portion of the prolate spheroid - since that portion would contribute few ions to the axial concentration, while contributing to power lost to collisions with the inner grid.
	fusor.net /board/view.php?bn=fusor_theory&key=1061862543 (195 words)

	Error Estimates for WGS-84 and Everest (India-1956) Transformation
		This spheroid can be defined in terms of its inherent characteristics such as the semi-major axis, semi-minor axis, eccentricity etc. on the basis of which it is possible to mathematically work out the distances and bearings of any two points by geometrically plotting these points on that spheroid.
		Accordingly a mathematical spheroid roughly representing the shape of Indian sub-continent has been assumed by the Survey of India and all measurements are related to this spheroid.
		The Indian spheroid has been marginally modified on a number of occasions so that the parameters assumed for the spheroid have been refined slightly from time to time.
	www.gisdevelopment.net /technology/ip/ma03037pf.htm (2954 words)

	Numerical Prediction of Flow over a Prolate Spheroid Undergoing a Pitchup Maneuver
		Prediction of the time-dependent flow around a 6:1 prolate spheroid undergoing a pitchup maneuver was obtained using Detached-Eddy Simulation (DES).
		DES is a hybrid formulation which attempts to capitalize on the often adequate performance of Reynolds-Averaged Navier-Stokes (RANS) models in predicting boundary layer growth and separation, and to use Large-Eddy Simulation (LES) away from solid surfaces to model the typically geometry-dependent and unsteady scales of motion in separated regions.
		Solutions of the compressible Navier-Stokes equations are obtained on unstructured grids, rigid-body motion of the spheroid is accomplished using an Arbitrary Lagrangian-Eulerian (ALE) formulation.
	home.gwu.edu /~rupesh/spheroid.html (436 words)

	Surface Area of the Spheroid
		In this section we derive the area of the spheroid, which is a surface of revolution.
		When this ellipse is spun around the x axis, a spheroid appears, prolate if a > b and oblate if b > a.
		For both formulas, scale a and b by a common factor, and the area is squared, as it should be.
	www.mathreference.com /ca-surf,oid.html (389 words)

	A Bench-top Fluid-bed Tablet and Spheroid (Pellet) Coater for small scale Pharmaceutical Product Development and ...
		Fluid bed tablet and spheroid coater for 1 to 50 tablets or a few grams of spheroids.
		With its ability to apply a high quality coating to very small quantities of tablets (as little as a single tablet) or spheroids the Caleva spray coater/drier is ideal for this situation.
		A mix of coated and uncoated spheroids in a single dosage form is an easy way to manage modified release rates.
	www.caleva.co.uk /6_1.html (708 words)

	CSPICE Routines: GEOREC_C
		This is the angle between the prime meridian and the meridian containing `rectan'.
		Given the geodetic coordinates of a point, and the constants describing the reference spheroid, this routine returns the bodyfixed rectangular coordinates of the point.
		Using the equatorial radius of the Clark66 spheroid (CLARKR = 6378.2064 km) and the Clark 66 flattening factor (CLARKF = 1.0 / 294.9787) convert to body fixed rectangular coordinates.
	www.gps.caltech.edu /~marsdata/cspice/georec_c.html (577 words)

	In praise of the prolate spheroid \| csmonitor.com
		When it's jarred loose we are reminded that the football may be symmetrical, but it is far from spherical.
		The unusual shape, known as a prolate spheroid, means that this ball bounces with more maddening unpredictability than any other in sports.
		By the mid-1870s, a rugby ball had become the ball of choice, but it wasn't until 1911 that the rules specified use of a prolate spheroid.
	www.csmonitor.com /2003/1119/p18s03-hfes.html?entryBottomStory (1384 words)

	The Dimpled Spheroid:Stephan, Robert J.:1587361876:eCampus.com
		The Dimpled Spheroid chronicles the wild and hilarious adventures of Kirby Walsh and his three college buddies on their quest for birdies and laughs.
		From Bourbon Street to San Francisco, from the gates of Graceland to the Austin city limits, Kirby and the boys manage to stumble ass-backwards into money and weasel their way out of trouble at every turn.
		And, when all is said and done, their journey leads them to a pot of gold at the end of the rainbow, as they somehow transform their passion for golf into a million-dollar business plan.
	www.ecampus.com /bk_detail.asp?isbn=1587361876&referrer=yah04 (117 words)

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