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Topic: Oblate spheroid

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	Oblate - Wikipedia, the free encyclopedia
		An oblate spheroid is ellipsoid having a shorter axis and two equal longer axes.
		The oblateness, ellipticity, or flattening is a measure for a planet that is a spheroid in shape, bulging outward in the center due to its rotation.
		Gravity tends to contract celestial bodies into a perfect sphere, the shape where all the mass is as close to the center of gravity as possible.
	en.wikipedia.org /wiki/Oblate (429 words)

	references - light scattering (Site not responding. Last check: 2007-10-08)
		The prolate spheroids at parallel incidence have steep and high resonance maxima in the scattering efficiency factors and broad and low forwardscattering peaks in the intensity functions; on the other hand, the oblate spheroids at parallel incidence have broad and low resonance maxima and sharp and high forwardscattering peaks.
		With an increase of the incidence angle, the scattering behavior of prolate spheroids approaches that of oblate spheroids at parallel incidence and vice versa.
		The size-shape distributions of spheroids exhibit stronger side scattering near 120 degrees and weaker backscattering, the ratio F/sub 22//F/sub 11/ of the elements of the scattering matrix substantially deviates from unity, and the element F/sub 33/ is greatly different from F/sub 44/.
	atol.ucsd.edu /~pflatau/scatlib/scatlib/scatrefs/ref-spheroid.html (6080 words)

	SPHEROID - LoveToKnow Article on SPHEROID (Site not responding. Last check: 2007-10-08)
		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 - Wikipedia, the free encyclopedia
		A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes.
		A prolate spheroid has one semiaxis longer than the other two, (b > a); an oblate spheroid has one semiaxis shorter than the other two (b < a) 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 (171 words)

	Flaw Reconstruction Techniques
		A scan in the PSP of the 2:1 oblate spheroid tilted at 30ƒ showed a peak in flaw signal amplitude at the intersection of the VSP and the PSP (direction M), whereas a scan in the PSP of the tilted 2.5:1 prolate spheroid showed a constant flaw signal amplitude.
		The 2:1 oblate spheroidal void tilted at a 30ƒ angle in a titanium disk was investigated, again, following the procedure of predetermining a favorable data-acquisition pattern based on angular scan results.
		This is consistent with the fact that the oblate spheroid has a smaller aspect ratio and a smaller tilt angle and is therefore not nearly a "low leverage" flaw to reconstruct using the normal (untilted) data-acquisition pattern.
	www.ndt-ed.org /EducationResources/CommunityCollege/Ultrasonics/MeasurementTech/flawreconstruction.htm (2963 words)

	Spheroid -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a (A form of football played with an oval ball) rugby ball or (A roll of tobacco for smoking) cigar).
		If the minor axis is chosen, the surface is called an (Click link for more info and facts about oblate spheroid) oblate spheroid (similar to the shape of the (Click link for more info and facts about planet Earth) planet Earth).
		The (A particular environment or walk of life) sphere is a special case of the spheroid in which the generating ellipse is a circle.
	www.absoluteastronomy.com /encyclopedia/s/sp/spheroid.htm (192 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Consider scattering of an oblate spheroid of a = 8 mm and c = 0.125 mm with permittivity equal to (10+i0.1) [[epsilon]]0 by a plane wave with frequency = 10 GHz.
		The axis of symmetry of the oblate spheroid be along z axis.
		Note that the oblate spheroid has the same volume as the sphere of the previous problem.
	www.ee.washington.edu /faculty/tsang/EE575HW1W.html (153 words)

	Spheroid Geometry
		However, in reality, the earth's mean sea-level surface is better approximated by a different geometric shape, an oblate spheroid- the surface created by rotating an ellipse about its polar axis.
		Compared to a sphere, an oblate spheroid is flattened at the poles.
		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)

	earth - Article and Reference from OnPedia.com
		The earth is approximately a slightly oblate spheroid, with an average diameter of approximately 12,742 km.
		Thus the Earth is an oblate spheroid within a tolerance of one part in about 584, or 0.17 percent.
		Since Earth is rather large, it is not immediately obvious to the naked eye viewing from the surface that it is an oblate spheroid, bulging slightly at the equator and slightly flattened at the poles.
	www.onpedia.com /encyclopedia/earth (3424 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Even the spheroid was an inadequate description for the shape of the earth, and in the twentieth century the concept of the geoid was developed.
		The concept assumes the shape of the earth to be defined by the surface that would be taken up by mean sea level, if mean sea level could be extended under the land masses of the earth.
		The theoretical geoidal surface thus created is generally spheroidal, but is flatter at one pole than at the other, and has a number of lumps and hollows spread across it.
	www.geomatics.org.uk /geodhist.htm (768 words)

	Measuring the Length of the Meridian
		However, Isaac Newton believed that the earth was slightly flattened at the poles, an oblate spheroid, and that the length of a degree at the poles was longer than it was at the equator.
		If the length of a degree were longer at the Arctic Circle than at the Equator the spheroid would be oblate, flat at the poles; if it were shorter, prolate, and if the degrees were equal, then the earth would be spherical.
		Although his measurements were not absolutely accurate, the length of a degree at the Arctic Circle was nearly half a kilometer longer than in France, proving that the shape of the earth was an oblate spheroid.
	sio.midco.net /mapstamps/arc.htm (551 words)

	CelesTrak: "Orbital Coordinate Systems, Part III"
		However, on an oblate spheroid, this is not the case since a line from the center of the Earth to the observer's position would not point to the local zenith (except on the equator and at the poles).
		The term reference spheroid is used to define the oblate spheroid which 'best' defines the shape of the Earth.
		However, on an oblate spheroid, geodetic latitude is the angle between the local zenith direction and the Earth's equatorial plane.
	www.celestrak.com /columns/v02n03 (1370 words)

	WGS 84 Mathematics (Site not responding. Last check: 2007-10-08)
		This is the radius at the equator, approximately 7 km higher than the radius of a sphere of equal volume (the value 6,371,008 that most textbooks use for the radius of the earth).
		The equation for radius at a given latitude is simpler; an oblate spheroid is simply a sphere that has one axis (in this case, Z) reduced by a factor of f.
		While a sphere would be incorrect by approximately 14 km at the poles and 7 km at the equator, this oblate spheroid is only incorrect by at most 110 meters (as discussed in the EGM 96 section), with an average error of 20-30m.
	www.pha.jhu.edu /~hanish/WGS.html (440 words)

	RE: oblate spheroid (Site not responding. Last check: 2007-10-08)
		(Geom.) Flattened or depressed at the poles; as, the earth is an oblate spheroid.
		"Oblate ellipsoid or spheroid (Geom.), a solid generated by the revolution of an ellipse about its minor axis; an oblatum.
		sph['e]ro["i]de.] A body or figure approaching to a sphere, but not perfectly spherical; esp., a solid generated by the revolution of an ellipse about one of its axes.
	www.ku.edu /carrie/archives/mediev-l/melcher/2003/04/msg00577.html (316 words)

	Highly Oblate Microspheroid as an Optical Resonator
		The highly oblate microspheroid resonator is not subject to the disadvantages of microsphere, microdisk, or microring resonators.
		In the highly oblate microspheroid resonator, the greater curvature of the surface in the direction transverse to the desired equatorial circulation effectively decouples the partly transverse modes from the input/output device.
		The Highly Oblate Spheroidal portion protruding from the cylindrical portion of this object acts as a high-finesse optical resonator.
	www.nasatech.com /Briefs/Apr01/NPO20951.html (600 words)

	Untitled Document
		Assume mandm's are oblate spheroids with a major axis radius of 0.6 cm (a) and a minor axis radius of 0.3 cm (b).
		The volume of oblate spheroid is (4/3)p a2b].
		It was found that although the assumption of an oblate spheroid for a single mandm is quite reasonable.
	www.kleinbottle.com /Bernie_Tao.htm (1482 words)

	Space station: Sphere large work & living area 1G gravity pictures atmosphere
		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.angelfire.com /space/where-i-want-to-be/station.html (1333 words)

	[Regents Prep Earth Science] Introduction: Oblate Spheroid
		The term "Spheroid" means that it is almost a sphere, but not quite.
		supports the conclusion that the earth is a slightly oblate spheroid.
		Since the Earth is so slightly oblate, and the Earth's relief is so insignificant in comparison with its size, the best scale models of the Earth would actually be very round and very smooth.
	regentsprep.org /Regents/earthsci/units/introduction/oblate.cfm (555 words)

	Calculation of Cell Areas on an Oblate Planet
		Purpose: To calculate the cell areas on an oblate spheroidal planet.
		Note a > b for an oblate spheroid.
		However, the definite integrals remain to be evaluated after the dust settles.
	www.lpl.arizona.edu /~umpire/work/spheroid_area.html (283 words)

	GDA94 - GEOCENTRIC DATUM OF AUSTRALIA
		This discussion reviews the spheroids and datums that are used for national and international mapping, the definition of the GDA and its associated geometrical parameters, and presents a rigorous method to update current Australian maps and spatial information systems from the AGD to the GDA.
		Therefore, there is a distinction between the spheroid and the datum: The spheroid is a geometrical reference surface, whereas the datum is the adopted coordinate set, which is based on a particular spheroid.
		Regional spheroids have generally been established using astronomical observations to define the deflection of the vertical (difference between geoidal and spheroidal normals) to be zero at an origin point.
	www.cage.curtin.edu.au /~will/datum.html (5432 words)

	[No title]
		There is no standard result for geodesics computed on an oblate spheroid, so the approach taken here is to use the solution provided by the class, after it has been shown to perform well on a spherical earth, and call that the standard.
		The "gold standard" for oblate spheroids: This testing does not say whether the DF solution or the WCP solution is more accurate for oblate spheroids.
		When the "oblate spheroid" is reduced to the simple case of a perfect sphere, both solutions work well.
	staff.washington.edu /rxandrew/geodesy/odyssey.txt (1753 words)

	The Straight Dope Mailbag: The Straight Dope Mailbag: What is the definition of "down"? (revisited)
		The same effect that causes the Earth to be oblate also causes objects to fall away from the center of the earth.
		When treating the Earth as an oblate spheroid, down is the perpendicular (or normal) to the tangent.
		The geoid is only approximately the same shape as an oblate spheroid, and has almost no correlation with the local surface terrain.
	www.straightdope.com /mailbag/mgeoid.html (531 words)

	Oblate - Open Encyclopedia (Site not responding. Last check: 2007-10-08)
		Oblate also refers to a member of the Roman Catholic religious order of the Missionary Oblates of Mary Immaculate, or in some cases to a lay or religious person who has officially associated himself (or herself) with a monastic community such as the Benedictines for reasons of personal enrichment without actually assuming a monastic lifestyle.
		An oblate spheroid is an ellipsoid having a shorter axis and two equal longer axes (see the spheroid page for a picture).
		Effectively the (fictitious) centrifugal force fights against gravity causing the planet to look more like a sphere stretched at the equator.
	open-encyclopedia.com /Oblateness (185 words)

	IUGG 2003 Scientific Program
		An oblate spheroid may become unstable if the aspect ratio is larger than 1.62, even if the inclination angle is very small.Weakly unstable prolate spheroidal vortices emit thin filaments from their top and bottom, whereas strongly unstable slender prolate spheroidal vortices are broken up into two pieces.
		Unstable oblate spheroids emit thin sheets of vorticity to become stable oblate (or prolate) spheroid.
		When a spheroidal vortex is embedded in an otherwise quiesent fluid, it rotates rigidly with a constant angular velocity.
	www.olympus.net /IAPSO/abstracts03/JSP10/06/018629-1.html (424 words)

	Oblate - Biocrawler definition:Oblate - Biocrawler (Site not responding. Last check: 2007-10-08)
		Oblateness is a measure for a planet that is a spheroid in shape, bulging outward in the center due to its rotation.
		(Earth is slightly oblate.) Effectively the (fictitious) centrifugal force fights against gravity causing the planet to look more like a sphere stretched at the equator.
		You can find it there under the keyword Oblateness (http://en.wikipedia.org/wiki/Oblateness)The list of previous authors is available here: version history (http://en.wikipedia.org/w/index.php?title=Oblatenessandaction=history).
	www.biocrawler.com /biowiki/Oblateness (202 words)

	UnitMath Example: ( Geometric Solids )
		An oblate spheroid is formed by the rotation of an ellipse about its minor axis.
		The volume and surface area of a oblate spheroid is:.
		The volume and surface area of a prolate spheroid is:.
	unitmath.com /um/p/Examples/GeometricSolids/GeometricSolids.html (905 words)

	Lecture 28, Earth Dynamics
		The first hint of isostasy was provided in the middle of the eighteenth century when Piere Bouguer participated in a survey to measure the length of a degree of latitude at the equator.
		For an oblate spheroid the opposite would be true.
		During this work Bouguer noted that there was a difference between the vertical direction as based on the position of stars and that based on a spirit level or plumb bob.
	earth.unh.edu /esci658/docs/lecture_28.html (1706 words)

	The SeisSoft Company - Projection and Datum FAQ (Site not responding. Last check: 2007-10-08)
		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)

	Math Forum - Ask Dr. Math
		I think a better example might be the earth - it is technically called an oblate spheroid which is a fancy way to say ellipsoid flattened along the spin axis.
		Because large spinning objects (like the earth) are sort of plastic- like, they tend to have larger equatorial diameters than polar diameters due to the centrifugal spinning forces, which are always perpendicular to the spin axis.
		Another theory (incorrect), during the time of Newton, held that the earth had the shape of a prolate spheroid, which is an ellipsoid that has a polar radius that is longer than its equatorial radius.
	mathforum.org /library/drmath/view/57799.html (271 words)

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