A spheroid is a
quadric surfaceobtained by rotating an ellipseabout one of its principal axes; in other words, an ellipsoidwith two equal semi-diameters.
If the ellipse is rotated about its major axis, the result is a prolate (elongated) spheroid, somewhat similar to a rugby ball. If the ellipse is rotated about its minor axis, the result is an oblate (flattened) spheroid, somewhat similar to a
lentil. If the generating ellipse is a circle, the surface is a sphere.
Because of its rotation, the
Earth's shape is more similar to an oblate spheroid with "a" ≈ 6,378.137 km and "b" ≈ 6,356.752 km, than to a sphere.
A spheroid centered at the origin and rotated about the "z" axis is defined by the implicit equation:where "a" is the horizontal, transverse radius at the equator, and "b" is the vertical, conjugate radius. [http://books.google.com/books?id=F9sVAAAAYAAJ&pg=PA177]
A prolate spheroid has
surface area:where is the angular eccentricityof the ellipse, and is its (ordinary) eccentricity.
An oblate spheroid has surface area :.
The volume of a spheroid (of any kind) is
If a spheroid is parameterized as:where is the reduced or parametric latitude, is the
longitude, and and
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spheroid — spheroid; spheroid·ic·i·ty; spheroid·ism; spheroid·iza·tion; spheroid·ize; … English syllables
Spheroid — Sphe roid, n. [L. spheroides ball like, spherical, Gr. ???; ???? sphere + e i^dos form: cf. F. 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… … The Collaborative International Dictionary of English
spheroid — index sphere Burton s Legal Thesaurus. William C. Burton. 2006 … Law dictionary
spheroid — 1660s, from L. sphaeroides, from Gk. sphairoeides, from sphaira (see SPHERE (Cf. sphere)) + oeides вЂњformвЂќ (see OID (Cf. oid)) … Etymology dictionary
spheroid — ► NOUN ▪ a sphere like but not perfectly spherical body. DERIVATIVES spheroidal adjective … English terms dictionary
spheroid — [sfir′oid] n. [L sphaeroides < Gr sphairoeidēs: see SPHERE & OID] a body that is almost but not quite a sphere, esp. one generated by the rotation of an ellipse about one of its axes adj. of this shape: also spheroidal … English World dictionary
spheroid — A three dimensionalform shaped like a sphere but not perfectly round. An egg is typically a spheroid. Commonly a spheroid is an ellipsoid generated by revolving an ellipse around one of its axes. Also see conglobe and ovoid … Glossary of Art Terms
spheroid — n. 1 a spherelike but not perfectly spherical body. 2 a solid generated by a half revolution of an ellipse about its major axis (prolate spheroid) or minor axis (oblate spheroid). Derivatives: spheroidal adj. spheroidicity n … Useful english dictionary
spheroid — noun Date: 1570 a figure resembling a sphere; also an object of approximately spherical shape • spheroidal also spheroid adjective • spheroidally adverb … New Collegiate Dictionary
spheroid — n. sphere like figure. ♦ spheroidal, ♦ spheroidic, a. ♦ spherometer, n. instrument measuring curvature. ♦ spherule, n. small sphere or spheroid … Dictionary of difficult words