Oblate spheroid

Oblate spheroid
An oblate spheroid

An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it.[1] Oblate spheroids stand in contrast to prolate spheroids.

It can be formed by rotating an ellipse about its minor axis, forming an equator with the end points of the major axis. As with all ellipsoids, it can also be described by the lengths of three mutually perpendicular principal axes, which are in this case two arbitrary equatorial semi-major axes and one semi-minor axis.

An everyday example of an oblate spheroid is the shape of the UK candy Smarties or US candy M&M's. The shape of the Earth is very close to that of an oblate spheroid. Though local topography deviates from this idealized spheroid, on a global scale these deviations are very small.

An oblate spheroid can be formed by rotating an ellipse about its minor axis.

The aspect ratio of an oblate spheroid/ellipse, b:a, is the ratio of the polar to equatorial lengths,[2] while the flattening (also called oblateness) f, is the ratio of the equatorial-polar length difference to the equatorial length:

f=\frac{a-b}{a}=1 - b:a.\,\!

These are just two of several different parameters used to define an ellipse and its solid body counterparts, all of which are ultimately trigonometric functions of the ellipse's modular angle, or angular eccentricity.

The oblate spheroid is the approximate shape of many planets and celestial bodies, including Saturn and Altair, and – to a lesser extent – the Earth (with a = 6378.137 km and b ≈ 6356.752 km, providing an aspect ratio of 0.99664717, a flattening of 0.003352859934, and inverse flattening of 298.2572). It is therefore the most-used geometric figure for defining reference ellipsoids, upon which cartographic and geodetic systems are based.

See also

References

  1. ^ "Oblate Spheroid - from Wolfram MathWorld". Mathworld.wolfram.com. 2009-10-04. http://mathworld.wolfram.com/OblateSpheroid.html. Retrieved 2009-10-23. 
  2. ^ "Circumference/Perimeter of an Ellipse: Formula(s) - Numericana". Numericana.com. http://www.numericana.com/answer/ellipse.htm#cantrell. Retrieved 2010-03-20. 

External links



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  • Oblate spheroid — Oblate Ob*late , a. [L. oblatus, used as p. p. of offerre to bring forward, offer, dedicate; ob (see {Ob }) + latus borne, for tlatus. See {Tolerate}.] [1913 Webster] 1. (Geom.) Flattened or depressed at the poles; as, the earth is an oblate… …   The Collaborative International Dictionary of English

  • Oblate spheroid — 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… …   The Collaborative International Dictionary of English

  • Oblate — Ob*late , a. [L. oblatus, used as p. p. of offerre to bring forward, offer, dedicate; ob (see {Ob }) + latus borne, for tlatus. See {Tolerate}.] [1913 Webster] 1. (Geom.) Flattened or depressed at the poles; as, the earth is an oblate spheroid.… …   The Collaborative International Dictionary of English

  • Oblate ellipsoid — Oblate Ob*late , a. [L. oblatus, used as p. p. of offerre to bring forward, offer, dedicate; ob (see {Ob }) + latus borne, for tlatus. See {Tolerate}.] [1913 Webster] 1. (Geom.) Flattened or depressed at the poles; as, the earth is an oblate… …   The Collaborative International Dictionary of English

  • 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

  • oblate — oblate1 [äb′lāt΄, äb lāt′] adj. [ModL oblatus < OB + latus as in prolatus (see PROLATE): from being thrust forward at the equator] Geom. flattened at the poles [an oblate spheroid] oblate2 [äb′lāt΄] n. [ML oblatus, offered, thrust forward < …   English World dictionary

  • Spheroid — A spheroid is a quadric surfaceobtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi diameters. If the ellipse is rotated about its major axis, the result is a prolate (elongated)… …   Wikipedia

  • Oblate spheroidal coordinates — Figure 1: Coordinate isosurfaces for a point P (shown as a black sphere) in oblate spheroidal coordinates (μ, ν, φ). The z axis is vertical, and the foci are at ±2. The red oblate spheroid (flattened sphere) corresponds to μ=1, whereas the blue… …   Wikipedia

  • Oblate — For the geometrical concept, see Oblate spheroid. Contents 1 Origins and history 2 Oblates today 2.1 Secular oblates …   Wikipedia

  • 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

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