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An oblate spheroid
Spheroid

A spheroid 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....
 is a rotationally symmetric
Rotational symmetry

File:The armoured triskelion on the flag of the Isle of Man.svgGenerally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation....
 ellipsoid
Ellipsoid

An ellipsoid is a type of Quadric that is a higher dimensional analogue of an ellipse. The equation of a standard axis-aligned ellipsoid body in an xyz-Cartesian coordinate system is...
 having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it. An M&M's candy
M&M's

M&M's are candy-coated pieces of milk chocolate with the letter "m" printed on them, produced by Mars, Incorporated. Popular in the United States, several variations of the candies exist, including plain milk chocolate, peanut, peanut butter, dark chocolate , and almond....
 (US) or Skittles
Skittles (confectionery)

Skittles is a brand of chewy fruit candies produced and marketed by Mars, Incorporated. They have hard sugar shells which carry the letter S....
 (Canada, UK, US and Europe) is an approximate example of an oblate spheroid.

It can be formed by rotating an ellipse
Ellipse

In mathematics, an ellipse is the apparent shape of a circle viewed obliquely from outside it, as distinct from a hyperbola which is the shape seen from inside....
 about its minor axis, forming an equator with the end points of the major axis.






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Elpsminr
An oblate spheroid
Spheroid

A spheroid 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....
 is a rotationally symmetric
Rotational symmetry

File:The armoured triskelion on the flag of the Isle of Man.svgGenerally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation....
 ellipsoid
Ellipsoid

An ellipsoid is a type of Quadric that is a higher dimensional analogue of an ellipse. The equation of a standard axis-aligned ellipsoid body in an xyz-Cartesian coordinate system is...
 having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it. An M&M's candy
M&M's

M&M's are candy-coated pieces of milk chocolate with the letter "m" printed on them, produced by Mars, Incorporated. Popular in the United States, several variations of the candies exist, including plain milk chocolate, peanut, peanut butter, dark chocolate , and almond....
 (US) or Skittles
Skittles (confectionery)

Skittles is a brand of chewy fruit candies produced and marketed by Mars, Incorporated. They have hard sugar shells which carry the letter S....
 (Canada, UK, US and Europe) is an approximate example of an oblate spheroid.

It can be formed by rotating an ellipse
Ellipse

In mathematics, an ellipse is the apparent shape of a circle viewed obliquely from outside it, as distinct from a hyperbola which is the shape seen from inside....
 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
Semi-major axis

In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
 and one semi-minor axis
Semi-minor axis

In geometry, the semi-minor axis is a line segment associated with most conic sections . One end of the segment is the center of the conic section, and it is at right angles with the semi-major axis....
.

The opposite of oblate is prolate.

Oblatespheroid
For a discussion of the physics that determines the shape of a spinning celestial body, see Equatorial bulge
Equatorial bulge

An equatorial bulge is a bulge which a planet may have around its equator, distorting it into an oblate spheroid. The Earth has an equatorial bulge of 42.72 km due to its rotation: its diameter measured across the equatorial plane is 42.72 km more than that measured between the poles ....


The aspect ratio
Aspect ratio

The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements, such as the length and diameter of a rod....
 of an oblate spheroid/ellipse, b:a, is the ratio of the polar to equatorial lengths , while the flattening
Flattening

The flattening, ellipticity, or oblateness of an oblate spheroid is the "squashing" of the spheroid's Geographical pole, towards its equator....
 (also called oblateness), f, is the ratio of the equatorial-polar length difference to the equatorial length:




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
Angular eccentricity

In the study of ellipses and related geometry, various parameters in the distortion of a circle into an ellipse are identified and employed: Aspect ratio, flattening and Eccentricity ....
.

The oblate spheroid is interesting because it is the approximate shape of many planet
Planet

A planet , as 2006 definition of planet by the International Astronomical Union , is a celestial body orbiting a star or Stellar evolution#Stellar remnants that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared the neighbourhood of planetesimals....
s and celestial bodies
Astronomical object

s are significant entity, associations or structures which current science has confirmed to exist in outer space. This does not necessarily mean that more current science will not disprove their existence....
, including most notably Saturn and Altair
Altair

Altair is the brightest star in the constellation Aquila and the list of brightest stars in the night sky. It is an Stellar classification#Class A main sequence star with an apparent visual magnitude of 0.77 and is one of the vertices of the Summer Triangle; the other two are Deneb and Vega....
, but also to a lesser extent the Earth
Earth

Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
 (with a = 6378.137 km and b ˜ 6356.752 km, providing an aspect ratio of 0.99664717 and inverse flattening of 298.2572 [1
World Geodetic System

The World Geodetic System is a standard for use in cartography, geodesy, and navigation. It comprises a standard Cartesian coordinates for the Earth, a standard spheroid reference surface for raw altitude data, and a gravitation equipotential surface that defines the "nominal sea level"....
]). It is therefore the geometric figure most used for defining reference ellipsoid
Reference ellipsoid

In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body....
s, upon which cartographic and geodetic systems are based.

See also

  • Aspect ratio
    Aspect ratio

    The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements, such as the length and diameter of a rod....
  • Flattening
    Flattening

    The flattening, ellipticity, or oblateness of an oblate spheroid is the "squashing" of the spheroid's Geographical pole, towards its equator....
  • Lentoid
    Lentoid

    Lentoid is a geometric shape of a three dimensional body, best described as a circle viewed from one direction and a convex lens viewed from an orthogonal direction....
  • Reference ellipsoid
    Reference ellipsoid

    In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body....
  • Spheroid
    Spheroid

    A spheroid 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....
  • Prolate
  • Equatorial bulge
    Equatorial bulge

    An equatorial bulge is a bulge which a planet may have around its equator, distorting it into an oblate spheroid. The Earth has an equatorial bulge of 42.72 km due to its rotation: its diameter measured across the equatorial plane is 42.72 km more than that measured between the poles ....
  • Oblate spheroidal coordinates
    Oblate spheroidal coordinates

    Oblate spheroidal coordinates are a three-dimensional orthogonal coordinates coordinate system that results from rotating the two-dimensional elliptic coordinates about the non-focal axis of the ellipse, i.e., the symmetry axis that separates the foci....
  • Equidimensional
    Equidimensional

    Equidimensional is an adjective applied to objects that have nearly the same size or spread in multiple directions. As a mathematical concept, it may be applied to objects that extend across any number of dimensions....


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