Oblate

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This article is about the geometric solid figure. For a member of a Roman Catholic religious order, see Oblate (religion).

Basis of a non-scalene ellipsoid

An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it. 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 oblate spheroid

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.

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

The aspect ratio, b:a, is the ratio of the polar to equatorial lengths, while the flattening, f, is the ratio of the equatorial-polar length difference to the equatorial length: <math>f=\frac{a-b}{a}=1 - (\mathrm{aspect\;ratio}).\,\!</math>
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.