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Surface formed by rotating an ellipse

+ Spheroids with vertical rotational axesoblateprolate

A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, 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. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a prolate spheroid, elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an oblate spheroid, flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a sphere. The current World Geodetic System model uses a spheroid whose radius is at the Equator and at the poles. The word spheroid originally meant "an approximately spherical body", admitting irregularities even beyond the bi or tri axial ellipsoidal shape; that is how the term is used in some older papers on geodesy (for example, referring to truncated spherical harmonic expansions of the Earth's gravity geopotential model).

The most common shapes for the density distribution of protons and neutrons in an atomic nucleus are spherical, prolate, and oblate spheroidal, where the polar axis is assumed to be the spin axis (or direction of the spin angular momentum vector). Deformed nuclear shapes occur as a result of the competition between electromagnetic repulsion between protons, surface tension and quantum shell effects.

The oblate spheroid is the approximate shape of rotating planets and other celestial bodies, including Earth, Saturn, Jupiter, and the quickly spinning star Altair. Saturn is the most oblate planet in the Solar System, with a flattening of 0.09796. See planetary flattening and equatorial bulge for details. Enlightenment scientist Isaac Newton, working from Jean Richer's pendulum experiments and Christiaan Huygens's theories for their interpretation, reasoned that Jupiter and Earth are oblate spheroids owing to their centrifugal force. Earth's diverse cartographic and geodetic systems are based on reference ellipsoids, all of which are oblate.

The prolate spheroid is the approximate shape of the ball in several sports, such as in the rugby ball. Several moons of the Solar System approximate prolate spheroids in shape, though they are actually triaxial ellipsoids. Examples are Saturn's satellites Mimas, Enceladus, and Tethys and Uranus' satellite Miranda. In contrast to being distorted into oblate spheroids via rapid rotation, celestial objects distort slightly into prolate spheroids via tidal forces when they orbit a massive body in a close orbit. The most extreme example is Jupiter's moon Io, which becomes slightly more or less prolate in its orbit due to a slight eccentricity, causing intense volcanism. The major axis of the prolate spheroid does not run through the satellite's poles in this case, but through the two points on its equator directly facing toward and away from the primary. This combines with the smaller oblate distortion from the synchronous rotation to cause the body to become triaxial. The term is also used to describe the shape of some nebulae such as the Crab Nebula. Fresnel zones, used to analyze wave propagation and interference in space, are a series of concentric prolate spheroids with principal axes aligned along the direct line of sight between a transmitter and a receiver. The atomic nuclei of the actinide and lanthanide elements are shaped like prolate spheroids. In anatomy, near spheroid organs such as testis may be measured by their long and short axes. Many submarines have a shape which can be described as prolate spheroid.