For spheroids in cell culturing, see 3D cell culture. For rotating equilibrium spheroids, see Maclaurin spheroid and Jacobi ellipsoid. For the type of archaeological artifact, see Spheroid (lithic).
Spheroids with vertical rotational axes
oblate
prolate
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 6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) 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).[1]
^Torge, Wolfgang (2001). Geodesy (3rd ed.). Walter de Gruyter. p. 104. ISBN 9783110170726.
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...
A Maclaurin spheroid is an oblate spheroid which arises when a self-gravitating fluid body of uniform density rotates with a constant angular velocity...
Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate...
Spheroidal weathering is a form of chemical weathering that affects jointed bedrock and results in the formation of concentric or spherical layers of highly...
Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system...
Hammerscale, also written hammer scale, is a flaky or spheroidal byproduct of the iron forging process (for modern equivalent, see mill scale). Hammerscale...
Center), or in a spheroidal galactic bulge around the galactic core. However, some stars inhabit a spheroidal halo or galactic spheroid, a type of galactic...
Spheroidal wave functions are solutions of the Helmholtz equation that are found by writing the equation in spheroidal coordinates and applying the technique...
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy...
0° The equator is a circle of latitude that divides a spheroid, such as Earth, into the Northern and Southern hemispheres. On Earth, the Equator is an...
The Sagittarius Dwarf Spheroidal Galaxy (Sgr dSph), also known as the Sagittarius Dwarf Elliptical Galaxy (Sgr dE or Sag DEG), is an elliptical loop-shaped...
1983 is denoted by 'GCS North American 1983'. On the GRS 80 or WGS 84 spheroid at sea level at the Equator, one latitudinal second measures 30.715 m,...
A dwarf spheroidal galaxy (dSph) is a term in astronomy applied to small, low-luminosity galaxies with very little dust and an older stellar population...
triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry (Euler 1755). If the Earth is treated as a sphere, the geodesics...
length, then the ellipsoid is an ellipsoid of revolution, also called a spheroid. In this case, the ellipsoid is invariant under a rotation around the third...
Multicellular tumor spheroids are scaffold-free spherical self-assembled aggregates of cancer cells. It is a 3 dimensional culture model which closely...
The Pegasus Dwarf Spheroidal (also known as Andromeda VI or Peg dSph for short) is a dwarf spheroidal galaxy about 2.7 million light-years away in the...
on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) (equatorial...
German mathematician Carl Gustav Jacob Jacobi. Before Jacobi, the Maclaurin spheroid, which was formulated in 1742, was considered to be the only type of ellipsoid...
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial...
On Conoids and Spheroids (Ancient Greek: Περὶ κωνοειδέων καὶ σφαιροειδέων) is a surviving work by the Greek mathematician and engineer Archimedes (c. 287...
small capsules in which the cells can grow into spheroids, or 3D cell colonies. Approximately 300 spheroids are usually cultured per bioreactor. 3D cell...
and spheroids found in the United States. The website World's Tallest Water Sphere describes the distinction between a water sphere and water spheroid thus:...
two points on a spheroid and having the same center as that of the spheroid. Equivalently, it is an ellipse on the surface of a spheroid and centered on...
"blown" spheroids transformed to lithophysae "Blown" spheroid transformed to a lithophysa "Blown" spheroid transformed to a lithophysa "Blown" spheroids transformed...
"Ball" is used metaphorically sometimes to denote something spherical or spheroid, e.g., armadillos and human beings curl up into a ball, making a fist into...
approximation assumes the Earth is a slightly-squashed sphere (an oblate spheroid); azimuth then has at least two very slightly different meanings. Normal-section...
Catasetum globiflorum, the spheroid-flowered catasetum, is a species of orchid found in Brazil. "Catasetum globiflorum Hook. | Plants of the World Online...
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