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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.
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, ... and therefore an ideal Earth ellipsoid has the same volume as the geoid.
An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
This equation reduces to that of the volume of a sphere when all three elliptic radii are equal, and to that of an oblate or prolate spheroid when two of them are equal. The volume of an ellipsoid is 2 / 3 the volume of a circumscribed elliptic cylinder, and π / 6 the volume of the circumscribed box.
For a Maclaurin spheroid of eccentricity greater than 0.812670, [3] a Jacobi ellipsoid of the same angular momentum has lower total energy. If such a spheroid is composed of a viscous fluid (or in the presence of gravitational radiation reaction), and if it suffers a perturbation which breaks its rotational symmetry, then it will gradually elongate into the Jacobi ellipsoidal form, while ...
Electrodynamics of Continuous Media (Volume 8 of the Course of Theoretical Physics) (2nd ed.). New York: Pergamon Press. pp. 19– 29. ISBN 978-0-7506-2634-7. Treats the prolate spheroidal coordinates as a limiting case of the general ellipsoidal coordinates. Uses (ξ, η, ζ) coordinates that have the units of distance squared.
The nation’s debt ceiling was reinstated Thursday, giving congressional Republicans yet another divisive challenge to contend with in 2025.
The oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis. It is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other celestial body is called a reference ellipsoid.