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A spheroid is a quadric surfaceobtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters.
If the ellipse is rotated about its major axis, the result is a prolate (elongated) spheroid, somewhat similar to a rugby ball. If the ellipse is rotated about its minor axis, the result is an oblate (flattened) spheroid, somewhat similar to a lentil. If the generating ellipse is a circle, the surface is a sphere.
Because of its rotation, the Earth's shape is more similar to an oblate spheroid with a ≈ 6,378.137 km and b ≈ 6,356.752 km, than to a sphere.
A spheroid centered at the origin and rotated about the z
axis is defined by the implicit
is the horizontal, transverse radius at the equator, and b
is the vertical, conjugate radius.
A prolate spheroid has surface area
is the angular eccentricity
of the ellipse, and
is its (ordinary) eccentricity
An oblate spheroid has surface area
The volume of a spheroid (of any kind) is
If a spheroid is parameterized as
is the reduced
or parametric latitude
is the longitude