Spheroid
If the ellipse is rotated about its major axis, the result is a prolate spheroid, elongated like a rugby ball.
If the ellipse is rotated about its minor axis, the result is an oblate spheroid, flattened like a lentil or a plain M&M.
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 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] The equation of a tri-axial ellipsoid centred at the origin with semi-axes a, b and c aligned along the coordinate axes is The equation of a spheroid with z as the symmetry axis is given by setting a = b: The semi-axis a is the equatorial radius of the spheroid, and c is the distance from centre to pole along the symmetry axis.
The volume inside a spheroid (of any kind) is If A = 2a is the equatorial diameter, and C = 2c is the polar diameter, the volume is Let a spheroid be parameterized as where β is the reduced latitude or parametric latitude, λ is the longitude, and −π/2 < β < +π/2 and −π < λ < +π.
To avoid confusion, an ellipsoidal definition considers its own values to be exact in the form it gives.
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.
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.
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.
[8] 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.
