Prolate spheroid

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A prolate spheroid is a spheroid in which the polar diameter is greater than the equatorial diameter.

A prolate spheroid

[edit] Prolate spheroids in sport

The prolate spheroid is the shape of the ball in several sports, such as in Rugby Football and Australian Rules Football. In American Football and Canadian Football, a more pointed prolate spheroid is used (one resembling a rotated vesica piscis).^[1]

[edit] Prolate spheroids in astronomy

The prolate spheroid, like its opposite, the oblate spheroid, is the shape of some of the moons in the solar system. Examples are Mimas, Enceladus, and Tethys (satellites of Saturn) and Miranda (a satellite of Uranus).^{[citation needed]} The dwarf planet Haumea is a scalene ellipsoid.^{[citation needed]}

It is also used to describe the shape of some nebulae (nebulas) such as the Crab Nebula.^[2]

[edit] Prolate spheroids in nuclear physics

It is used as a description of the nuclear deformation due to the external electrons effect. It´s mostly used while comparing to the shell model.

[edit] Surface area

A prolate spheroid has the surface area

$A = 2\pi\left(a^2+\frac{a b o\!\varepsilon}{\sin(o\!\varepsilon)}\right)$

where $o\!\varepsilon=\arccos\left(\frac{a}{b}\right)$ is the angular eccentricity of the ellipse, $e=\sin(o\!\varepsilon)$ is its (ordinary) eccentricity, $\ b$ is the polar radius, and $\ a$ is the equatorial radius.