Prolate spheroid: Information from Answers.com

A prolate spheroid

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

1 Properties
2 Uses
3 See also
4 References

Properties

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.

The volume of a prolate spheroid is calculated by $V = \frac{4}{3}\pi a^2 b$

Uses

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

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]

The most common shapes for the density distribution of protons and neutrons in an atomic nucleus are spherical, prolate and oblate spheroidal. Deformed shapes occur as a result of the competition between electromagnetic repulsion between protons, surface tension and quantum shell effects.

References

^ See 2008 NCAA Football Rules and Interpretations, Sec. 1, Art. 1
^ Trimble, Virginia Louise (October 1973), "The Distance to the Crab Nebula and NP 0532", Publications of the Astronomical Society of the Pacific 85 (507): 579, doi:10.1086/129507, http://adsabs.harvard.edu/abs/1973PASP...85..579T

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Prolate spheroid

Contents

Properties

Uses

See also

References