#jsDisabledContent { display:none; } My Account | Register | Help

# Prolate

Article Id: WHEBN0016303552
Reproduction Date:

 Title: Prolate Author: World Heritage Encyclopedia Language: English Subject: Rotational spectroscopy Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Prolate

A prolate spheroid is a spheroid in which the polar axis is greater than the equatorial diameter. Prolate spheroids are elongated along a line, whereas oblate spheroids are contracted. The prolate spheroid is defined by the equation $\mu = c$ for some arbitrary constant c, in prolate spheroidal coordinates.

## Properties

A prolate spheroid with b > a has surface area $S_\left\{\rm prolate\right\}=2\pi a^2\left\left(1+\frac\left\{b\right\}\left\{ae\right\}\sin^\left\{-1\right\}e\right\right)\qquad\mbox\left\{where\right\}\qquad e^2=1-\frac\left\{a^2\right\}\left\{b^2\right\}$ and volume $V_\left\{\rm prolate\right\} = \frac\left\{4\right\}\left\{3\right\}\pi a^2 b$.

The prolate spheroid is generated by rotation about the major axis of an ellipse with semi-major axis b and semi-minor axis a, therefore e may be identified as the eccentricity (see ellipse). A derivation of this result may be found at.[1]

## Uses

The prolate spheroid is the shape of the ball in several sports, such as in Rugby union, Rugby league, and Australian rules football. In American football and Canadian football, a more pointed prolate spheroid is used (one resembling a vesica piscis in cross section).[2]

Several moons of the Solar system approximate prolate spheroids in shape, though they are actually scalene. Examples are Mimas, Enceladus, and Tethys (satellites of Saturn) and Miranda (a satellite of Uranus). In contrast to being distorted into oblate spheroids via rapid rotation, celestial objects distort slightly into prolate spheroids via tidal forces when they orbit a massive body in a close orbit. The most extreme example is Jupiter's moon Io, which becomes slightly more or less prolate in its orbit due to a slight eccentricity, causing spectacular volcanism. It should be noted that 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. A famous example in science fiction is Jinx in Larry Niven's Known Space.

It is also used to describe the shape of some nebulae (nebulas) such as the Crab Nebula.[3]

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.

Many submarines have a shape which can be described as prolate spheroid.

## References

es:Esferoide prolato
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.

Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.