# oblate spheroid

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## oblate spheroid

[′ä‚blāt ′sfir‚ȯid]
(mathematics)
The surface or ellipsoid generated by rotating an ellipse about one of its axes so that the diameter of its equatorial circle exceeds the length of the axis of revolution. Also known as oblate ellipsoid.
References in periodicals archive ?
Since one semiaxis can be recovered from central section, we condition on the knowledge of its length and we are interested in the other semiaxis length, that is, A for prolate spheroids, C for oblate spheroids and D for profiles.
Similar result holds for the population of oblate spheroids.
n] be independent and identically distributed oblate spheroids with isotropic orientation.
Equation (20) is an approximate expression for the parameter [xi] of an oblate spheroid to collapse to a black hole.
The covariant metric tensor in the gravitational field of a homogeneous oblate spheroid in oblate spheroidal coordinates (n, <p) has been obtained [4, 5] as;
0] is the uniform density of the oblate spheroid and a is a constant parameter.
We can now conveniently formulate astrophysical solutions for the equation in the next section; which are convergent in the exterior space time of a homogeneous massive oblate spheroid placed in empty space.
The gravitational scalar potential interior to a homogeneous oblate spheroid is well known  to be given as
2] (where c is the speed of light in vacuum) can be constructed in gravitational fields interior and exterior to static homogeneous oblate spheroids placed in empty space.
2 Metric tensor exterior to a homogeneous oblate spheroid
The gravitational scalar potential exterior to a homogeneous static oblate spheroid  is given as
This relation has been derived recently (Pabst and Berthold, 2007), using a modified Stokes law for oblate spheroids and taking into account random orientation in the laser diffraction measurement via Cauchy's stereological theorem.

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