latest definition for "Sphere" and also relative probable theories please.thanks?

Question

i have checked into wikipedia.org
http://en.wikipedia.org/wiki/Sphere

i believe that the definition of sphere in maths differs from
one the one in physics particularly in astrophysics.i need to know them both please.

thank BOND it is fine but one more thing i like to know
are black holes considered as a perfect shperical object?if so does difinations by wiki perfect?
please add me more
thanks in advance.

Answer 1

A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R3) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. Thus, in three dimensions, a mathematical sphere is considered to be a (two-dimensional) spherical surface,
rather than the volume contained within it. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.

In astronomy and navigation, the celestial sphere is an imaginary rotating sphere of "gigantic radius", concentric and coaxial with the Earth

An armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a model of the celestial sphere.


A sphere of influence (SOI) in astrodynamics and astronomy is the spherical region around a celestial body where the primary gravitational influence on an orbiting object is that body. This is usually used to describe the areas in our solar system where planets dominate the orbits of surrounding objects (such as moons), despite the presence of the much more massive (but distant) Sun. In a more general sense, the patched conic approximation is only valid within the SOI.

(EDITED)

Since the gravitational force of a body on itself, at the surface of a body of any shape, increases in inverse proportion to its characteristic lengthscale squared (as volume-2/3 ), an object of ANY SHAPE and mass that is sufficiently compressed will collapse under its own gravity and form a BLACK HOLE.

Answer 2

Drawing from memory, a black hole is not a perfect spheroid because it continues to rotate, realizing the centrifugal effects against its gravity. That would be false if electromagnetism ceases on its becoming, but I do not understand the connection of the magnetic field of a rotating celestial solar spheroid body and its rotational motion.

http://en.wikipedia.org/wiki/Black_hole#Accretion_disk

They say disk, not spheroid.