Sphäralen

Sphäralen is a term sometimes used in mathematics and physics to refer to spherical shells or regions within a sphere. The concept is often encountered when discussing properties that vary radially, meaning their value depends only on the distance from the center of the sphere. For instance, in astrophysics, a stellar atmosphere might be modeled as a series of sphäralen, each with different temperature or density.

In a more abstract mathematical context, a sphäralen can be defined as the region between two concentric spheres. If the inner sphere has radius r1 and the outer sphere has radius r2, then the sphäralen encompasses all points whose distance from the center is between r1 and r2. This is analogous to a cylindrical shell but in three dimensions and with a spherical boundary.

The volume of a sphäralen can be calculated by subtracting the volume of the inner sphere from the volume of the outer sphere. For a sphere with radius R, the volume is given by the formula (4/3)πR³. Therefore, the volume of a sphäralen with inner radius r1 and outer radius r2 is (4/3)πr2³ - (4/3)πr1³. This type of calculation is fundamental in integral calculus when dealing with spherical coordinates. The term is not as universally standardized as "spherical shell" but conveys a similar meaning.