Spherical shell

A spherical shell ( known colloquially as hollow sphere ) is the difference of two concentric spheres with different radius.

The plane sections of a spherical shell are circular discs or annuli.

Shell models of celestial bodies

In the natural sciences spherical shells are often used for modeling of inhomogeneous bodies when they have approximate spherical shape.

In celestial bodies - which are spherically from about 500 km Size - these spherical shells are set up so that they have a constant density (average rock or gas density). For such a celestial body in hydrostatic equilibrium, its ( ball-like ) layer surfaces must be level surfaces simultaneously.

Some examples are:

  • Erdinneres: crust, upper / lower mantle, Earth's core
  • Earth's atmosphere: peplo and troposphere, stratosphere and mesosphere, ionosphere
  • Terrestrial Planets: thick lithosphere, otherwise Earth-like structure
  • Gas planets: dense atmosphere, liquid gas envelope, metallic hydrogen, iron core
  • Sun and fixed stars: solar corona, chromosphere, photosphere, convection, zone of fusion.

In the calculation models the spherical shells must also comply with other conditions that affect the pressure and the heat transport in particular. So have to choose a star in a stable state, the gravitational radiation and the gas pressure maintain balance throughout, and the urgent outward energy must always be the same in the outer spherical shells. Otherwise heat build-up and the star would be unstable there (see Supernova ).

Weightlessness inside a spherical shell

Of particular importance are spherical shells in the calculation of the gravitational field. In the interior of a hollow spherical shell the gravitational potential is constant because the gravitational forces cancel each other ( see picture). Therefore, if one of a spherically symmetric body layer by layer " takes off " ( mathematically eliminated ), then the gravity in the remaining body does not change. The geophysicist Charles Steger leather calls this principle of defoliation.

This allows every major celestial body 's gravitational field relatively accurately calculated. However, a complication is arising due to rotation and centrifugal flattening. It is smaller than in the interior close to the surface so that the parallelism of the stack trays or density is no longer given. The corresponding calculations but you can solve using computers by the body are broken down into many small elementary bodies today.

Galactic rotation

The o e weightlessness inside a spherical shell means in our galaxy that is located outside our solar system, stars have no gravitational effect, if they are distributed on the different sides of the galaxy roughly the same. Thus, the Kepler laws no longer apply for a single, centrally located mass is a prerequisite. For the actual rotation of the outer Milky Way ( near the Sun about 250 million years) the Oort rotation formula was derived several decades ago. Today, similar spherical shell models can help assess the extent of the dark matter.

Applications in electrical engineering

Also in the calculation of charges and currents, the specific properties of the spherical shells are significant. How can you prove that distribute electrical loads evenly on a conducting sphere. This was a prerequisite to be able to derive Coulomb's law in the 18th century.

Also the effect of the Faraday cage can be proved by a spherical shell model, and the charge and current in an electrical conductor in an analogous manner.

Other examples

Other examples of spherical shells or hollow spheres are

  • Geode ( Earth Sciences ), a rounded, limited by a single outer layer of rock cavity, with and without mineral or fossil filling
  • Druse (mineralogy ), a partially filled with crystals, rounded cavity
  • Blastula, a hollow ball formed from a single layer of cells
  • Fullerenes, hollow spheres, consisting of a network of carbon atoms
  • Baoding balls, hollow balls with built-in sound elements
  • Ball, soap bubble
  • A cannonball with bursting charge
  • Astronomical coordinate system
  • Geophysics
  • Electrostatics
  • Space geometry
Set (mathematics) Annulus (mathematics) Structure of the Earth Gas giant Radiation pressure Instability Karl Ledersteger Centrifugal force Druse (geology)
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