Circle of a sphere

Under small circle refers to those circles on a sphere whose planes do not contain the center of the sphere.

The name " small circles " was coined as a contrast to the " great circles ", the planes containing the sphere center and include all the largest possible circles on a spherical surface.

The most important small circles are

  • The parallels (constant latitude ) and
  • The distance circles (circles equidistant from a given point ).

They are not suitable for trigonometric calculations. For the formulas of which only great circles are to be used - for example, meridians or " orthodromic (shortest connecting lines between ball points ) ". A triangle of such great circles is called after its main applications astronomical or nautical triangle, but is also named after its vertices pole - zenith star-delta.

The Spherical trigonometry used small circles only establishing metrics and angular distances. They have the same geometrical loci distances from a starting point - for example in the analysis of seismic waves, in the navigation or for the measurement of the elevation angle of stars. For example, all points of the earth's surface, on which a star at the same height h appears on a small circle around the " pixel " of the star ( where he is at the zenith ). The associated with this measure h small circle has the radius 90 ° - h, which corresponds to the zenith distance. This size occurs as a side ( in degrees specified distance ) in nautical triangle, between star and the zenith ( position of the observer ) on.