Small circle
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 of which contain the spherical center and which 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 of equal distance to a given point).
But they are not suitable for trigonometric calculations. Only great circles are to be used for their formulas - for example meridians or " orthodromes (shortest connecting lines between spherical points)". A triangle made up of such great circles is called an astronomical or nautical triangle after its most important uses , but is also called a pole-zenith-star triangle after its corner points .
The spherical trigonometry only uses small circles to define measured variables and angular distances. They are geometric locations at the same distance from a starting point - for example when analyzing earthquake waves , in navigation or for measuring the elevation angle of stars . For example, all points on the earth's surface on which a star appears at the same height h lie on a small circle around the star's “image point” (where it is at the zenith ). The small circle belonging to this measured variable h has a radius of 90 ° - h , which also corresponds to the zenith distance . This quantity appears as one side (distance specified in degrees) in the nautical triangle, namely between the star and the zenith (location of the observer).