spherical coordinates

spherical coordinates

Spherical coordinates are a system for specifying positions in terms of angles on a sphere, such as the celestial sphere or the surface of a planet or large moon. In spherical coordinates, a point P in space is located by its position relative to three mutually perpendicular axes (the x-, y-, and z-axes) in terms of (1) its distance r from the origin, O, (2) the angle (θ) between the x-axis and the projection of OP onto the x-y plane, and (3) the angle (φ) between OP and the z-axis. The coordinates of P are thus expressed in the form (r, θ, φ). See also analytic geometry.


In the accompanying diagram, a spherical coordinates system is shown defining point P in terms of distance r and angles θ and φ. (2) The spherical triangle ABC has "sides" a, b, c which are the angles BOC, AOC, and AOB respectively and "angles" A, B, C where A is the angle between the tangents to the arcs AC and AB at A; B that between the tangents to the arcs AB and BC at B; and C that between the tangents to the arcs AC and BC at C respectively.


spherical coordinates calculations