Spherical coordinates

From Glossary of Meteorology

spherical coordinates

(Also called polar coordinates in space, geographical coordinates.) A system of curvilinear coordinates in which the position of a point in space is designated by its distance r from the origin or pole along the radius vector, the angle φ between the radius vector and a vertically directed polar axis called the cone angle or colatitude, and the angle θ between the plane of φ and a fixed meridian plane through the polar axis, called the polar angle or longitude.

A constant-amplitude radius vector r confines a point to a sphere of radius r about the pole. The angles φ and θ serve to determine the position of the point on the sphere. The relations between the spherical coordinates and the rectangular Cartesian coordinates (x, y, z) are x = r cos θ sin φ; y = r sin θ sin φ; z = r cos φ.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact [email protected]. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.