# Spherical Coordinates

## Spherical Coordinates

Triplet (ρθφ) of numbers associated with the position of a point P in a three‑dimensional space in a spherical locating system. The numbers ρθ and φ are the distance from P to the centre of the sphere and the angles of rotation with the x‑axis and the z‑axis.

In this system, ρ represents the distance from the point P to the centre O of the reference sphere; the angle θ is the rotation angle of the x-axis toward the orthogonal projection OP’ of the radius OP on the plane xy (represented in colour in the figure); φ is the rotation angle of the z‑axis on the radius OP.

A spherical coordinate system is a synthesis between the Cartesian coordinate system in a three-dimensional space and a polar coordinate system.

### Examples

• The spherical coordinate system is used in astrometry to study the distance and the movement of stars in relation to the solar system or in relation to one another.
• Earth’s coordinate system is not, properly speaking, a spherical coordinate system because the distance from one point on the globe to the centre of the Earth is not involved.