Category:Definitions/Spherical Coordinates

This category contains definitions related to Spherical Coordinates.
Related results can be found in Category:Spherical Coordinates.

A spherical coordinate system is a polar coordinate system in $3$ dimensions.

A distinct point $O$ is identified, and referred to as the origin.

Polar Axis

The polar axis of a spherical coordinate system is the vertical straight line which passes through the origin $O$.

Horizontal Axis

Having identified the polar axis of a spherical coordinate system, one then selects a distinct horizontal straight line, also passing through the origin $O$, perpendicular to the polar axis

This horizontal straight line is referred to as the horizontal axis.

Initial Meridian Plane

The initial meridian plane of a spherical coordinate system is the vertical plane in which the polar axis and horizontal axis both lie.

Hence, let $P$ be an arbitrary point $P$ in space.

Let $\mathbf r$ be the radius vector of $P$ with respect to $O$.

The position of $P$ is specified in spherical coordinates by:

$(1): \quad$ the length of $\mathbf r$, that is, the distance of $P$ from the origin $O$, denoted by $r$.

$(2): \quad$ the angle between $\mathbf r$ and the polar axis, known as the colatitude of $P$, denoted by $\theta$

$(3): \quad$ the angle between the horizontal axis and the projection of $\mathbf r$ onto the horizontal plane, known as the longitude of $P$, denoted by $\phi$.