Definition:Longitude

Definition

In a general spherical coordinate system, the longitude $\phi$ of a point is angle the between the horizontal axis and the projection of the radius vector onto the horizontal plane.

In other more specialised coordinate systems the definition is similar:

Terrestrial Longitude

Let $J$ be a point on Earth's surface that is not one of the two poles $N$ and $S$.

Let $\bigcirc NJS$ be a meridian passing through $J$, whose endpoints are by definition $N$ and $S$.

The longitude of $J$, and of the meridian $\bigcirc NJS$ itself, is the (spherical) angle that $\bigcirc NJS$ makes with the principal meridian $\bigcirc NKS$.

If $\bigcirc NJS$ is on the eastern hemisphere, the longitude is defined as longitude $n \degrees$ east, where $n \degrees$ denotes $n$ degrees (of angle), written $n \degrees \, \mathrm E$.

If $\bigcirc NJS$ is on the western hemisphere, the longitude is defined as longitude $n \degrees$ west, written $n \degrees \, \mathrm W$.

If $\bigcirc NJS$ is the principal meridian itself, the longitude is defined as $0 \degrees$ longitude.

If $\bigcirc NJS$ is the other half of the great circle that contains the principal meridian, the longitude is defined as $180 \degrees$ longitude.

Celestial Longitude

Let $P$ be a point on the celestial sphere.

Let $J$ be a great circle on the celestial sphere passing through $P$ and both of the north ecliptic pole and south ecliptic pole.

The celestial longitude $\lambda$ of $P$ is the (spherical) angle (measuring east) that $J$ makes with the vernal equinox.

It ranges from $0$ to $360 \degrees$.

Linguistic Note

When the word longitude is spoken, an extraneous d is often added: long-di-tude.

This is technically incorrect.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): spherical coordinate system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): spherical coordinate system