Definition:Geographical Coordinates

Theorem

Let $J$ be a point on Earth's surface.

The geographical coordinates of $J$ are the definition of the position of $J$ with respect to the equator and the principal meridian.

Latitude

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 $S$.

Let $\bigcirc NJS$ pass through the equator at $L$.

The latitude of $J$ is the (spherical) angle $\sphericalangle LOJ$ , where $O$ is the center of Earth.

If $J$ is in the northern hemisphere of Earth, the latitude is defined as latitude $n \degrees$ north, where $n \degrees$ denotes $n$ degrees (of angle), written $n \degrees \, \mathrm N$.

If $J$ is in the southern hemisphere of Earth, the latitude is defined as latitude $n \degrees$ south, written $n \degrees \, \mathrm S$.

At the North Pole, the latitude is $90 \degrees \, \mathrm N$.

At the South Pole, the latitude is $90 \degrees \, \mathrm S$.

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.

Also see

• Results about geographical coordinates can be found here.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $2$. Coordinates
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): geographical coordinates
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): geographical coordinates