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