Definition:Latitude

From ProofWiki
Jump to navigation Jump to search

Definition

Terrestrial 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.


Longitude-Terrestrial.png


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 $90 \degrees \, \mathrm S$.


Celestial Latitude

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

The celestial latitude of $P$ is the angle subtended by the the arc of the vertical circle through $P$ between $P$ and the ecliptic.


If $P$ is closer to the north ecliptic pole, the celestial latitude is defined as latitude $\beta \degrees$ north, where $\beta \degrees$ denotes $\beta$ degrees (of angle), written $\beta \degrees \, \mathrm N$.

If $P$ is closer to the south ecliptic pole, the celestial latitude is defined as latitude $\beta \degrees$ south, written $\beta \degrees \, \mathrm S$.

At the north ecliptic pole, the celestial latitude is $90 \degrees \, \mathrm N$.

At the south ecliptic pole, the celestial latitude is $90 \degrees \, \mathrm S$.


Also see

  • Results about latitude can be found here.