Azimuth

In cartography/navigation, an azimuth between two points is the angle (in the plane) formed by the straight line passing through the two points and the line passing through the two poles.

In other words, it is the angle formed between a given direction and north (measured clockwise from true or magnetic north).

It is generally expressed in degrees, from 0° (facing north) to 360° (returning to north after a complete rotation).

From 2 GPS points (Point 1: latitude $ lat_1 $, longitude $ long_1 $ and Point 2 latitude $ lat_2 $, longitude $ long_2 $), the formula to calculate an azimuth $ A $ is $$ A = \operatorname{atan2}(y, x) $$

with $ x = \cos(lat_1) \cdot \sin(lat_2) - \sin(lat_1) \cdot \cos(lat_2) \cdot \cos(long_2-long_1) $ and $ y = \sin(long_2-long_1) \cdot \cos(lat_2) $

Reminder: the arctan2 formula is $$ \operatorname{atan2}(y,x) = 2 \arctan \left( \frac{ y }{ \sqrt{x^2+y^2} + x } \right) $$

Every hour, the Earth rotates on itself about 15 degrees, so every hour on Earth, the sun is seen 15 degrees further west.

By knowing the azimuth of the sun, solar time can be calculated. At noon, the sun is 180 degrees. Each difference of 15 degrees is 1 hour.

— Geographic azimuth: Measured relative to geographic north (true north).

— Magnetic azimuth: Measured relative to magnetic north indicated by the compass.

The difference between the two is called magnetic declination and depends on location and time.

Azimuth, with or without h, are 2 identical terms, despite the spelling variant, both spellings are accepted.