Latitude from zenith angle and declination¶

Knowing the zenith angles and declinations of the northern and southern stars, it is possible to determine the latitude of the observation site.

Notes:

Northern star is any star north of the zenith with known declination.
Southern star is any star south of the zenith with known declination.

Conditions:

Both stars are at upper transit (culmination).

latitude¶

latitude of the observation site.

Symbol:: phi
Latex:: \(\phi\)
Dimension:: angle

north_zenith_angle¶

zenith_angle of the northern star.

Symbol:: theta_N
Latex:: \(\theta_\text{N}\)
Dimension:: angle

south_zenith_angle¶

zenith_angle of the southern star.

Symbol:: theta_S
Latex:: \(\theta_\text{S}\)
Dimension:: angle

north_declination¶

declination of the northern star.

Symbol:: delta_N
Latex:: \(\delta_\text{N}\)
Dimension:: angle

south_declination¶

declination of the southern star.

Symbol:: delta_S
Latex:: \(\delta_\text{S}\)
Dimension:: angle

law¶

phi = (theta_S - theta_N + delta_S + delta_N) / 2

Latex:: \[\phi = \frac{\theta_\text{S} - \theta_\text{N} + \delta_\text{S} + \delta_\text{N}}{2}\]