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).

..
    TODO find link

.. py:currentmodule:: symplyphysics.laws.astronomy.latitude_from_zenith_distances_and_declinations

.. py:data:: latitude

    :attr:`~symplyphysics.symbols.classical_mechanics.latitude` of the observation site.

Symbol:
    :code:`phi`

Latex:
    :math:`\phi`

Dimension:
    :code:`angle`


.. py:data:: north_zenith_angle

    :attr:`~symplyphysics.symbols.astronomy.zenith_angle` of the northern star.

Symbol:
    :code:`theta_N`

Latex:
    :math:`\theta_\text{N}`

Dimension:
    :code:`angle`


.. py:data:: south_zenith_angle

    :attr:`~symplyphysics.symbols.astronomy.zenith_angle` of the southern star.

Symbol:
    :code:`theta_S`

Latex:
    :math:`\theta_\text{S}`

Dimension:
    :code:`angle`


.. py:data:: north_declination

    :attr:`~symplyphysics.symbols.astronomy.declination` of the northern star.

Symbol:
    :code:`delta_N`

Latex:
    :math:`\delta_\text{N}`

Dimension:
    :code:`angle`


.. py:data:: south_declination

    :attr:`~symplyphysics.symbols.astronomy.declination` of the southern star.

Symbol:
    :code:`delta_S`

Latex:
    :math:`\delta_\text{S}`

Dimension:
    :code:`angle`


.. py:data:: law

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


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