At sunrise or sunset, the sun's rays are parallel to the earth's surface. At point P on the Earth's surface, approximating the sun to be far away, we obtain the equation for time of sunrise and sunset:
Substituting angles of vector P
but leaving the Sun's vector in simple
xyz form, we can obtain a simple expression for
, the time of sunrise or sunset,
where
is the latitude of point P. Rearranging,
To good accuracy, the dependence of
components on time of day can be ignored and
evaluated at noon rather than at sunrise or sunset for a particular day.
This is equivalent to using values of d given by
.
At winter solstice
and
, so
We leave a more general calculation for the next section.