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.