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Equation for Time of Sunrise and Simple Evaluation

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:

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Substituting angles of vector P but leaving the Sun's vector in simple xyz form, we can obtain a simple expression for tex2html_wrap_inline262 , the time of sunrise or sunset,

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where tex2html_wrap_inline210 is the latitude of point P. Rearranging,

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To good accuracy, the dependence of tex2html_wrap_inline228 components on time of day can be ignored and tex2html_wrap_inline228 evaluated at noon rather than at sunrise or sunset for a particular day. This is equivalent to using values of d given by tex2html_wrap_inline272 . At winter solstice tex2html_wrap_inline274 and tex2html_wrap_inline276 , so

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We leave a more general calculation for the next section.