# solar declination angle derivations

1. solar declination angle from datetime

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(t\) | datetime (UTC) | \(s\) since 2000-01-01 | datetime {time}
   \(\delta\) | solar declination angle | \(deg\) | solar_declination_angle {time}

   \begin{eqnarray} A & = & 2\pi \left( \frac{t + 10 \cdot 86400}{365.2422 \cdot 86400} - \lfloor \frac{t + 10 \cdot 86400}{365.2422 \cdot 86400} \rfloor \right) \\ B & = & A + 2 \cdot 0.0167 \sin( 2\pi \left( \frac{t - 2 \cdot 86400}{365.2422 \cdot 86400} - \lfloor \frac{t - 2 \cdot 86400}{365.2422 \cdot 86400} \rfloor \right) ) \\ \delta & = & -\frac{180}{\pi} \arcsin( \sin(\frac{\pi}{180} 23.44) \cos(B) ) \end{eqnarray}