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}