solar hour angle derivations

1. solar hour angle from datetime and longitude

symbol

description

unit

variable name

$$EOT$$

equation of time

$$minutes$$

$$t$$

datetime (UTC)

$$s$$ since 2000-01-01

datetime {time}

$$\eta$$

orbit angle of the earth around the sun

$$rad$$

$$\lambda$$

longitude

$$degE$$

longitude {time}

$$\omega$$

solar hour angle

$$deg$$

solar_hour_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) ) \\ C & = & \frac{A - \arctan(\frac{\tan(B)}{cos(\frac{\pi}{180} 23.44)})}{\pi} \\ EOT & = & 720 \left( C - \lfloor C + 0.5 \rfloor \right) \\ \omega & = & \lambda + 360 \left( \frac{t}{86400} - \lfloor \frac{t}{86400} \rfloor + \frac{EOT}{24 \cdot 60} \right) - 180 \end{eqnarray}

The solar hour angle will be mapped to [-180,180].