Solar Position

Based on BS 8206-2 mathematical methods.

Note on 12.1.6: The standard hour angle formula is implemented as \(\xi = \frac{\pi}{12} \text{TST}\) instead of \(\frac{\pi}{15}\) to correctly map 24 hours to \(2\pi\) radians.

12.1.2 Day angle

\(\tau_d = \frac{2\pi(J - 1)}{365}\)
Day Number (\(J\)):
Day Angle (\(\tau_d\)):

12.1.3 Solar declination

\(\delta_s = 0.006918 - 0.399912\cos\tau_d + 0.070257\sin\tau_d - \dots\)
Declination (\(\delta_s\)):

12.1.4 Equation of time

\(\text{ET} = 0.170\sin\left[\frac{4\pi(J - 80)}{373}\right] - \dots\)
Eq. of Time (\(\text{ET}\)):

12.1.5 True solar time

\(\text{TST} = LT + \frac{\lambda_s - \lambda}{15} + \text{ET} - \text{TD}\)
Local Time (\(LT\)):
True Solar Time (\(\text{TST}\)):

12.1.6 Hour angle

\(\xi = \frac{\pi}{12}\text{TST}\)
Hour Angle (\(\xi\)):

12.1.7 Solar altitude

\(a = \sin^{-1}(\sin\phi\sin\delta_s - \cos\phi\cos\delta_s\cos\xi)\)
Altitude (\(a\)):

12.1.8 Solar azimuth

\(g = \cos^{-1}\left(\frac{-\sin\phi\sin a + \sin\delta_s}{\cos\phi\cos a}\right)\)
Azimuth (\(g\)):