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How fast the days are getting longer (2023)
Here in the northern hemisphere the vernal equinox just passed and the days arequickly getting longer. One of my col...
\[\frac{dt_{\textrm{daylight}}}{dT} = \frac{576 \epsilon \cos 2\pi \widetilde{T} \tan \lambda \sec^2 (\epsilon \sin 2\pi \widetilde{T})}{73\sqrt{1 - \tan^2 \lambda \tan^2 (\epsilon \sin 2\pi \widetilde{T})}} \, \frac{\textrm{min}}{\textrm{day}},\] where to make the equation a little cleaner, I’ve used \(\widetilde{T}\) to represent the fraction of the year since the vernal equinox. Image credit: Hong Kong ObservatoryTo take into account atmospheric refraction, we would not want to calculate the hour angle of the Sun when its altitude is zero, but when it is slightly less than zero. At those latitudes the ecliptic runs almost parallel to the horizon, so the Sun has to move quite a ways horizontally to make much progress in the vertical direction.
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