# I Calculation of the hour angle of the Sun

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1. Jul 14, 2017

### jones123

Hi all,

According to the sunrise equation, the hour angle of the sun at sunset is:

cos H = -tan(a)tan(d)
where H = the hour angle, a = latitude and d = solar declination angle.

This equation says that H at sunset = -H at sunrise. Now, I have a few questions concerning that:

1) I was wondering how you could calculate the change of the hour angle in between...? So,

dH/dt = d(H at sunset - H at sunrise)/(time of sunset - time or sunrise)...?

2) I was calculating some values and found that, for example,

when the sun rises with at an hour angle of -1.641 radians, it must go down at the angle of +1.641 rad, but if you calculate the difference between both it is not equal to pi (or 180 degrees)? How does that come?

2. Jul 14, 2017

### Baluncore

The solar declination will cycle once per year through the seasons. The equinox is when the day and night are of equal length, which is when there will be a Pi radian difference between sunrise and sunset.
https://en.wikipedia.org/wiki/Sunrise_equation
https://en.wikipedia.org/wiki/Analemma

Last edited: Jul 14, 2017