Calculation of the hour angle of the Sun

[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?

Thanks already!

 

[Baluncore]

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?

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