Astronomy Principles and Practice Fourth Edition.pdf

Sunset and sunrise 75
Figure 8.15. The celestial sphere illustrating sunrise.
showing that in a given latitude, the value of the Sun’s hour angle at setting depends on the Sun’s
declination.
Thus, if the latitude is north and the declination is positive,
6 h ≤ H t ≤ 12 h .
If the latitude is north and the declination is negative,
0 h ≤ H t ≤ 6 h .
To obtain the azimuth at sunset, we apply the cosine formula to △PZX again. Thus,
cos(90 − δ) = cos(90 − φ)cos 90 + sin(90 − φ)sin90cos(360 − A t )
or
cos A t = sin δ
cos φ .
Note that for sunset, the azimuth, measured eastwards from north, is necessarily greater than 180 ◦ .
For northern latitudes, if the declination is positive,
270 ◦ ≤ A t ≤ 360 ◦
but if the declination is negative,
180 ◦ ≤ A t ≤ 270 ◦ .
The total number of hours of daylight in a given 24 h period is obtained approximately by doubling
H t , the hour angle of sunset (see equation (8.6)), for it is easily seen from the diagram for sunrise
(figure 8.15) that the hours of daylight for sunrise to apparent noon equal H t , being given by h or
ZPX.
The hour angle at sunrise, H r ,isgivenby
H r = 360 − h
where
cos h =−tan φ tan δ.