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I added in the time remaining till sunset based on the time the photo was shot
Interesting to note the sun sets faster around the equinoxes
Summer sun sits longer in the late evening before fully setting
Winter noon may be low sun, but it does sit out for a while at that low angle before it dips under
The more north you go towards the arctic circle, the more slow the sun sets around the solstices. Once you go above the arctic circle, you can't even measure this out to the solstice because sun won't set at all on some of the nights. But fastest sunsets on equinox is true for all latitudes except right around the poles
20:00 on 24/4/2014
50 minutes before sunset at 8:50pm
Matches these
15:48 on 24/1/2014
61 minutes before sunset
17:04 on 24/2/2014
49 minutes before sunset
18:03 on 24/3/2014
46 minutes before sunset
20:00 on 24/4/2014 "today"
50 minutes before sunset
20:47 on 24/5/2014
57 minutes before sunset
21:10 on 24/6/2014
60 minutes before sunset
20:50 on 24/7/2014
54 minutes before sunset
19:52 on 24/8/2014
48 minutes before sunset
18:35 on 24/9/2014
47 minutes before sunset
17:17 on 24/10/2014
51 minutes before sunset
15:09 on 24/11/2014
63 minutes before sunset
14:51 on 24/12/2014
72 minutes before sunset
Mac15 solar elevation angle equivalents for the evening photo taken, adjusted for DST, for NW Ireland 54"54"N 7"00W
And time remaining till sunset
For 24th of each month of 2014
According to wikipedia, the formula is solar noon +/- arccos ( -(sin(L)*sin(D) - sin(a)) / cos(L)*cos(D) ) / 15, with L = latitude, D = sun declination, a = sun angle (here 5.9 deg). But you said that you calculate those times with your excel model. How to calculate arccos (inverse cosine) with excel?
According to wikipedia, the formula is solar noon +/- arccos ( -(sin(L)*sin(D) - sin(a)) / cos(L)*cos(D) ) / 15, with L = latitude, D = sun declination, a = sun angle (here 5.9 deg). But you said that you calculate those times with your excel model. How to calculate arccos (inverse cosine) with excel?
Inverse cosine in excel is =(acos(value))/(3.1515927/180)
I also use a formula for the angle of declination and another formula for equation of time (the forms of these that factor the earth's eccentric orbit and for example, recognize that earth spins slower in January and faster in July and that the time length of northern hemisphere summer is 6 days longer than Southern Hemisphere summer
And also I have an adjustment for the angle of declination within the fraction of the day as it is continuously changing
Also I adjust for longitude degrees and timezone and DST
So there's a couple moving pieces
Also not every year is the same.
But you get close enough approximation if you use the solar elevation angle formula, convert hour angle by dividing by 15 like you said. Find the solar noon time around the longitude you are interested in using. Solar noon minus 12 will convert your solar time to clock time if you adjust by that amount of minutes.
And for sunrise assume a solar elevation angle of -0.83, not 0
Actually for solar elevation angle formula, you would need to convert the clock time to solar time, convert that to the hour angle to plug in, then all you need is latitude and angle of declination
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