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2.8 Range of the sun measured along the sky

 

Frank L. Preuss

 

The formula for the longest day is
L = 2 arccos(-tan(|φ|)tan(ε))

To obtain the shortest angle, the minus sign is removed from the formula:
L = 2 arccos(tan(|φ|)tan(ε))

The associated length of the day is equal to L/15 if one measures L in degrees and time in hours.

The following table results from the above formula:

 

The range of the sun measured along the sky
1234567891011
Latitude Obli-quity of the eclip-tic Values Length of time measured as angle Length of time measured as hours
Des-crip-tion φ ε tan(φ) tan(ε) tan(φ) tan(ε) Length of lon-gest day Length of shor-test day Mean length of day Time of lon-gest day Time of shor-test day
de-grees de-grees de-grees de-grees de-grees h h
Equa-tor023.44 0.00000.43360.0000 180.0180.0180.0 12.0012.00
1023.44 0.17630.43360.0764 188.8171.2180.0 12.5811.42
2023.44 0.36400.43360.1578 198.2161.8180.0 13.2110.79
Tropic23,4423.44 0.43360.43360.1880 201.7158.3180.0 13.4410.56
3023.44 0.57740.43360.2503 209.0151.0180.0 13.9310.07
4023.44 0.83910.43360.3638 222.7137.3180.0 14.84 9.16
5023.44 1.19180.43360.5167 242.2117.8180.0 16.15 7.85
6023.44 1.73210.43360.7510 277.3 82.7180.0 18.49 5.51
6623.44 2.24600.43360.9738 333.7 26.3180.0 22.25 1.75
Polar circle66.5623.44 2.30640.43361.0000
7023.44 2.74750.43361.1912
8023.44 5.67130.43362.4589
Pole9023.44 0.4336

 

This is the end of "2.8 Range of the sun measured on the horizon"
To the German version of this chapter: 2.8 Bereich der Sonne horizontal gemessen

 

 

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