DURATA MINIMA E MASSIMA DEI CREPUSCOLI
Le seguenti tabelle elencano i momenti in cui durata dei crepuscoli è minima, sia analizzando il problema ristretto che quello generale
Problema ristretto: si suppone che l'ora del sorgere e del tramonto del Sole si riferiscono all'istante in cui la sua altitudine vera è esattamente zero.
Gli effetti della rifrazione atmosferica e della dimensione del disco solare sono trascurati.
Problema generale : si considera il diametro solare e la rifrazione.
CREPUSCOLO CIVILE : ALTEZZA DEL SOLE -6°
Lat. Dec. Min. Dec1. Min1.
-90 3.00 3.42
-88 3.00 3.42
-86 3.00 3.41 322.0
-84 2.99 360.0 3.40 204.3
-82 2.97 194.7 3.39 151.2
-80 2.96 148.0 3.37 120.4
-78 2.94 120.7 3.35 100.2
-76 2.91 102.4 3.32 85.9
-74 2.89 89.1 3.29 75.3
-72 2.86 79.1 3.25 67.1
-70 2.82 71.2 3.21 60.6
-68 2.79 64.8 3.17 55.3
-66 2.74 59.6 3.12 50.9
-64 2.70 55.2 3.07 47.2
-62 2.65 51.5 3.02 44.1
-60 2.60 48.3 2.96 41.4
-58 2.55 45.5 2.90 39.0
-56 2.49 43.1 2.83 37.0
-54 2.43 41.0 2.77 35.2
-52 2.37 39.1 2.69 33.6
-50 2.30 37.4 2.62 32.2
-48 2.23 35.9 2.54 30.9
-46 2.16 34.6 2.46 29.8
-44 2.09 33.4 2.38 28.7
-42 2.01 32.3 2.29 27.8
-40 1.93 31.4 2.20 27.0
-38 1.85 30.5 2.10 26.2
-36 1.77 29.7 2.01 25.5
-34 1.68 29.0 1.91 24.9
-32 1.59 28.3 1.81 24.4
-30 1.50 27.7 1.71 23.9
-28 1.41 27.2 1.60 23.4
-26 1.32 26.7 1.50 23.0
-24 1.22 26.3 1.39 22.6
-22 1.12 25.9 1.28 22.3
-20 1.03 25.5 1.17 22.0
-18 0.93 25.2 1.06 21.7
-16 0.83 25.0 0.94 21.5
-14 0.73 24.7 0.83 21.3
-12 0.62 24.5 0.71 21.1
-10 0.52 24.4 0.59 21.0
-8 0.42 24.2 0.48 20.9
-6 0.31 24.1 0.36 20.8
-4 0.21 24.1 0.24 20.7
-2 0.10 24.0 0.12 20.7
0 0.00 24.0 0.00 20.7
2 -0.10 24.0 -0.12 20.7
4 -0.21 24.1 -0.24 20.7
6 -0.31 24.1 -0.36 20.8
8 -0.42 24.2 -0.48 20.9
10 -0.52 24.4 -0.59 21.0
12 -0.62 24.5 -0.71 21.1
14 -0.73 24.7 -0.83 21.3
16 -0.83 25.0 -0.94 21.5
18 -0.93 25.2 -1.06 21.7
20 -1.03 25.5 -1.17 22.0
22 -1.12 25.9 -1.28 22.3
24 -1.22 26.3 -1.39 22.6
26 -1.32 26.7 -1.50 23.0
28 -1.41 27.2 -1.60 23.4
30 -1.50 27.7 -1.71 23.9
32 -1.59 28.3 -1.81 24.4
34 -1.68 29.0 -1.91 24.9
36 -1.77 29.7 -2.01 25.5
38 -1.85 30.5 -2.10 26.2
40 -1.93 31.4 -2.20 27.0
42 -2.01 32.3 -2.29 27.8
44 -2.09 33.4 -2.38 28.7
46 -2.16 34.6 -2.46 29.8
48 -2.23 35.9 -2.54 30.9
50 -2.30 37.4 -2.62 32.2
52 -2.37 39.1 -2.69 33.6
54 -2.43 41.0 -2.77 35.2
56 -2.49 43.1 -2.83 37.0
58 -2.55 45.5 -2.90 39.0
60 -2.60 48.3 -2.96 41.4
62 -2.65 51.5 -3.02 44.1
64 -2.70 55.2 -3.07 47.2
66 -2.74 59.6 -3.12 50.9
68 -2.79 64.8 -3.17 55.3
70 -2.82 71.2 -3.21 60.6
72 -2.86 79.1 -3.25 67.1
74 -2.89 89.1 -3.29 75.3
76 -2.91 102.4 -3.32 85.9
78 -2.94 120.7 -3.35 100.2
80 -2.96 148.0 -3.37 120.4
82 -2.97 194.7 -3.39 151.2
84 -2.99 360.0 -3.40 204.3
86 -3.00 -3.41 322.0
88 -3.00 -3.42
90 -3.00 -3.42
CREPUSCOLO NAUTICO : ALTEZZA DEL SOLE -12°
Lat. Dec. Min. Dec1. Min1.
-90 6.03 6.45
-88 6.03 6.44
-86 6.02 6.43
-84 6.00 6.41 548.5
-82 5.97 6.38 354.8
-80 5.94 6.35 272.6
-78 5.90 360.0 6.31 223.2
-76 5.85 237.0 6.26 189.7
-74 5.80 195.9 6.20 165.4
-72 5.74 169.1 6.13 146.8
-70 5.67 149.7 6.06 132.2
-68 5.59 134.8 5.98 120.4
-66 5.51 123.0 5.89 110.7
-64 5.42 113.3 5.79 102.6
-62 5.32 105.1 5.69 95.7
-60 5.22 98.3 5.58 89.8
-58 5.11 92.4 5.46 84.6
-56 5.00 87.3 5.34 80.2
-54 4.88 82.9 5.21 76.2
-52 4.75 78.9 5.08 72.7
-50 4.62 75.5 4.93 69.6
-48 4.48 72.4 4.79 66.9
-46 4.34 69.7 4.63 64.4
-44 4.19 67.2 4.47 62.2
-42 4.03 65.0 4.31 60.2
-40 3.87 63.0 4.14 58.4
-38 3.71 61.2 3.96 56.7
-36 3.54 59.6 3.78 55.3
-34 3.37 58.1 3.60 53.9
-32 3.19 56.8 3.41 52.7
-30 3.01 55.6 3.22 51.6
-28 2.83 54.5 3.02 50.6
-26 2.64 53.5 2.82 49.7
-24 2.45 52.6 2.62 48.9
-22 2.26 51.8 2.41 48.2
-20 2.06 51.1 2.20 47.5
-18 1.86 50.5 1.99 47.0
-16 1.66 50.0 1.77 46.5
-14 1.46 49.5 1.56 46.0
-12 1.25 49.1 1.34 45.7
-10 1.05 48.8 1.12 45.4
-8 0.84 48.5 0.90 45.1
-6 0.63 48.3 0.67 44.9
-4 0.42 48.1 0.45 44.8
-2 0.21 48.0 0.22 44.7
0 0.00 48.0 0.00 44.7
2 -0.21 48.0 -0.22 44.7
4 -0.42 48.1 -0.45 44.8
6 -0.63 48.3 -0.67 44.9
8 -0.84 48.5 -0.90 45.1
10 -1.05 48.8 -1.12 45.4
12 -1.25 49.1 -1.34 45.7
14 -1.46 49.5 -1.56 46.0
16 -1.66 50.0 -1.77 46.5
18 -1.86 50.5 -1.99 47.0
20 -2.06 51.1 -2.20 47.5
22 -2.26 51.8 -2.41 48.2
24 -2.45 52.6 -2.62 48.9
26 -2.64 53.5 -2.82 49.7
28 -2.83 54.5 -3.02 50.6
30 -3.01 55.6 -3.22 51.6
32 -3.19 56.8 -3.41 52.7
34 -3.37 58.1 -3.60 53.9
36 -3.54 59.6 -3.78 55.3
38 -3.71 61.2 -3.96 56.7
40 -3.87 63.0 -4.14 58.4
42 -4.03 65.0 -4.31 60.2
44 -4.19 67.2 -4.47 62.2
46 -4.34 69.7 -4.63 64.4
48 -4.48 72.4 -4.79 66.9
50 -4.62 75.5 -4.93 69.6
52 -4.75 78.9 -5.08 72.7
54 -4.88 82.9 -5.21 76.2
56 -5.00 87.3 -5.34 80.2
58 -5.11 92.4 -5.46 84.6
60 -5.22 98.3 -5.58 89.8
62 -5.32 105.1 -5.69 95.7
64 -5.42 113.3 -5.79 102.6
66 -5.51 123.0 -5.89 110.7
68 -5.59 134.8 -5.98 120.4
70 -5.67 149.7 -6.06 132.2
72 -5.74 169.1 -6.13 146.8
74 -5.80 195.9 -6.20 165.4
76 -5.85 237.0 -6.26 189.7
78 -5.90 360.0 -6.31 223.2
80 -5.94 -6.35 272.6
82 -5.97 -6.38 354.8
84 -6.00 -6.41 548.5
86 -6.02 -6.43
88 -6.03 -6.44
90 -6.03 -6.45
CREPUSCOLO ASTRONOMICO : ALTEZZA DEL SOLE -18°
Lat. Dec. Min. Dec1. Min1.
-90 9.11 9.52
-88 9.11 9.52
-86 9.09 9.50
-84 9.06 9.47
-82 9.02 9.43
-80 8.97 9.38 474.1
-78 8.91 9.31 367.0
-76 8.84 9.24 304.7
-74 8.76 9.15 262.3
-72 8.66 360.0 9.05 231.0
-70 8.56 258.5 8.95 207.0
-68 8.44 222.3 8.83 187.8
-66 8.32 197.8 8.69 172.2
-64 8.18 179.3 8.55 159.2
-62 8.04 164.7 8.40 148.3
-60 7.88 152.7 8.24 138.9
-58 7.72 142.7 8.07 130.9
-56 7.55 134.2 7.88 123.8
-54 7.36 126.9 7.69 117.7
-52 7.17 120.5 7.49 112.2
-50 6.97 114.9 7.28 107.4
-48 6.76 110.0 7.06 103.1
-46 6.54 105.7 6.84 99.3
-44 6.32 101.8 6.60 95.8
-42 6.08 98.3 6.36 92.7
-40 5.84 95.2 6.11 89.9
-38 5.60 92.4 5.85 87.3
-36 5.34 89.8 5.58 85.0
-34 5.08 87.5 5.31 83.0
-32 4.81 85.5 5.03 81.1
-30 4.54 83.6 4.75 79.4
-28 4.26 81.9 4.46 77.9
-26 3.98 80.4 4.16 76.5
-24 3.69 79.1 3.86 75.2
-22 3.40 77.9 3.55 74.1
-20 3.11 76.8 3.24 73.1
-18 2.81 75.8 2.93 72.2
-16 2.50 75.0 2.61 71.5
-14 2.20 74.3 2.29 70.8
-12 1.89 73.7 1.97 70.2
-10 1.58 73.1 1.65 69.7
-8 1.26 72.7 1.32 69.3
-6 0.95 72.4 0.99 69.0
-4 0.63 72.2 0.66 68.8
-2 0.32 72.0 0.33 68.7
0 0.00 72.0 0.00 68.7
2 -0.32 72.0 -0.33 68.7
4 -0.63 72.2 -0.66 68.8
6 -0.95 72.4 -0.99 69.0
8 -1.26 72.7 -1.32 69.3
10 -1.58 73.1 -1.65 69.7
12 -1.89 73.7 -1.97 70.2
14 -2.20 74.3 -2.29 70.8
16 -2.50 75.0 -2.61 71.5
18 -2.81 75.8 -2.93 72.2
20 -3.11 76.8 -3.24 73.1
22 -3.40 77.9 -3.55 74.1
24 -3.69 79.1 -3.86 75.2
26 -3.98 80.4 -4.16 76.5
28 -4.26 81.9 -4.46 77.9
30 -4.54 83.6 -4.75 79.4
32 -4.81 85.5 -5.03 81.1
34 -5.08 87.5 -5.31 83.0
36 -5.34 89.8 -5.58 85.0
38 -5.60 92.4 -5.85 87.3
40 -5.84 95.2 -6.11 89.9
42 -6.08 98.3 -6.36 92.7
44 -6.32 101.8 -6.60 95.8
46 -6.54 105.7 -6.84 99.3
48 -6.76 110.0 -7.06 103.1
50 -6.97 114.9 -7.28 107.4
52 -7.17 120.5 -7.49 112.2
54 -7.36 126.9 -7.69 117.7
56 -7.55 134.2 -7.88 123.8
58 -7.72 142.7 -8.07 130.9
60 -7.88 152.7 -8.24 138.9
62 -8.04 164.7 -8.40 148.3
64 -8.18 179.3 -8.55 159.2
66 -8.32 197.8 -8.69 172.2
68 -8.44 222.3 -8.83 187.8
70 -8.56 258.5 -8.95 207.0
72 -8.66 360.0 -9.05 231.0
74 -8.76 -9.15 262.3
76 -8.84 -9.24 304.7
78 -8.91 -9.31 367.0
80 -8.97 -9.38 474.1
82 -9.02 -9.43
84 -9.06 -9.47
86 -9.09 -9.50
88 -9.11 -9.52
90 -9.11 -9.52
Lat = latitudine geografica dell'osservatore
Dec = declinazione del Sole in cui avviene la durata minima del crepuscolo. Dalla declinazione si può risalire ai giorni dell'anno
Min = durata del crepuscolo
Dec1 e Min 1 = stessi valori nel problema generale
DURATA MASSIMA DEI CREPUSCOLI
Crepuscolo civile :
per latitudini tra 0° e 60°34' il più lungo crepuscolo civile avviene il giorno del solstizio d'estate.
per latitudini tra 60°34' e 87° il giorno con il più lungo crepuscolo civile corrisponde a declinazione=84-latitudine
per latitudini oltre 87° non vi è un vero e proprio crepuscolo civile
Crepuscolo astronomico :
per latitudini tra 0° e 48°34' il più lungo crepuscolo civile avviene il giorno del solstizio d'estate.
per latitudini tra 48°34' e 81° il giorno con il più lungo crepuscolo civile corrisponde a declinazione=72-latitudine
per latitudini oltre 81° non vi è un vero e proprio crepuscolo civile