緯度ａを固定するとき，公転角度と経度の対 (τ, b ) に対し，太陽の仰角余角αがつぎのように決まる (  太陽の高度)：
\[
\alpha_c = a_c \tau_s \ b_c - n_c a_c \tau_c \ b_s + n_s a_s \tau_c
\]
\( n \) : 地軸の傾き (公転面の法線と地軸がなす角の大きさ)
太陽の仰角余角がαのとき，水平面に垂直に立てた棒の影の長さは，棒の高さの \( tan( \alpha ) \) 倍。
よって，計算によりつぎの表を得る：
北緯50度の場合
公転
角度 |
月日 |
南中
の時刻 |
○時の影の長さ (倍率) |
| 4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
| 0 |
6/20 |
12:0:0 |
─ |
6.5 |
3.1 |
1.9 |
1.3 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.3 |
1.9 |
3.1 |
6.5 |
─ |
| 5 |
6/25 |
12:1:47 |
─ |
6.8 |
3.2 |
2 |
1.4 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.3 |
1.9 |
3.1 |
6.4 |
84.1 |
| 10 |
6/30 |
12:3:30 |
|
7.2 |
3.3 |
2 |
1.4 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.3 |
1.9 |
3.1 |
6.4 |
85.6 |
| 15 |
7/5 |
12:5:5 |
|
7.8 |
3.4 |
2.1 |
1.4 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.3 |
1.9 |
3.1 |
6.5 |
─ |
| 20 |
7/10 |
12:6:31 |
|
8.6 |
3.6 |
2.1 |
1.4 |
1 |
0.8 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.3 |
1.9 |
3.1 |
6.7 |
─ |
| 25 |
7/15 |
12:7:43 |
|
9.8 |
3.8 |
2.2 |
1.5 |
1.1 |
0.8 |
0.6 |
0.6 |
0.6 |
0.7 |
1 |
1.4 |
2 |
3.2 |
7.1 |
|
| 30 |
7/20 |
12:8:40 |
|
11.7 |
4 |
2.3 |
1.5 |
1.1 |
0.8 |
0.6 |
0.6 |
0.6 |
0.8 |
1 |
1.4 |
2 |
3.3 |
7.7 |
|
| 35 |
7/25 |
12:9:21 |
|
14.7 |
4.3 |
2.4 |
1.6 |
1.1 |
0.8 |
0.7 |
0.6 |
0.6 |
0.8 |
1 |
1.4 |
2.1 |
3.5 |
8.6 |
|
| 40 |
7/31 |
12:9:43 |
|
20.1 |
4.7 |
2.5 |
1.7 |
1.2 |
0.9 |
0.7 |
0.6 |
0.7 |
0.8 |
1.1 |
1.5 |
2.2 |
3.7 |
10 |
|
| 45 |
8/5 |
12:9:48 |
|
33.2 |
5.2 |
2.7 |
1.7 |
1.2 |
0.9 |
0.7 |
0.7 |
0.7 |
0.8 |
1.1 |
1.5 |
2.3 |
4 |
12.3 |
|
| 50 |
8/10 |
12:9:35 |
|
─ |
5.8 |
2.8 |
1.8 |
1.3 |
1 |
0.8 |
0.7 |
0.7 |
0.9 |
1.2 |
1.6 |
2.4 |
4.4 |
16.6 |
|
| 55 |
8/15 |
12:9:4 |
|
|
6.6 |
3 |
1.9 |
1.3 |
1 |
0.8 |
0.8 |
0.8 |
0.9 |
1.2 |
1.7 |
2.6 |
4.9 |
27.3 |
|
| 60 |
8/20 |
12:8:18 |
|
|
7.7 |
3.3 |
2 |
1.4 |
1.1 |
0.9 |
0.8 |
0.8 |
1 |
1.3 |
1.8 |
2.8 |
5.6 |
88.6 |
|
| 65 |
8/25 |
12:7:18 |
|
|
9.2 |
3.5 |
2.1 |
1.5 |
1.1 |
0.9 |
0.9 |
0.9 |
1.1 |
1.4 |
1.9 |
3 |
6.6 |
|
|
| 70 |
8/30 |
12:6:6 |
|
|
11.4 |
3.8 |
2.2 |
1.5 |
1.2 |
1 |
0.9 |
1 |
1.1 |
1.5 |
2.1 |
3.4 |
8.2 |
|
|
| 75 |
9/4 |
12:4:43 |
|
|
15.2 |
4.2 |
2.4 |
1.6 |
1.2 |
1 |
1 |
1 |
1.2 |
1.6 |
2.2 |
3.8 |
10.8 |
|
|
| 80 |
9/9 |
12:3:13 |
|
|
22.8 |
4.7 |
2.5 |
1.7 |
1.3 |
1.1 |
1 |
1.1 |
1.3 |
1.7 |
2.4 |
4.3 |
16.1 |
|
|
| 85 |
9/14 |
12:1:38 |
|
|
45.6 |
5.2 |
2.7 |
1.8 |
1.4 |
1.2 |
1.1 |
1.2 |
1.4 |
1.8 |
2.7 |
5 |
32.1 |
|
|
| 90 |
9/19 |
12:0:0 |
|
|
|
5.9 |
2.9 |
2 |
1.5 |
1.3 |
1.2 |
1.3 |
1.5 |
2 |
2.9 |
5.9 |
|
|
|
| 95 |
9/24 |
11:58:22 |
|
|
|
6.9 |
3.2 |
2.1 |
1.6 |
1.4 |
1.3 |
1.4 |
1.6 |
2.1 |
3.3 |
7.3 |
|
|
|
| 100 |
9/29 |
11:56:47 |
|
|
|
8.1 |
3.5 |
2.2 |
1.7 |
1.4 |
1.4 |
1.5 |
1.7 |
2.3 |
3.7 |
9.5 |
|
|
|
| 105 |
10/4 |
11:55:17 |
|
|
|
10 |
3.8 |
2.4 |
1.8 |
1.5 |
1.5 |
1.6 |
1.9 |
2.6 |
4.2 |
13.5 |
|
|
|
| 110 |
10/10 |
11:53:54 |
|
|
|
12.9 |
4.3 |
2.6 |
2 |
1.7 |
1.6 |
1.7 |
2 |
2.8 |
4.9 |
22.6 |
|
|
|
| 115 |
10/15 |
11:52:42 |
|
|
|
18.2 |
4.8 |
2.8 |
2.1 |
1.8 |
1.7 |
1.8 |
2.2 |
3.1 |
5.8 |
63.3 |
|
|
|
| 120 |
10/20 |
11:51:42 |
|
|
|
30.3 |
5.4 |
3.1 |
2.3 |
1.9 |
1.8 |
2 |
2.4 |
3.5 |
6.9 |
|
|
|
|
| 125 |
10/25 |
11:50:56 |
|
|
|
88.1 |
6.2 |
3.4 |
2.4 |
2.1 |
2 |
2.1 |
2.6 |
3.9 |
8.5 |
|
|
|
|
| 130 |
10/30 |
11:50:25 |
|
|
|
|
7.2 |
3.7 |
2.6 |
2.2 |
2.1 |
2.3 |
2.9 |
4.3 |
10.8 |
|
|
|
|
| 135 |
11/4 |
11:50:12 |
|
|
|
|
8.6 |
4.1 |
2.8 |
2.4 |
2.3 |
2.5 |
3.1 |
4.8 |
14.2 |
|
|
|
|
| 140 |
11/9 |
11:50:17 |
|
|
|
|
10.4 |
4.5 |
3.1 |
2.6 |
2.4 |
2.7 |
3.4 |
5.4 |
19.9 |
|
|
|
|
| 145 |
11/14 |
11:50:39 |
|
|
|
|
13.1 |
5 |
3.3 |
2.7 |
2.6 |
2.9 |
3.6 |
6.1 |
30.3 |
|
|
|
|
| 150 |
11/19 |
11:51:20 |
|
|
|
|
17.2 |
5.5 |
3.6 |
2.9 |
2.8 |
3 |
3.9 |
6.7 |
54.7 |
|
|
|
|
| 155 |
11/24 |
11:52:17 |
|
|
|
|
24.1 |
6.1 |
3.8 |
3.1 |
2.9 |
3.2 |
4.2 |
7.4 |
─ |
|
|
|
|
| 160 |
11/29 |
11:53:29 |
|
|
|
|
37.2 |
6.7 |
4.1 |
3.2 |
3.1 |
3.4 |
4.4 |
8 |
|
|
|
|
|
| 165 |
12/4 |
11:54:55 |
|
|
|
|
69.9 |
7.3 |
4.3 |
3.4 |
3.2 |
3.5 |
4.6 |
8.5 |
|
|
|
|
|
| 170 |
12/9 |
11:56:30 |
|
|
|
|
─ |
7.9 |
4.5 |
3.5 |
3.3 |
3.6 |
4.7 |
8.9 |
|
|
|
|
|
| 175 |
12/14 |
11:58:13 |
|
|
|
|
|
8.4 |
4.6 |
3.6 |
3.3 |
3.6 |
4.8 |
8.9 |
|
|
|
|
|
| 180 |
12/20 |
12:0:0 |
|
|
|
|
|
8.8 |
4.7 |
3.6 |
3.4 |
3.6 |
4.7 |
8.8 |
|
|
|
|
|
| 185 |
12/25 |
12:1:47 |
|
|
|
|
|
8.9 |
4.8 |
3.6 |
3.3 |
3.6 |
4.6 |
8.4 |
|
|
|
|
|
| 190 |
12/30 |
12:3:30 |
|
|
|
|
|
8.9 |
4.7 |
3.6 |
3.3 |
3.5 |
4.5 |
7.9 |
─ |
|
|
|
|
| 195 |
1/4 |
12:5:5 |
|
|
|
|
|
8.5 |
4.6 |
3.5 |
3.2 |
3.4 |
4.3 |
7.3 |
69.9 |
|
|
|
|
| 200 |
1/9 |
12:6:31 |
|
|
|
|
|
8 |
4.4 |
3.4 |
3.1 |
3.2 |
4.1 |
6.7 |
37.2 |
|
|
|
|
| 205 |
1/14 |
12:7:43 |
|
|
|
|
─ |
7.4 |
4.2 |
3.2 |
2.9 |
3.1 |
3.8 |
6.1 |
24.1 |
|
|
|
|
| 210 |
1/19 |
12:8:40 |
|
|
|
|
54.7 |
6.7 |
3.9 |
3 |
2.8 |
2.9 |
3.6 |
5.5 |
17.2 |
|
|
|
|
| 215 |
1/24 |
12:9:21 |
|
|
|
|
30.3 |
6.1 |
3.6 |
2.9 |
2.6 |
2.7 |
3.3 |
5 |
13.1 |
|
|
|
|
| 220 |
1/29 |
12:9:43 |
|
|
|
|
19.9 |
5.4 |
3.4 |
2.7 |
2.4 |
2.6 |
3.1 |
4.5 |
10.4 |
|
|
|
|
| 225 |
2/3 |
12:9:48 |
|
|
|
|
14.2 |
4.8 |
3.1 |
2.5 |
2.3 |
2.4 |
2.8 |
4.1 |
8.6 |
|
|
|
|
| 230 |
2/8 |
12:9:35 |
|
|
|
|
10.8 |
4.3 |
2.9 |
2.3 |
2.1 |
2.2 |
2.6 |
3.7 |
7.2 |
|
|
|
|
| 235 |
2/13 |
12:9:4 |
|
|
|
|
8.5 |
3.9 |
2.6 |
2.1 |
2 |
2.1 |
2.4 |
3.4 |
6.2 |
88.1 |
|
|
|
| 240 |
2/18 |
12:8:18 |
|
|
|
|
6.9 |
3.5 |
2.4 |
2 |
1.8 |
1.9 |
2.3 |
3.1 |
5.4 |
30.3 |
|
|
|
| 245 |
2/23 |
12:7:18 |
|
|
|
63.3 |
5.8 |
3.1 |
2.2 |
1.8 |
1.7 |
1.8 |
2.1 |
2.8 |
4.8 |
18.2 |
|
|
|
| 250 |
2/28 |
12:6:6 |
|
|
|
22.6 |
4.9 |
2.8 |
2 |
1.7 |
1.6 |
1.7 |
2 |
2.6 |
4.3 |
12.9 |
|
|
|
| 255 |
3/6 |
12:4:43 |
|
|
|
13.5 |
4.2 |
2.6 |
1.9 |
1.6 |
1.5 |
1.5 |
1.8 |
2.4 |
3.8 |
10 |
|
|
|
| 260 |
3/11 |
12:3:13 |
|
|
|
9.5 |
3.7 |
2.3 |
1.7 |
1.5 |
1.4 |
1.4 |
1.7 |
2.2 |
3.5 |
8.1 |
|
|
|
| 265 |
3/16 |
12:1:38 |
|
|
|
7.3 |
3.3 |
2.1 |
1.6 |
1.4 |
1.3 |
1.4 |
1.6 |
2.1 |
3.2 |
6.9 |
|
|
|
| 270 |
3/21 |
12:0:0 |
|
|
|
5.9 |
2.9 |
2 |
1.5 |
1.3 |
1.2 |
1.3 |
1.5 |
2 |
2.9 |
5.9 |
|
|
|
| 275 |
3/26 |
11:58:22 |
|
|
32.1 |
5 |
2.7 |
1.8 |
1.4 |
1.2 |
1.1 |
1.2 |
1.4 |
1.8 |
2.7 |
5.2 |
45.6 |
|
|
| 280 |
3/31 |
11:56:47 |
|
|
16.1 |
4.3 |
2.4 |
1.7 |
1.3 |
1.1 |
1 |
1.1 |
1.3 |
1.7 |
2.5 |
4.7 |
22.8 |
|
|
| 285 |
4/5 |
11:55:17 |
|
|
10.8 |
3.8 |
2.2 |
1.6 |
1.2 |
1 |
1 |
1 |
1.2 |
1.6 |
2.4 |
4.2 |
15.2 |
|
|
| 290 |
4/10 |
11:53:54 |
|
|
8.2 |
3.4 |
2.1 |
1.5 |
1.1 |
1 |
0.9 |
1 |
1.2 |
1.5 |
2.2 |
3.8 |
11.4 |
|
|
| 295 |
4/15 |
11:52:42 |
|
|
6.6 |
3 |
1.9 |
1.4 |
1.1 |
0.9 |
0.9 |
0.9 |
1.1 |
1.5 |
2.1 |
3.5 |
9.2 |
|
|
| 300 |
4/20 |
11:51:42 |
|
88.6 |
5.6 |
2.8 |
1.8 |
1.3 |
1 |
0.8 |
0.8 |
0.9 |
1.1 |
1.4 |
2 |
3.3 |
7.7 |
|
|
| 305 |
4/25 |
11:50:56 |
|
27.3 |
4.9 |
2.6 |
1.7 |
1.2 |
0.9 |
0.8 |
0.8 |
0.8 |
1 |
1.3 |
1.9 |
3 |
6.6 |
|
|
| 310 |
4/30 |
11:50:25 |
|
16.6 |
4.4 |
2.4 |
1.6 |
1.2 |
0.9 |
0.7 |
0.7 |
0.8 |
1 |
1.3 |
1.8 |
2.8 |
5.8 |
─ |
|
| 315 |
5/5 |
11:50:12 |
|
12.3 |
4 |
2.3 |
1.5 |
1.1 |
0.8 |
0.7 |
0.7 |
0.7 |
0.9 |
1.2 |
1.7 |
2.7 |
5.2 |
33.2 |
|
| 320 |
5/10 |
11:50:17 |
|
10 |
3.7 |
2.2 |
1.5 |
1.1 |
0.8 |
0.7 |
0.6 |
0.7 |
0.9 |
1.2 |
1.7 |
2.5 |
4.7 |
20.1 |
|
| 325 |
5/16 |
11:50:39 |
|
8.6 |
3.5 |
2.1 |
1.4 |
1 |
0.8 |
0.6 |
0.6 |
0.7 |
0.8 |
1.1 |
1.6 |
2.4 |
4.3 |
14.7 |
|
| 330 |
5/21 |
11:51:20 |
|
7.7 |
3.3 |
2 |
1.4 |
1 |
0.8 |
0.6 |
0.6 |
0.6 |
0.8 |
1.1 |
1.5 |
2.3 |
4 |
11.7 |
|
| 335 |
5/26 |
11:52:17 |
|
7.1 |
3.2 |
2 |
1.4 |
1 |
0.7 |
0.6 |
0.6 |
0.6 |
0.8 |
1.1 |
1.5 |
2.2 |
3.8 |
9.8 |
|
| 340 |
5/31 |
11:53:29 |
─ |
6.7 |
3.1 |
1.9 |
1.3 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.8 |
1 |
1.4 |
2.1 |
3.6 |
8.6 |
|
| 345 |
6/5 |
11:54:55 |
─ |
6.5 |
3.1 |
1.9 |
1.3 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.4 |
2.1 |
3.4 |
7.8 |
|
| 350 |
6/10 |
11:56:30 |
85.6 |
6.4 |
3.1 |
1.9 |
1.3 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.4 |
2 |
3.3 |
7.2 |
|
| 355 |
6/15 |
11:58:13 |
84.1 |
6.4 |
3.1 |
1.9 |
1.3 |
1 |
0.7 |
0.6 |
0.5 |
0.6 |
0.7 |
1 |
1.4 |
2 |
3.2 |
6.8 |
─ |
表中の「─」は，無効値を示す。
日出・日入は，太陽の仰角余角αが∠Ｒに近いときであり， tan(α) が極端に大きくなる。
|
|