Up <時刻─日影の長さ>対応表 作成: 2021-11-17
更新: 2021-11-17


    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