S. Yamauchi 2017 7 22 1 1 2 2 2.1............................................. 2 2.2............................................. 3 2.3.......................................... 5 3 7 4 () 9 5 11 5.1............................................. 11 5.2................................... 11 5.3........................................ 12 1 1
2 Fig.1 O NESW N Z P Z X Q Y N E W O X' S P' Fig. 1 NZS ( ) P P' EQW () () X X PXYP' 2.1 A h 0 0 360 0 90 Fig. 1 X Z X' A = NOX h = X OX POP' 2
2.2 X EQW P P' ( ) - ( ) PZQP' 0 0 24 (1 15 ) () - () 0 0 24 - Fig. 1 X () Y δ = Y OX T = QOY - ( 1 ) 1 () 27.3 ( 29.5 ) 8.85 18.60 (sidereal time) ( ) () () ( ) 23 56 4 24 1 (23 + 56/60 + 4/3600)/24 = 1/1.002739 ( ) GST LST LST ( ) = GST () + λ() UT GST ( 5.2 ) Fig.2 3
天球の回転方向 Z S 時角 T 天体 地球 Q 経度 λ 赤経 α E N G 地方恒星時 LST W グリニッジ恒星時 GST 春分点 Fig. 2 Q () G ( ) ( 1 = 15 ) ( 9 ) 24 T () + α() = LST ( ) = GST () + λ() (1) ( 25,800 ) - 2000 1 1 (J2000.0 ) 1950 (B1950.0) 4
2.3 Fig.3 NESW (N ) Z WQE N P φ 90 δ T 90 φ T P W X' h X 90 h δ Y Z Q A E 90 δ X A 90 h 90 φ Z S Fig. 3 Fig. 4 P ( ) φ NP 1 NP ( ) X A h T δ Fig.1 PZX PZX 3 5.3 ( ) (21), (23), (24), (26), (29) A = A, C = T, a = 90 δ, b = 90 φ, c = 90 h cos(90 δ) = cos(90 φ) cos(90 h) + sin(90 φ) sin(90 h) cos( A) cos(90 h) = cos(90 δ) cos(90 φ) + sin(90 δ) sin(90 φ) cos T sin( A) sin(90 δ) = sin T sin(90 h) sin(90 δ) cos T = cos(90 h) sin(90 φ) sin(90 h) cos(90 φ) cos( A) sin(90 h) cos( A) = cos(90 δ) sin(90 φ) sin(90 δ) cos(90 φ) cos T 5
sin δ = sin φ sin h + cos φ cos h cos A (2) sin h = sin δ sin φ + cos δ cos φ cos T (3) sin A cos δ = sin T cos h (4) cos δ cos T = sin h cos φ cos h sin φ cos A (5) cos h cos A = sin δ cos φ cos δ sin φ cos T (6) (3) (4) (6) δ T h A sin h = sin δ sin φ + cos δ cos φ cos T (7) cos δ sin T sin A = cos h (8) sin δ cos φ cos δ sin φ cos T cos A = cos h (9) A (8) sin A (9) cos A (2) (4) (5) h A δ T sin δ = sin φ sin h + cos φ cos h cos A (10) cos h sin A sin T = cos δ (11) sin h cos φ cos h sin φ cos A cos T = cos δ (12) T (11) sin T (12) cos T (1a) (7), (8), (9) (1a) (10), (11), (12) ( ) + ( ) = ( = ) (1a) () + () = ( ) (1b) 6
3 () ( ) () h δ φ Fig. 5 天頂 地球 N 観測位置 φ 90 h 天体 δ 赤道 h S 水平線 Fig. 5 φ = 90 h + δ (13) (7) (10) sin h = cos(δ φ) = sin(90 δ + φ) = sin(90 + δ φ) sin δ = cos(φ + h) = sin(90 φ h) = sin(90 + φ + h) δ h h = 90 + δ φ (13) A = 180 T = 0 (1) λ = α GST (14) GST α 7
(1) ( δ α) ( ) ( ) (2) ( ) (3) h t (4) (13) φ (5) t GST ( 5.2) (6) (14) λ (5) GST GST t E = GST t α ( ) [3] (5) E T G = t + E = GST α (15) *1 λ = T G (16) T G T 0 (16) (λ = T T G ) ( ) ( ) ( ) ( ) [3] *1 [3] E t (15) 8
4 () ([4],[5]) (7) (9) () ( ) 1 1 = 1 mile (nautical) = 1.852km () ( ) (LOP, Line Of Position) (Fig.6) 20' 15' 位置の線 2 推定航路推定現在位置位置の線 1 h 2 = 2.2' h 1 = 5.1' 補正航路 10' 補正後現在位置 05' 天体 2 天体 1 N 25 00' E 135 00' 05 ' 10' 15' ( 9 : 00) (9 : 01) 20 ' 25' 30' (9 : 02) Fig. 6 9
(1) φ λ (2) t GST α (1) T t T G = t + E T = T G + λ T (3) (7) (9) A h (4) A h (5) h = h h h > 0 ( ), h < 0, (1 = 1.852km) (6) () 90 3 20' 推定航路 15' 10' 05' 推定現在位置 A 推定現在位置 B 補正航路 h 1 = 5.1' h 2 = 2.2' 位置の線 2 位置の線 1 補正後現在位置位置の線 1' 天体 1 N 25 00' 天体 2 E 135 00' 05 ' 10' 15' ( 9 : 00) (9 : 01) 20 ' 25' Fig. 7 ( ) 30' (9 : 02) 1 2 Fig.7 10
5 5.1 Table 1 12 h 180 1 h 15 4 min 1 1 min 15' 4 sec 1' 1 sec 15 5.2 ([1][2]) 1968 5 24 0 0.671262 day (16:6'37.0368") (UT ) = (JST ) 9 (UT) MJD (1858 11 17 0 0 0 ) UT Y M D h m s 1 2 (Y -1 ) 13 14 ( : 2013 2 5 Y=2012, M=14, D=5) MJD = 365.25Y + Y/400 Y/100 + 30.59(M 2) + D 678912 + h 24 + x x ( ) m 1440 + s 86 400 (17) MJD ( )GST GSD = 0.671 262 + 1.002 737 9094 MJD (18) GSD = GSD GSD (19) GST = 24 h GSD (20) GSD day GSD' 11
5.3 3 ( ) A, B, C C a B A b O c Fig. 8 a, b, c a, b, c cos a = cos b cos c + sin b sin c cos A (21) cos b = cos c cos a + sin c sin a cos B (22) cos c = cos a cos b + sin a sin b cos C (23) sin A sin a = sin B sin b = sin C sin c (24) sin a cos B = cos b sin c sin b cos c cos A (25) sin a cos C = cos c sin b sin c cos b cos A (26) sin b cos C = cos c sin a sin c cos a cos B (27) sin b cos A = cos a sin c sin a cos c cos B (28) sin c cos A = cos a sin b sin a cos b cos C (29) sin c cos B = cos b sin a sin b cos a cos C (30) 12
[1] Web Page "http://ja.wikipedia.org/wiki/ " (2014.1.13). [2] Web Page "http://hoshizora.yokochou.com/calculation/sidereal_time.html" (2014.1.13). [3], " 26 ", (2013). [4] Web Page "http://www.nexyzbb.ne.jp/ j_sunami76/ichi_ten.html" (2014.1.13). [5] Web Page "http://ja.wikipedia.org/wiki/" (2014.1.13). 13