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[null,null,null,null,null,null,null,null,null,null,null,"作成年月日：",null,null,{"$f":"TODAY()","v":"2012-09-21"}]
[null,null,null,null,null,null,null,null,null,null,null,"作成者：",null,"益永八尋"]
[null,"日の出・日入りの計算"]
[]
[null,"理科年表によらいない日の出・日入りの計算は以下のとおりとなる。"]
[]
[]
[null,"「日の出・日の入りの計算」（長沢　工　著　地人書館　ｐ.95～104）により計算を行う。"]
[]
[null,"観測地の地名、経緯度、標高および観測年は"]
[]
[]
[null,null,null,"表　1　観測地の諸元"]
[null,null,"観測地",null,"昭和基地"]
[null,null,"経度","°",39.591700000000003]
[null,null,"緯度","°",-69.008300000000006]
[null,null,"標高","m",0]
[null,null,"年月日",null,"1999-11-21"]
[null,null,"時差","hr",3]
[]
[null,"である。"]
[]
[null,"また､1999/11/21前後の太陽位置を､理科年表1999年版の暦部､太陽の表から､"]
[]
[null,"表2に転記する｡"]
[]
[]
[null,"表2　太陽位置"]
[]
[null,"日付",null,null,"赤経",null,null,"赤緯"]
[null,"年","月","日","h","m","s","°","′",null,"\""]
[null,1999,11,20,15,39,41.4,-19,32,null,2]
[null,1999,11,21,15,43,51.9,-19,45,null,41]
[null,1999,11,22,15,48,3.2,-19,58,null,59]
[null,1999,11,23,15,52,15.3,-20,11,null,55]
[null,null,null,null,"距離（AU)"]
[null,1999,11,18,0.98860000000000003]
[null,1999,11,28,0.98665000000000003]
[]
[]
[null,"さらに、1999/11/21世界時0時のグリニジ恒星時は、『理科年表』から"]
[]
[null,null,null,"h","m","s"]
[null,null,"ΘG=",3,58,12.6]
[]
[null,"以上のデータを計算し易いように度単位の数値に変換すると表3のようになる｡"]
[]
[null,"表3　太陽位置"]
[null,"日付",null,null,"赤経",null,null,"赤緯"]
[null,"年","月","日","°",null,null,"°"]
[null,1999,11,20,234.92250061035156,null,null,-19.533889770507813]
[null,1999,11,21,235.96624755859375,null,null,-19.761388778686523]
[null,1999,11,22,237.01333618164062,null,null,-19.983055114746094]
[null,1999,11,23,238.06375122070312,null,null,-20.198610305786133]
[null,1999,11,21,"ΘG=",null,59.552500005789454]
[]
[null,"1999/11/21の日の出、日の入りの時刻をdとすれば、その時の"]
[null,"太陽の赤経､赤緯は3次の補間式で求められる｡"]
[]
[]
[]
[]
[null,"このとき､係数A , B, C, Dは下記の式で計算できる｡"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,"表4 与えられた時刻とその関数xj"]
[]
[null,null,"月日",null,"d","xj","赤経",null,null,null,"赤緯"]
[null,null,"2010-11-11",null,-1,"x-1",234.92250061035156,null,null,null,-19.533889770507813]
[null,null,"2010-11-11",null,0,"x0",235.96624755859375,null,null,null,-19.761388778686523]
[null,null,"2010-11-11",null,1,"x1",237.01333618164062,null,null,null,-19.983055114746094]
[null,null,"2010-11-11",null,2,"x2",238.06375122070312,null,null,null,-20.198610305786133]
[]
[]
[null,"上記式と表4により赤経､赤緯の係数を求めれば､以下のようになる｡なおα､δの添字"]
[]
[null,"はそれぞれ赤経､赤緯をしめす｡"]
[]
[]
[null,null,"Aα=",-5.0862631724157836E-6]
[]
[null,null,"Bα=",1.67083740234375E-3]
[]
[null,null,"Cα=",1.0454254150390625]
[]
[null,null,"Dα=",235.96624755859375]
[]
[]
[null,"が計算できる｡同様に赤緯に対してはδの添字を付けて"]
[]
[]
[null,null,"Aδ=",4.673004150390625E-5]
[]
[null,null,"Bδ=",2.9163360595703125E-3]
[]
[null,null,"Cδ=",-0.22462940216064453]
[]
[null,null,"Dδ=",-19.761388778686523]
[]
[null,"が計算できる｡これによって､1999/11/21の太陽の赤経α､赤緯δは､"]
[]
[null,"が計算できる。"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"によって計算できる。世界時で1999/11/21の24時間に対しては0≦d＜1である。"]
[]
[null,"次に考慮するのは太陽の距離である｡計算に､距離rは常に逆数の形で入ってくる"]
[]
[null,"から、距離そのものを補完するよりも、距離の逆数1/rを補間計算する方が便利である。"]
[]
[null,"表2の太陽までの距離を逆数に置き換えると表5のようになる｡"]
[]
[]
[null,"表5　太陽の距離の逆数"]
[]
[null,"日付",null,null,"距離（AU)"]
[null,"年","月","日","r（AU)",null,"1/r（1/AU)"]
[null,1999,11,18,0.98860001564025879,null,{"$f":"1/E138","v":1.011531442625315}]
[null,1999,11,28,0.98664999008178711,null,{"$f":"1/E139","v":1.0135306441518397}]
[]
[]
[null,"これを1次補間して世界時における1999/11/21を0≦d＜1の範囲で表すと、dに対する1/rの"]
[]
[null,"値は"]
[]
[]
[null,"1/r=","1.01153+( 1.01353- 1.01153 )/10・( 3 + d )"]
[]
[null,"=","1.01213 + 0.00019992・d"]
[]
[]
[null,"となる。「理科年表」を使って1次補間するときはこれでよいが、毎日の太陽の距離が分か"]
[]
[null,"っている場合には､赤経､赤緯と同様に､20日から23日までの毎日の距離の逆数を3次式"]
[]
[null,"で補間してもよい｡"]
[]
[null,"一方、観測地の恒星時Θは、（2.14）式から"]
[]
[]
[]
[]
[null,"=","59.5525 + 39.5917 + 360.985647・d"]
[]
[null,"=","99.1442 + 360.985647・d"]
[]
[]
[null,"が得られ、この式から計算できる。"]
[]
[null,"以上の結果をまとめると､世界時の1999/11/21に対し､太陽赤経α､赤緯δ､","以上の結果をまとめると､世界時の1999/11/21に対し､太陽赤経α､赤緯δ､"]
[]
[null,"距離の逆数1/r、昭和基地の恒星時Θは、"]
[]
[null,"α=","-0.0000051d^3 + 0.0016708 d^2 + 1.0454254d + 235.9662476"]
[]
[null,"δ=","0.0000467d^3 + 0.0029163 d^2 + -0.2246294d + -19.7613888"]
[]
[null,"1/r=","1.01213 + 0.00019992・d"]
[]
[null,"Θ=","99.1442 + 360.985647・d"]
[]
[]
[null,"で表すことができる。ただし、dは1999/11/21世界時0時を0とした日単位の","で表すことができる。ただし、dは1999/11/21世界時0時を0とした日単位の"]
[]
[null,"経過時間である｡"]
[]
[null,"以上の計算結果より太陽の出没方程式を解く｡太陽の出没方程式は以下の手順により解く｡"]
[]
[]
[]
[]
[]
[]
[null,"(1)　f'(d)の計算"]
[]
[null,"6時間おきに、つまりｄ＝0,0.25,0.5,0.75,1.0に対して、f'(d)を計算する。"]
[]
[null,"δ’、ｔ’、ｋ’は、δ、ｔ、kの補間式を微分した下記式から求める。"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"実際の計算過程は表6にしめす。微分式計算の単位は1日あたり角度の度（°）である。"]
[]
[null,"表6から、"]
[]
[null,null,"ｆ’（ｄ）＝0"]
[]
[null,"となるd=eiは、ｆ’（ｄ）の符号が変わる"]
[]
[null,null,"0.25 ＜e1 ＜ 0.50"]
[]
[null,null,"0.75 ＜ e2 ＜ 1.0"]
[]
[null,"の2か所にあることが分かる。"]
[]
[]
[null,"表6　ｆ’(d)の計算"]
[]
[null,"d",0,null,0.25,null,0.5,null,0.75,null,null,1,null,null,null,null,null,"d","f'(d)"]
[null,"α",235.96624755859375,null,236.22770826021829,null,236.48937733968097,null,236.7512543201446,null,null,237.01333872477198,null,null,null,null,null,0,83.252099999999999]
[null,"δ",-19.761388778686523,null,-19.817363128066063,null,-19.872968554496765,null,-19.928200677037239,null,null,-19.983055114746094,null,null,null,null,null,0.25,88.659300000000002]
[null,"Θ",99.144203186035156,null,189.39061493603515,null,279.63702668603514,null,9.8834384360351351,null,null,100.12985018603513,null,null,null,null,null,0.5,-82.754599999999996]
[null,"ｔ",-136.82204437255859,null,-46.837093324183144,null,43.147649346354171,null,-226.86781588410946,null,null,-136.88348853873686,null,null,null,null,null,0.75,-88.252399999999994]
[null,"1/r",1.0121312141418457,null,1.0121811941789929,null,1.0122311742161401,null,1.0122811542532872,null,null,1.0123311342904344,null,null,null,null,null,1,83.034800000000004]
[null,"k",-0.85331593211116796,null,-0.85332915440996326,null,-0.85334237670875868,null,-0.85335559900755398,null,null,-0.85336882130634928]
[null,"α’",1.0454254150390625,null,1.0462598800658895,null,1.0470924377440269,null,1.0479230880734747,null,null,1.0487518310542328]
[null,"δ’",-0.22462940216064453,null,-0.22317123413085938,null,-0.22171306610107422,null,-0.22025489807128906,null,null,-0.21879673004150391]
[null,"ｔ’",359.94022198496094,null,359.93939038095715,null,359.93855877695336,null,359.93772717294956,null,null,359.93689556894577]
[null,"k’",5.2889195181382817E-5,null,5.2889195181382817E-5,null,5.2889195181382817E-5,null,5.2889195181382817E-5,null,null,5.2889195181382817E-5]
[null,"f'(d)",83.252090419819012,null,88.659340813980606,null,-82.754586995355638,null,-88.252448193511157,null,null,83.034798027493025]
[]
[]
[null,"(2)　f’(ei)＝0となるeiの計算"]
[]
[null,"この計算では2次のはさみうち法を使用する｡"]
[]
[null,"はじめに、ｄ＝0.250とｄ＝0.500の間にある解を求める。ｘ1=0.2505、x3=0.500と置き、ｘ2は"]
[]
[null,"その中間のｘ2=(x1+x3)/2=0.375として、それぞれについてyi=f’(xi)を計算する。"]
[]
[]
[null,null,"y1 = f'(0.250) = 88.65933"]
[]
[null,null,"y2 = f'(0.375) = 4.07244"]
[]
[null,null,"y3 = f'(0.500) = -82.75462"]
[]
[]
[null,"である。ここから（4.12)式によって近似解ｘ(0)を求め、f’(x(0))を計算すると、"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null," x(0) =0.38094",0.38094]
[]
[null,null,"y(0) = f '(x(0))=-0.45108"]
[]
[]
[null,"が求められる。ここではｙ2＞0、y(0)＜0であるから、ｘ2とx(0)の間に真の解がある。"]
[]
[null,"そこでx2→x1、x(0)→x3と置きなおしをする。このときx2=(x1+x3)/2=0.37797になる。"]
[]
[null,"ここで近似解をもう一度計算すると"]
[]
[]
[null,null,"y1 = f'(0.37500) = 4.07244"]
[]
[null,null,"y2 = f'(0.37797) = 1.81095"]
[]
[null,null,"y3 = f'(0.38094) = -0.45108"]
[]
[]
[null,"表7　2次のはさみうち法によるｆ’(x)=0の解"]
[]
[null,null,"i",1,null,2,null,3]
[null,null,"x1",0.25,null,0.375,null,0.37796890735626221]
[null,null,"x2",0.375,null,0.37796890735626221,null,0.37915736436843872]
[null,null,"x3",0.5,null,0.38093781471252441,null,0.38034582138061523]
[null,null,"y1",88.659332275390625,null,4.0724425315856934,null,1.81095290184021]
[null,null,"y2",4.0724425315856934,null,1.81095290184021,null,0.90547972917556763]
[null,null,"y3",-82.754615783691406,null,-0.45107972621917725,null,-2.9957667720736936E-5]
[null,null,"x(i)",0.38093781471252441,null,0.38034582138061523,null,0.38034576177597046]
[null,null,"y(i)",0.4153180718421936,null,-5.7575060054659843E-5,null,3.3187672670464963E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,3.3187672670464963E-5]
[]
[null,null,"i",1,null,2,null,3]
[null,null,"x1",0.75,null,0.875,null,0.87773418426513672]
[null,null,"x2",0.875,null,0.87773418426513672,null,0.87882852554321289]
[null,null,"x3",1,null,0.88046842813491821,null,0.87992286682128906]
[null,null,"y1",-88.252525329589844,null,-3.7475318908691406,null,-1.6663957834243774]
[null,null,"y2",-3.7475318908691406,null,-1.6663957834243774,null,-0.83324962854385376]
[null,null,"y3",83.034660339355469,null,0.4153180718421936,null,-5.7575060054659843E-5]
[null,null,"x(i)",0.88046842813491821,null,0.87992286682128906,null,0.87992298603057861]
[null,null,"y(i)",0.4153180718421936,null,-5.7575060054659843E-5,null,3.3187672670464963E-5]
[]
[]
[null,"が得られる｡以下､同様の計算を繰り返す｡"]
[]
[null,"計算の結果x(2) = 0.380346の第1近似の解が得られる。そこからもう一度計算"]
[]
[null,"を繰り返せば、x(3) = 0.380346の第2近似解が得られが、小数以下5桁の範囲"]
[]
[null,"では近似解は変化しない｡そこで､f'(e1) = 0 の真の解はe1 = 0.380346になる。"]
[]
[null,"同様にして、と1の間にある解はe2=0.879923であることがわかる。"]
[]
[null,"これらの計算過程は表7に示す｡"]
[]
[null,"ここから、e1=0.380346およびe2=0.879923にf(d)の極値があることが"]
[]
[null,"わかる。0.380346が極大値、0.879923が極小値に対応する。"]
[]
[null,"(3)　e0=0、極値を与えるe1=0.380346、e2=0.879923およびe3=1のf(ei)計算"]
[]
[null,"計算過程は表8に示す｡この結果から､"]
[]
[null,null,"0.380346＜ｄ1＜0.879923"]
[]
[null,"にf(d1)=0となるd1がある。f(0.380346)　＞0およびｆ(0.879923）＜0であるから"]
[]
[null,"この間f(d)は減少し、この解は日の入りに対応することが分かる。"]
[]
[null,"同様にして、0.879923＜d2＜1の間の解は日の出に対応することが分かる。"]
[]
[null,"以上により、日の出・日の入りの計算ができる。計算方法は2次のはさみうち"]
[]
[null,"法を用いる｡計算過程は表9に示す｡表9より"]
[]
[]
[null,null,"d1=      （日の入り）",0.85807,null,null,"（日の入り）"]
[]
[null,null,"d2=      （日の出）",0.90178000000000003,null,null,"（日の出）"]
[]
[]
[null,"となる｡日単位のこの数値を通常の時刻表示に直せば､"]
[]
[]
[null,null,"(日)=      （日の入り）",null,null,"20:36:00",null,"（日の入り）"]
[]
[null,null,"(日)=      （日の出）",null,null,"21:39:00",null,"（日の出）"]
[]
[]
[null,"となる｡これは世界時の時刻であるため､地方時に変換する｡"]
[]
[null,"昭和基地の時差は3時間であるから"]
[]
[null,"3時間を加えて現地時刻に直せば"]
[]
[]
[null,null,"日の入り        ：  1999/11/2123時35分",null,"：","11月21日 23時36分"]
[]
[null,null,"日の出          ：  1999/11/220時38分",null,"：","11月22日   0時39分"]
[]
[]
[null,"になる｡"]
[]
[]
[null,null,"    表8　期間の両端と極値に対するf(ei)の値"]
[]
[null,null,"    ei",0,null,0.38034576177597046,null,0.87992298603057861,null,null,1,null,null,null,null,null,null,{"$f":"D374","v":0},{"$f":"D381","v":8.4706924884767595E-2}]
[null,null,"    α",235.96624755859375,null,236.36411211278232,null,236.88743161625251,null,null,237.01333872477198,null,null,null,null,null,null,{"$f":"F374","v":0.38034576177597046},{"$f":"F381","v":0.66881651409796716}]
[null,null,"    δ",-19.761388778686523,null,-19.846401162964593,null,-19.956755500763027,null,null,-19.983055114746094,null,null,null,null,null,null,{"$f":"H374","v":0.87992298603057861},{"$f":"H381","v":-3.1682483438340405E-3}]
[null,null,"    Θ",99.144203186035156,null,236.4435640844417,null,56.783771608455538,null,null,100.12985018603513,null,null,null,null,null,null,{"$f":"K374","v":1},{"$f":"K381","v":8.8201445789732422E-2}]
[null,null,"    t",-136.82204437255859,null,7.9451971659381115E-2,null,-180.10366000779698,null,null,-136.88348853873686]
[null,null,"1/r",1.0121312141418457,null,1.012207252923055,null,1.0123071284759595,null,null,1.0123311342904344]
[null,null,"k",-0.85331593211116796,null,-0.85333604829239895,null,-0.8533624705297207,null,null,-0.85336882130634928]
[null,null,"f (ei)",8.4706924884767595E-2,null,0.66881651409796716,null,-3.1682483438340405E-3,null,null,8.8201445789732422E-2]
[]
[]
[]
[null,null,"    表9　2次はさみうち法によるf(d)=0の解"]
[null,null,"    （日の入り）"]
[]
[null,null,"i",1,null,2,null,3,null,null,4]
[null,null,"x1",0.38034576177597046,null,0.63013434410095215,null,0.75385069847106934,null,null,0.81345301866531372,null,null,null,null,null,null,null,null,null,null,-239.67047119140625]
[null,null,"x2",0.63013434410095215,null,0.75385069847106934,null,0.81345301866531372,null,null,0.83982181549072266,null,null,null,null,null,null,null,null,null,null,-239.68997192382812]
[null,null,"x3",0.87992298603057861,null,0.87756699323654175,null,0.87305533885955811,null,null,0.86619055271148682,null,null,null,null,null,null,null,null,null,null,-239.70948791503906]
[null,null,"y1",0.66881650686264038,null,0.33278021216392517,null,9.6999108791351318E-2,null,null,2.5758793577551842E-2,null,null,null,null,null,null,null,null,null,null,0.16023187339305878]
[null,null,"y2",0.33278021216392517,null,9.6999108791351318E-2,null,2.5758793577551842E-2,null,null,7.4588614515960217E-3,null,null,null,null,null,null,null,null,null,null,-2.1429221630096436]
[null,null,"y3",-3.1682481057941914E-3,null,-3.131374716758728E-3,null,-2.8549463022500277E-3,null,null,-1.9161318195983768E-3,null,null,null,null,null,null,null,null,null,null,-4.3595414161682129]
[null,null,"x (i)",0.87756699323654175,null,0.87305533885955811,null,0.86619055271148682,null,null,0.8600928783416748,null,null,null,null,null,null,null,null,null,null,-239.67178344726562]
[null,null,"y (i)",-3.131374716758728E-3,null,-2.8549463022500277E-3,null,-1.9161318195983768E-3,null,null,-5.5906485067680478E-4,null,null,null,null,null,null,null,null,null,null,3.196632256731391E-3]
[]
[null,null,"i",5,null,6,null,7,null,null,8]
[null,null,"x1",0.83982181549072266,null,0.84995734691619873,null,0.8540922999382019,null,null,0.85608214139938354]
[null,null,"x2",0.84995734691619873,null,0.8540922999382019,null,0.85608214139938354,null,null,0.8570752739906311]
[null,null,"x3",0.8600928783416748,null,0.85822725296020508,null,0.85807198286056519,null,null,0.85806840658187866]
[null,null,"y1",7.4588614515960217E-3,null,2.7797736693173647E-3,null,1.2548899976536632E-3,null,null,6.0091307386755943E-4]
[null,null,"y2",2.7797736693173647E-3,null,1.2548899976536632E-3,null,6.0091307386755943E-4,null,null,2.9396516038104892E-4]
[null,null,"y3",-5.5906485067680478E-4,null,-4.5829070586478338E-5,null,-1.0477450587131898E-6,null,null,-1.2574819407973337E-8]
[null,null,"x (i)",0.85822725296020508,null,0.85807198286056519,null,0.85806840658187866,null,null,0.85806834697723389]
[null,null,"y (i)",-4.5829070586478338E-5,null,-1.0477450587131898E-6,null,-1.2574819407973337E-8,null,null,4.6794439434449941E-9]
[]
[]
[null,null,"    （日の出）"]
[]
[null,null,"i",1,null,2,null,3,null,null,4]
[null,null,"x1",0.87992298603057861,null,0.88913154602050781,null,0.89909803867340088,null,null,0.90166079998016357]
[null,null,"x2",0.93996149301528931,null,0.91454648971557617,null,0.90682226419448853,null,null,0.90424156188964844]
[null,null,"x3",1,null,0.93996149301528931,null,0.91454648971557617,null,null,0.90682226419448853]
[null,null,"y1",-3.1682481057941914E-3,null,-2.6049560401588678E-3,null,-7.2807347169145942E-4,null,null,-3.3292548323515803E-5]
[null,null,"y2",2.0502690225839615E-2,null,4.7661606222391129E-3,null,1.6282714204862714E-3,null,null,7.5375568121671677E-4]
[null,null,"y3",8.8201448321342468E-2,null,2.0502690225839615E-2,null,4.7661606222391129E-3,null,null,1.6282714204862714E-3]
[null,null,"x (i)",0.88913154602050781,null,0.89909803867340088,null,0.90166079998016357,null,null,0.90177494287490845]
[null,null,"y (i)",-2.6049560401588678E-3,null,-7.2807347169145942E-4,null,-3.3292548323515803E-5,null,null,-3.3485849826320191E-7]
[]
[null,null,"i",5,null,6,null,7,null,null,8]
[null,null,"x1",0.90177494287490845,null,0.90177613496780396]
[null,null,"x2",0.90300822257995605,null,0.90239214897155762]
[null,null,"x3",0.90424156188964844,null,0.90300822257995605]
[null,null,"y1",-3.3485849826320191E-7,null,1.0252240834063286E-8]
[null,null,"y2",3.6669953260570765E-4,null,1.8084915063809603E-4]
[null,null,"y3",7.5375568121671677E-4,null,3.6669953260570765E-4]
[null,null,"x (i)",0.90177613496780396,null,0.90177607536315918]
[null,null,"y (i)",1.0252240834063286E-8,null,-7.0037411425971641E-9]
[]
[]
[]
[]
[]
[]
[]
[null,"日の出・日の入りの方位角計算"]
[]
[null,"日の出・日の入りに対して計算された時刻diを使えば、その時刻に対応する太陽の赤経α、"]
[]
[null,"赤緯δ､および恒星時Θを次の式から計算できる｡これによりt = Θ - αの関係から太陽の"]
[]
[null,"時角tが分かる。その次に、観測点の緯度ψ、時角t、赤緯δを使って（2.20）式からそのと"]
[]
[null,"きの太陽の方位角Aを求めることができる｡以下にその計算をしめす｡"]
[]
[]
[null,null,"α= -0.0000051・d^3+0.0016708・d^2+1.0454254・d+235.9662476"]
[]
[null,null,"δ= 0.0000467・d^30.0029163・d^2--0.2246294・d+-19.7613888"]
[]
[null,null,"1/r=1.0121310+0.0001999・d"]
[]
[null,null,"Θ= 99.1442000+ 360.985647・d"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"1999/11/21（世界時）の昭和基地の日の入りの方位角はｄ1＝0.8580683に対して"]
[]
[]
[null,null,"α = 236.8645210"]
[]
[null,null,"δ = -19.9519594"]
[]
[null,null,"1/r=1.0123028"]
[]
[null,null,"Θ = 172.0300396"]
[]
[]
[null,"が計算される｡ここから太陽の時角tは､t = Θ - αの関係から"]
[]
[null,null,"t = 172.0300378"]
[]
[null,"である。昭和基地の緯度ψ=-69.0083を考慮して（2.20）式を計算すると、"]
[]
[]
[null,null,"tanA = 0.1314679"]
[]
[]
[null,"が得られる｡tanAを計算する式の分母がマイナスであることから､求める方位角は"]
[]
[]
[null,null,"A = 187.4896000"]
[]
[null,"となる｡"]
[]
[]
[]
[]
[]
[null,"同様に、日の出に対しては、d2=0.9017761であり、ここから、"]
[]
[]
[null,null,"α = 236.9103422"]
[]
[null,null,"δ = -19.9615484"]
[]
[null,null,"1/r=1.0123115"]
[]
[null,null,"Θ = 10757.9749785"]
[]
[null,null,"t = 187.7620811"]
[]
[null,null,"tanA = -0.1279955"]
[]
[null,null,"A = 172.7061000"]
[]
[]
[null,"が計算できる｡ここから､昭和基地では､この日の太陽は南から7.5度あまり西寄り"]
[]
[null,"のところでちょっとだけ沈み､約1時間ほどして､南から7.3度あまり東寄りのところで"]
[]
[null,"また昇ってくることが分かる｡"]

{"sheet":"Sheet2","index":1,"n_rows":518,"n_cols":42,"rows_kept":518,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[]
[null,null,"d","f(d)"]
[null,null,0,8.4706924884767623E-2]
[null,null,5.000000074505806E-2,0.16819528284859661]
[null,null,0.10000000149011612,0.26757522990892657]
[null,null,0.15000000596046448,0.37313725865680103]
[null,null,0.20000000298023224,0.474568295200757]
[null,null,0.25,0.56196096314754795]
[null,null,0.30000001192092896,0.62678288938795479]
[null,null,0.34999999403953552,0.66271131605583722]
[null,null,0.40000000596046448,0.66625158901011416]
[null,null,0.44999998807907104,0.63707856368252924]
[null,null,0.5,0.57806798064280218]
[null,null,0.55000001192092896,0.49501469791533953]
[null,null,0.60000002384185791,0.39606521828928842]
[null,null,0.64999997615814209,0.29092037583472824]
[null,null,0.69999998807907104,0.18988542574742834]
[null,null,0.75,0.10286234577997957]
[null,null,0.80000001192092896,3.8380638420844E-2]
[null,null,0.85000002384185791,2.762893773811748E-3]
[null,null,0.89999997615814209,-4.9342583167463598E-4]
[null,null,0.94999998807907104,2.8942191909174568E-2]
[null,null,1,8.8201445761246861E-2]
[]
[]
[]
[]
[null,null,null,null,null,"注）dが増加、f(d)が減少の場合は日の入りとなり、dが増加、f(d)が増加の場合は日の出となる。"]
[]
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[]
[]
[null,null,8.4706924884767595E-2,null,0.66881651398784214,null,-3.1682482920491399E-3,null,null,null,8.8201445789732422E-2]
[]
[]
[null,"(2)　f’(ei)＝0となるeiの計算"]
[]
[null,"この計算では2次のはさみうち法を使用する｡"]
[]
[null,"はじめに、ｄ＝0.250とｄ＝0.500の間にある解を求める。ｘ1=0.250、x3=0.500と置き、ｘ2は"]
[]
[null,"その中間のｘ2=(x1+x3)/2=0.375として、それぞれについてyi=f’(xi)を計算する。"]
[]
[]
[null,null,"y1 = f'(0.250) = 88.65933"]
[]
[null,null,"y2 = f'(0.375) = 4.07244"]
[]
[null,null,"y3 = f'(0.500) = -82.75462"]
[]
[]
[null,"である。ここから（4.12)式によって近似解ｘ(0)を求め、f’(x(0))を計算すると、"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null," x(0) =0.38094"]
[]
[null,null,"y(0) = f '(x(0))=-0.45108"]
[]
[]
[null,"が求められる。ここではｙ2＞0、y(0)＜0であるから、ｘ2とx(0)の間に真の解がある。"]
[]
[null,"そこでx2→x1、x(0)→x3と置きなおしをする。このときx2=(x1+x3)/2=0.37797になる。"]
[]
[null,"ここで近似解をもう一度計算すると"]
[]
[]
[null,null,"y1 = f'(0.37500) = 4.07244"]
[]
[null,null,"y2 = f'(0.37797) = 1.81095"]
[]
[null,null,"y3 = f'(0.38094) = -0.45108"]
[]
[]
[null,null,"表7　2次のはさみうち法によるｆ’(x)=0の解"]
[]
[null,null,"i",1,"    i   1       2       3",2,"    i   1       2       3",3,"    i   1       2       3","    i   1       2       3","    i   1       2       3","    i   1       2       3","    i   1       2       3"]
[null,null,"    x1",0.25,0.375,0.375,0.34375,0.37796890735626221,0.3359375,0.37915736436843872,0.333984375,0.37975156307220459,0.33349609375]
[null,null,"    x2",0.375,0.3125,0.37796890735626221,0.328125,0.37915736436843872,0.33203125,0.37975156307220459,0.3330078125,0.38004866242408752,0.333251953125]
[null,null,"    x3",0.5,0.25,0.38093781471252441,0.3125,0.38034582138061523,0.328125,0.38034576177597046,0.33203125,0.38034576177597046,0.3330078125]
[null,null,"    y1",88.659332275390625,4.0724425315856934,4.0724425315856934,27.644718170166016,1.81095290184021,33.408088684082031,0.90547972917556763,34.836994171142578,0.45274901390075684,35.193416595458984]
[null,null,"    y2",4.0724425315856934,50.164527893066406,1.81095290184021,39.091606140136719,0.90547972917556763,36.260692596435547,0.45274901390075684,35.549507141113281,0.22638219594955444,35.371501922607422]
[null,null,"    y3",-82.754615783691406,88.659332275390625,-0.45107972621917725,50.164527893066406,-2.9957667720736936E-5,39.091606140136719,1.5456402252311818E-5,36.260692596435547,1.5456402252311818E-5,35.549507141113281]
[null,null,"    x (i)",0.38093781471252441,0.375,0.38034582138061523,0.34375,0.38034576177597046,0.3359375,0.38034576177597046,0.333984375,0.38034579157829285,0.33349609375]
[null,null,"    y (i)",-0.45107972621917725,4.0724425315856934,-2.9957667720736936E-5,27.644718170166016,1.5456402252311818E-5,33.408088684082031,1.5456402252311818E-5,34.836994171142578,-7.2506322794652078E-6,35.193416595458984]
[]
[null,null,"i",1,null,2,null,3]
[null,null,null,0.75,null,0.875,null,0.87773418426513672,null,0.87882852554321289,null,0.87937575578689575,null,0.87964928150177002,null,0.87978613376617432,null,0.87985455989837646,null,0.87988877296447754,null,0.87990587949752808,null,0.87991440296173096,null,0.87991863489151001,null,0.87992072105407715,null,0.87992179393768311,null,0.87992238998413086,null,0.87992268800735474,null,0.87992280721664429,null,0.87992286682128906,null,0.43996143341064453,null,0.6599421501159668]
[null,null,null,0.875,null,0.87773418426513672,null,0.87882852554321289,null,0.87937575578689575,null,0.87964928150177002,null,0.87978613376617432,null,0.87985455989837646,null,0.87988877296447754,null,0.87990587949752808,null,0.87991440296173096,null,0.87991863489151001,null,0.87992072105407715,null,0.87992179393768311,null,0.87992238998413086,null,0.87992268800735474,null,0.87992280721664429,null,0.87992286682128906,null,0.43996143341064453,null,0.6599421501159668,null,0.76993262767791748]
[null,null,null,1,null,0.88046842813491821,null,0.87992286682128906,null,0.87992298603057861,null,0.87992286682128906,null,0.87992292642593384,null,0.87992292642593384,null,0.87992298603057861,null,0.87992298603057861,null,0.87992298603057861,null,0.87992286682128906,null,0.87992286682128906,null,0.87992292642593384,null,0.87992304563522339,null,0.87992298603057861,null,0.87992292642593384,null,0.87992286682128906,null,0,null,0.87992292642593384,null,0.87992304563522339]
[null,null,null,-88.252525329589844,null,-3.7475318908691406,null,-1.6663957834243774,null,-0.83324962854385376,null,-0.41661152243614197,null,-0.20835775136947632,null,-0.10416236519813538,null,-5.2064608782529831E-2,null,-2.6015713810920715E-2,null,-1.2991263531148434E-2,null,-6.5017291344702244E-3,null,-3.2796519808471203E-3,null,-1.6913042636588216E-3,null,-8.7443966185674071E-4,null,-4.2062599095515907E-4,null,-1.9371917005628347E-4,null,-1.0295643005520105E-4,null,-5.7575060054659843E-5,null,-44.350791931152344,null,-118.92251586914062]
[null,null,null,-3.7475318908691406,null,-1.6663957834243774,null,-0.83324962854385376,null,-0.41661152243614197,null,-0.20835775136947632,null,-0.10416236519813538,null,-5.2064608782529831E-2,null,-2.6015713810920715E-2,null,-1.2991263531148434E-2,null,-6.5017291344702244E-3,null,-3.2796519808471203E-3,null,-1.6913042636588216E-3,null,-8.7443966185674071E-4,null,-4.2062599095515907E-4,null,-1.9371917005628347E-4,null,-1.0295643005520105E-4,null,-5.7575060054659843E-5,null,-44.350791931152344,null,-118.92251586914062,null,-77.204940795898437]
[null,null,null,83.034660339355469,null,0.4153180718421936,null,-5.7575060054659843E-5,null,3.3187672670464963E-5,null,-5.7575060054659843E-5,null,-1.219369369209744E-5,null,-1.219369369209744E-5,null,3.3187672670464963E-5,null,3.3187672670464963E-5,null,3.3187672670464963E-5,null,-5.7575060054659843E-5,null,-5.7575060054659843E-5,null,-1.219369369209744E-5,null,7.8569042671006173E-5,null,3.3187672670464963E-5,null,-1.219369369209744E-5,null,-5.7575060054659843E-5,null,83.252090454101563,null,-1.219369369209744E-5,null,7.8569042671006173E-5]
[null,null,null,0.88046842813491821,null,0.87992286682128906,null,0.87992298603057861,null,0.87992286682128906,null,0.87992292642593384,null,0.87992292642593384,null,0.87992298603057861,null,0.87992298603057861,null,0.87992298603057861,null,0.87992286682128906,null,0.87992286682128906,null,0.87992292642593384,null,0.87992304563522339,null,0.87992298603057861,null,0.87992292642593384,null,0.87992286682128906,null,0,null,0.87992292642593384,null,0.87992304563522339,null,0.87992304563522339]
[null,null,null,0.4153180718421936,null,-5.7575060054659843E-5,null,3.3187672670464963E-5,null,-5.7575060054659843E-5,null,-1.219369369209744E-5,null,-1.219369369209744E-5,null,3.3187672670464963E-5,null,3.3187672670464963E-5,null,3.3187672670464963E-5,null,-5.7575060054659843E-5,null,-5.7575060054659843E-5,null,-1.219369369209744E-5,null,7.8569042671006173E-5,null,3.3187672670464963E-5,null,-1.219369369209744E-5,null,-5.7575060054659843E-5,null,83.252090454101563,null,-1.219369369209744E-5,null,7.8569042671006173E-5,null,7.8569042671006173E-5]
[]
[]
[null,"が得られる｡以下､同様の計算を繰り返す｡"]
[]
[null,"計算の結果x(2) = 0.380346の第1近似の解が得られる。そこからもう一度計算"]
[]
[null,"を繰り返せば、x(3) = 0.380346の第2近似解が得られるが、小数以下5桁の範囲"]
[]
[null,"では近似解は変化しない｡そこで､f'(e1) = 0 の真の解はe1 = 0.380346になる。"]
[]
[null,"同様にして、0.880と1の間にある解はe2=0.879923であることがわかる。"]
[]
[null,"これらの計算過程は表7に示す｡"]
[]
[null,"ここから、e1=0.380346およびe2=0.879923にf(d)の極値があることが"]
[]
[null,"わかる。0.380346が極大値、0.879923が極小値に対応する。"]
[]
[null,"(3)　e0=0、極値を与えるe1=0.380346、e2=0.879923およびe3=1のf(ei)計算"]
[]
[null,"計算過程は表8に示す｡この結果から､"]
[]
[null,null,"0.380346＜ｄ1＜0.879923"]
[]
[null,"にf(d1)=0となるd1がある。f(0.380346)　＞0およびｆ(0.879923）＜0であるから"]
[]
[null,"この間f(d)は減少し、この解は日の入りに対応することが分かる。"]
[]
[null,"同様にして、0.879923＜d2＜1の間の解は日の出に対応することが分かる。"]
[]
[null,"以上により、日の出・日の入りの計算ができる。計算方法は2次のはさみうち"]
[]
[null,"法を用いる｡計算過程は表9に示す｡表9より"]
[]
[]
[null,null,"d1= 0.858068     （日の入り）"]
[]
[null,null,"d2= 0.901776     （日の出）"]
[]
[]
[null,"となる｡日単位のこの数値を通常の時刻表示に直せば､"]
[]
[]
[null,null,"0.858068(日)=21時38分      （日の入り）"]
[]
[null,null,"0.901776(日)=      （日の出）"]
[]
[]
[null,"となる｡これは世界時の時刻であるため､地方時に変換する｡"]
[]
[null,"昭和基地の時差は3時間であるから"]
[]
[null,"3時間を加えて現地時刻に直せば"]
[]
[]
[null,null,"日の入り        ：  1999/11/2123時35分"]
[]
[null,null,"日の出          ：  1999/11/220時38分"]
[]
[]
[null,"になる｡"]
[]
[]
[null,null,"    表8　期間の両端と極値に対するf(ei)の値"]
[]
[null,null,"ei",0,0.38034999370574951,0.38034576177597046,0.87992000579833984,0.87992298603057861,null,null,1]
[null,null,"α",235.96624755859375,236.3641165423187,236.36411211278232,236.88742849191408,236.88743161625251,null,null,237.01333872477198]
[null,null,"δ",-19.761388778686523,-19.846402104106321,-19.846401162964593,-19.956754846934153,-19.956755500763027,null,null,-19.983055114746094]
[null,null,"Θ",99.144203186035156,236.44509175035105,236.4435640844417,56.782695787392583,56.783771608455538,null,null,100.12985018603513]
[null,null,"t",223.17795562744141,8.097520803235625E-2,7.9451971659381115E-2,-180.1047327045215,179.89633999220302,null,null,223.11651146126314]
[null,null,"1/r",1.0121312141418457,1.0122072537691031,1.012207252923055,1.0123071278801512,1.0123071284759595,null,null,1.0123311342904344]
[null,null,"k",-0.85331593211116796,-0.85333604851622225,-0.85333604829239895,-0.85336247037209867,-0.8533624705297207,null,null,-0.85336882130634928]
[null,null,"f(ei)",8.4706900159414164E-2,null,0.66881651409796716,null,-3.1682482785404288E-3,null,null,8.8201421127162657E-2]
[]
[]
[]
[null,null,"    表9　2次はさみうち法によるf(d)=0の解"]
[null,null,"    （日の入り）"]
[]
[null,null,"i",1,null,2,null,3,null,null,4]
[null,null,"x1",0.38034576177597046,null,0.63013434410095215,null,0.75385069847106934,null,0.81345301866531372,0.81345301866531372,0.83982181549072266,null,0.84995734691619873,null,0.8540922999382019,null,0.85608214139938354,null,0.8570752739906311,null,0.85757184028625488,null,0.85782015323638916,null,0.85794425010681152,null,0.85800623893737793,null,0.85803729295730591,null,0.85805284976959229,null,0.85806059837341309,null,0.85806441307067871,null,0.85806643962860107,null,0.85806739330291748,null,0.85806787014007568]
[null,null,"x2",0.63013434410095215,null,0.75385069847106934,null,0.81345301866531372,null,0.83982181549072266,0.83982181549072266,0.84995734691619873,null,0.8540922999382019,null,0.85608214139938354,null,0.8570752739906311,null,0.85757184028625488,null,0.85782015323638916,null,0.85794425010681152,null,0.85800623893737793,null,0.85803729295730591,null,0.85805284976959229,null,0.85806059837341309,null,0.85806441307067871,null,0.85806643962860107,null,0.85806739330291748,null,0.85806787014007568,null,0.85806816816329956]
[null,null,"x3",0.87992298603057861,null,0.87756699323654175,null,0.87305533885955811,null,0.86619055271148682,0.86619055271148682,0.8600928783416748,null,0.85822725296020508,null,0.85807198286056519,null,0.85806840658187866,null,0.85806834697723389,null,0.85806840658187866,null,0.85806834697723389,null,0.85806828737258911,null,0.85806834697723389,null,0.85806846618652344,null,0.85806834697723389,null,0.85806828737258911,null,0.85806840658187866,null,0.85806834697723389,null,0.85806834697723389,null,0.85806846618652344]
[null,null,"y1",0.66881650686264038,null,0.33278021216392517,null,9.6999108791351318E-2,null,2.5758793577551842E-2,2.5758793577551842E-2,7.4588614515960217E-3,null,2.7797736693173647E-3,null,1.2548899976536632E-3,null,6.0091307386755943E-4,null,2.9396516038104892E-4,null,1.4535436639562249E-4,null,7.2256872954312712E-5,null,3.6029443435836583E-5,null,1.8009030100074597E-5,null,9.0005087258759886E-6,null,4.4923745008418337E-6,null,2.2481317500933073E-6,null,1.1435641908974503E-6,null,5.5684057542748633E-7,null,2.8075402269678307E-7,null,1.4271523696152144E-7]
[null,null,"y2",0.33278021216392517,null,9.6999108791351318E-2,null,2.5758793577551842E-2,null,7.4588614515960217E-3,7.4588614515960217E-3,2.7797736693173647E-3,null,1.2548899976536632E-3,null,6.0091307386755943E-4,null,2.9396516038104892E-4,null,1.4535436639562249E-4,null,7.2256872954312712E-5,null,3.6029443435836583E-5,null,1.8009030100074597E-5,null,9.0005087258759886E-6,null,4.4923745008418337E-6,null,2.2481317500933073E-6,null,1.1435641908974503E-6,null,5.5684057542748633E-7,null,2.8075402269678307E-7,null,1.4271523696152144E-7,null,5.6442512885723772E-8]
[null,null,"y3",-3.1682481057941914E-3,null,-3.131374716758728E-3,null,-2.8549463022500277E-3,null,-1.9161318195983768E-3,-1.9161318195983768E-3,-5.5906485067680478E-4,null,-4.5829070586478338E-5,null,-1.0477450587131898E-6,null,-1.2574819407973337E-8,null,4.6794439434449941E-9,null,-1.2574819407973337E-8,null,4.6794439434449941E-9,null,2.1933754368319569E-8,null,4.6794439434449941E-9,null,-2.9829035241846213E-8,null,4.6794439434449941E-9,null,2.1933754368319569E-8,null,-1.2574819407973337E-8,null,4.6794439434449941E-9,null,4.6794439434449941E-9,null,-2.9829035241846213E-8]
[null,null,"x(i)",0.87756699323654175,null,0.87305533885955811,null,0.86619055271148682,null,0.8600928783416748,0.8600928783416748,0.85822725296020508,null,0.85807198286056519,null,0.85806840658187866,null,0.85806834697723389,null,0.85806840658187866,null,0.85806834697723389,null,0.85806828737258911,null,0.85806834697723389,null,0.85806846618652344,null,0.85806834697723389,null,0.85806828737258911,null,0.85806840658187866,null,0.85806834697723389,null,0.85806834697723389,null,0.85806846618652344,null,0.85806834697723389]
[null,null,"y(i)",-3.131374716758728E-3,null,-2.8549463022500277E-3,null,-1.9161318195983768E-3,null,-5.5906485067680478E-4,-5.5906485067680478E-4,-4.5829070586478338E-5,null,-1.0477450587131898E-6,null,-1.2574819407973337E-8,null,4.6794439434449941E-9,null,-1.2574819407973337E-8,null,4.6794439434449941E-9,null,2.1933754368319569E-8,null,4.6794439434449941E-9,null,-2.9829035241846213E-8,null,4.6794439434449941E-9,null,2.1933754368319569E-8,null,-1.2574819407973337E-8,null,4.6794439434449941E-9,null,4.6794439434449941E-9,null,-2.9829035241846213E-8,null,4.6794439434449941E-9]
[]
[null,null,"i",5,null,6,null,7,null,null,8]
[null,null,"x1",0.83982181549072266,null,0.84995734691619873,null,0.8540922999382019,null,null,0.85608214139938354]
[null,null,"x2",0.84995734691619873,null,0.8540922999382019,null,0.85608214139938354,null,null,0.8570752739906311]
[null,null,"x3",0.8600928783416748,null,0.85822725296020508,null,0.85807198286056519,null,null,0.85806840658187866]
[null,null,"y1",7.4588614515960217E-3,null,2.7797736693173647E-3,null,1.2548899976536632E-3,null,null,6.0091307386755943E-4]
[null,null,"y2",2.7797736693173647E-3,null,1.2548899976536632E-3,null,6.0091307386755943E-4,null,null,2.9396516038104892E-4]
[null,null,"y3",-5.5906485067680478E-4,null,-4.5829070586478338E-5,null,-1.0477450587131898E-6,null,null,-1.2574819407973337E-8]
[null,null,"x(i)",0.85822725296020508,null,0.85807198286056519,null,0.85806840658187866,null,null,0.85806834697723389]
[null,null,"y(i)",-4.5829070586478338E-5,null,-1.0477450587131898E-6,null,-1.2574819407973337E-8,null,null,4.6794439434449941E-9]
[]
[]
[null,null,"    （日の出）"]
[]
[null,null,"i",1,null,2,null,3,null,null,4]
[null,null,"x1",0.87992298603057861,null,0.88913154602050781,null,0.89909803867340088,null,null,0.90166079998016357]
[null,null,"x2",0.93996149301528931,null,0.91454648971557617,null,0.90682226419448853,null,null,0.90424156188964844]
[null,null,"x3",1,null,0.93996149301528931,null,0.91454648971557617,null,null,0.90682226419448853]
[null,null,"y1",-3.1682481057941914E-3,null,-2.6049560401588678E-3,null,-7.2807347169145942E-4,null,null,-3.3292548323515803E-5]
[null,null,"y2",2.0502690225839615E-2,null,4.7661606222391129E-3,null,1.6282714204862714E-3,null,null,7.5375568121671677E-4]
[null,null,"y3",8.8201448321342468E-2,null,2.0502690225839615E-2,null,4.7661606222391129E-3,null,null,1.6282714204862714E-3]
[null,null,"x(i)",0.88913154602050781,null,0.89909803867340088,null,0.90166079998016357,null,null,0.90177494287490845]
[null,null,"y(i)",-2.6049560401588678E-3,null,-7.2807347169145942E-4,null,-3.3292548323515803E-5,null,null,-3.3485849826320191E-7]
[]
[null,null,"i",5,null,6,null,7,null,null,8]
[null,null,"x1",0.90177494287490845,null,0.90177613496780396]
[null,null,"x2",0.90300822257995605,null,0.90239214897155762]
[null,null,"x3",0.90424156188964844,null,0.90300822257995605]
[null,null,"y1",-3.3485849826320191E-7,null,1.0252240834063286E-8]
[null,null,"y2",3.6669953260570765E-4,null,1.8084915063809603E-4]
[null,null,"y3",7.5375568121671677E-4,null,3.6669953260570765E-4]
[null,null,"x(i)",0.90177613496780396,null,0.90177607536315918]
[null,null,"y(i)",1.0252240834063286E-8,null,-7.0037411425971641E-9]
[]
[]
[]
[]
[]
[]
[]
[null,"日の出・日の入りの方位角計算"]
[]
[null,"日の出・日の入りに対して計算された時刻diを使えば、その時刻に対応する太陽の赤経α、"]
[]
[null,"赤緯δ､および恒星時Θを次の式から計算できる｡これによりt = Θ - αの関係から太陽の"]
[]
[null,"時角tが分かる。その次に、観測点の緯度ψ、時角t、赤緯δを使って（2.20）式からそのと"]
[]
[null,"きの太陽の方位角Aを求めることができる｡以下にその計算をしめす｡"]
[]
[]
[null,null,"α= -0.0000051・d^3+0.0016708・d^2+1.0454254・d+235.9662476"]
[]
[null,null,"δ= 0.0000467・d^30.0029163・d^2--0.2246294・d+-19.7613888"]
[]
[null,null,"1/r=1.0121310+0.0001999・d"]
[]
[null,null,"Θ= 99.1442000+ 360.985647・d"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"1999/11/21（世界時）の昭和基地の日の入りの方位角はｄ1＝0.8580683に対して"]
[]
[]
[null,null,"α = 236.8645210"]
[]
[null,null,"δ = -19.9519594"]
[]
[null,null,"1/r=1.0123028"]
[]
[null,null,"Θ = 172.0300396"]
[]
[]
[null,"が計算される｡ここから太陽の時角tは､t = Θ - αの関係から"]
[]
[null,null,"t = 172.0300378"]
[]
[null,"である。昭和基地の緯度ψ=-69.0083を考慮して（2.20）式を計算すると、"]
[]
[]
[null,null,"tanA = 0.1314679"]
[]
[]
[null,"が得られる｡tanAを計算する式の分母がマイナスであることから､求める方位角は"]
[]
[]
[null,null,"A = 187.4896000"]
[]
[null,"となる｡"]
[]
[]
[]
[]
[]
[null,"同様に、日の出に対しては、d2=0.9017761であり、ここから、"]
[]
[]
[null,null,"α = 236.9103422"]
[]
[null,null,"δ = -19.9615484"]
[]
[null,null,"1/r=1.0123115"]
[]
[null,null,"Θ = 10757.9749785"]
[]
[null,null,"t = 187.7620811"]
[]
[null,null,"tanA = -0.1279955"]
[]
[null,null,"A = 172.7061000"]
[]
[]
[null,"が計算できる｡ここから､昭和基地では､この日の太陽は南から7.5度あまり西寄り"]
[]
[null,"のところでちょっとだけ沈み､約1時間ほどして､南から7.3度あまり東寄りのところで"]
[]
[null,"また昇ってくることが分かる｡"]

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[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[null,null,null,-72004868.279956773]
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[null,null,null,null,0,null,0,null,0]
[null,null,null,null,0,null,0,null,0]
[null,null,null,null,0,null,0,null,0]
[null,null,null,null,0,null,0,null,0]
[null,null,null,null,0,null,9.6004451745379864,null,9.6004451745379864]
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{"sheet":"Sheet4","index":3,"n_rows":22,"n_cols":2,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"Sub ワークシートのグラフをユーザーフォームに表示する()"]
[null,"10  Worksheets(\"Sheet2\").ChartObjects(1).Chart.Export ThisWorkbook.Path & \"\\Chart1.gif\""]
[null,"20  UserForm1.Image1.Picture = LoadPicture(ThisWorkbook.Path & \"\\Chart1.gif\")"]
[null,"30  UserForm1.Show"]
[null,"End Sub"]
[null,"-----------------------------------------------------------------------------------------"]
[]
[null,"Export メソッド"]
[null,"機能　グラフを図形形式でエクスポートする"]
[null,"構文　expression.Export(FileName, FilterName, Interactive)"]
[null,"expression Chart オブジェクトを返すオブジェクト式を指定する（必須）"]
[null,"FileName　 エクスポートするファイル名を文字列型 (String)で指定する（必須）"]
[null,"FilterName レジスタに表示される図形フィルタの言語独立型の名前をバリアント型 (Variant) で指定する（省略可）"]
[null,"Interactive フィルタ固有のオプションを含むダイアログボックスを表示するには True を設定する（省略するとフィルタの既定値が使用される）"]
[]
[null,"Pictureプロパティ"]
[null,"機能　オブジェクトの上に表示するビットマップを設定する"]
[null,"構文　object.Picture = LoadPicture( pathname )"]
[null,"object　　　オブジェクトの名前を指定する"]
[null,"pathname　ピクチャファイルの絶対パスを指定する"]

{"sheet":"太陽暦","index":4,"n_rows":150,"n_cols":32,"rows_kept":150,"cut":false,"hidden":false,"merged":[[7,11,8,12],[5,1,5,2],[7,23,8,23],[7,25,8,26],[7,27,7,28],[7,29,8,31],[7,13,8,14],[7,15,8,17],[7,18,8,19],[6,5,6,12],[6,2,9,2],[6,3,9,3],[6,4,9,4],[6,1,9,1],[7,24,8,24],[6,13,6,19],[7,20,8,22],[6,20,6,31],[7,5,8,7],[7,8,8,10]]}
[]
[]
[null,"理科年表の太陽より作成"]
[]
[]
[null,2010,null,"年"]
[null,"月","日次","七曜","通日","世界時　0h",null,null,null,null,null,null,null,"東京,中央標準時",null,null,null,null,null,null,"世界時　0h"]
[null,null,null,null,null,"視赤経",null,null,"視赤緯",null,null,"均時差",null,"出",null,"南中",null,null,"入",null,"黄経",null,null,"黄緯","距離","視半径",null,"章動",null,"黄道傾斜"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"黄経","黄道傾斜"]
[null,null,null,null,null,"h","m","s","°","′","″","m","s","h","m","h","m","s","h","m","°","′","″","″","AU","′","″","″","″","°","′","″"]
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[null,1,2,null,2,18,50,57.7,-22,55,22,-3,54,6,51,11,44,59,16,39]
[null,1,3,null,3,18,55,22.2,-22,49,47,-4,21.9,6,51,11,45,27,16,40]
[null,1,4,null,4,18,59,46.2,-22,43,44,-4,49.4,6,51,11,45,55,16,41]
[null,1,5,null,5,19,4,9.8000000000000007,-22,37,14,-5,16.5,6,51,11,46,22,16,42,284,39,14,4.0999999999999996,0.98326999999999998,16,17.5,13.2,5.6,23,26,22.8]
[null,1,6,null,6,19,8,33,-22,30,17,-5,43.1,6,51,11,46,48,16,43]
[null,1,7,null,7,19,12,55.7,-22,22,54,-6,9.1999999999999993,6,51,11,47,14,16,43]
[null,1,8,null,8,19,17,17.899999999999999,-22,15,4,-6,34.9,6,51,11,47,40,16,44]
[null,1,9,null,9,19,21,39.6,-22,6,48,-7,0,6,51,11,48,5,16,45,288,43,47.5,3.9,0.98333000000000004,16,17.5,13.6,5.4,23,26,22.6]
[null,1,10,null,10,19,26,0.7,-21,58,6,-7,24.5,6,51,11,48,29,16,46]
[null,1,11,null,11,19,30,21.2,-21,48,59,-7,48.5,6,51,11,48,53,16,47]
[null,1,12,null,12,19,34,41.2,-21,39,26,-8,11.9,6,51,11,49,17,16,48]
[null,1,13,null,13,19,39,0.5,-21,29,28,-8,34.6,6,51,11,49,39,16,49,292,48,15.1,3.2,0.98348000000000002,16,17.3,14.2,5.6,23,26,22.8]
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[null,1,15,null,15,19,47,37.299999999999997,-21,8,18,-9,18.3,6,50,11,50,23,16,51]
[null,1,16,null,16,19,51,54.7,-20,57,6,-9,39.200000000000003,6,50,11,50,44,16,52]
[null,1,17,null,17,19,56,11.5,-20,45,30,-9,59.4,6,50,11,51,4,16,53,296,52,38.9,2.6,0.98373999999999995,16,17.100000000000001,14,5.7,23,26,22.9]
[null,1,18,null,18,20,0,27.6,-20,33,30,-10,18.899999999999999,6,49,11,51,23,16,54]
[null,1,19,null,19,20,4,42.9,-20,21,7,-10,37.799999999999997,6,49,11,51,42,16,55]
[null,1,20,null,20,20,8,57.6,-20,8,20,-10,55.9,6,48,11,52,0,16,56]
[null,1,21,null,21,20,13,11.5,-19,55,11,-11,13.3,6,48,11,52,17,16,57,300,56,58.8,2.4,0.98407999999999995,16,16.7,14.1,5.6,23,26,22.7]
[null,1,22,null,22,20,17,24.7,-19,41,40,-11,29.9,6,47,11,52,34,16,58]
[null,1,23,null,23,20,21,37.200000000000003,-19,27,46,-11,45.8,6,47,11,52,50,16,59]
[null,1,24,null,24,20,25,48.9,-19,13,31,-12,0.9,6,46,11,53,5,17,0]
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[null,1,26,null,26,20,34,9.8000000000000007,-18,43,58,-12,28.8,6,45,11,53,32,17,2]
[null,1,27,null,27,20,38,19.100000000000001,-18,28,40,-12,41.5,6,45,11,53,45,17,3]
[null,1,28,null,28,20,42,27.6,-18,13,2,-12,53.4,6,44,11,53,57,17,4]
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