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{"sheet":"軌道","index":0,"n_rows":97,"n_cols":5,"rows_kept":97,"cut":false,"hidden":false,"merged":[]}
[]
["地球モデル定数"]
["長半径＝赤道半径","a",6378137,"m"]
["短半径＝極半径","b",6356752.3141400004,"m"]
["平均半径","Re＝ (2a+b)/3",{"$f":"(2*$C$3+$C$4)/3","v":6371008.7713799998},"m"]
["空気塊を含む地心重力定数","GM",398600500000000,"m^3/s^2"]
["自転角速度","ω",7.2921149999999999E-5,"s^-1"]
["扁平率","f＝ 1/298.257 222 101",{"$f":"1/298.257222101","v":3.3528106811823188E-3}]
["離心率の2乗","e^2 ＝f(2-f) ",{"$f":"$C$8*(2-$C$8)","v":6.6943800229007869E-3}]
["万有引力定数","G",6.6742799999999995E-11,"Nm^2/kg^2"]
["地球質量","M",5.9721872621466298E+24,"kg"]
[]
["自転による遠心力含む地表面重力加速度"]
["測地緯度","φD",35,"deg"]
["地心緯度","φC＝tan^-1{(1-e^2)sinφD/cosφD}",{"$f":"DEGREES(ATAN2(COS(RADIANS(C14)),(1-$C$9)*SIN(RADIANS(C14))))","v":34.819388701463829},"deg"]
["測地緯度","φD＝tan^-1{sinφc/(1-e^2)cosφc}",{"$f":"DEGREES(ATAN2((1-$C$9)*COS(RADIANS(C15)),SIN(RADIANS(C15))))","v":35},"deg"]
["測地距離1","N＝a/√(1－e^2sin^2φD)",{"$f":"$C$3/SQRT(1-$C9*SIN(RADIANS(C14))^2)","v":6385172.174926959},"m"]
["測地距離2","T＝(b^2/a^2)N",{"$f":"($C$4^2/$C$3^2)*C17","v":6342427.4058756363},"m"]
["地心半径","R＝√{(TsinφD)^2＋(NcosφD)^2}",{"$f":"SQRT((C18*SIN(RADIANS(C14)))^2+(C17*COS(RADIANS(C14)))^2)","v":6371141.2306272881},"m"]
["万有引力","Fg＝GM/R＾2",{"$f":"$C$6/C19^2","v":9.8198165499579328},"m/s^2"]
["遠心力","Fc＝ω^2Rcosφc",{"$f":"$C$7^2*C19*COS(RADIANS(C15))","v":2.7812763954000314E-2},"m/s^2"]
["遠心力半径方向","Fcr＝Fccosφc",{"$f":"C21*COS(RADIANS(C15))","v":2.2833056405440526E-2},"m/s^2"]
["遠心力接線方向","Fcn＝Fcsinφc",{"$f":"C21*SIN(RADIANS(C15))","v":1.588084928292283E-2},"m/s^2"]
["地表面重力加速度","g＝√{(Fg－Fcr)^2+Fcn^2}",{"$f":"SQRT((C20-C22)^2+C23^2)","v":9.7969963649229737},"m/s^2"]
["地表面重力加速度","g＝√{(GM/R^2)^2－2(GM/R)(ωcosφc)^2+(ω^2Rcosφc)^2}",{"$f":"SQRT(($C$6/C19^2)^2-2*(C$6/C19)*($C$7*COS(RADIANS(C15)))^2+($C$7^2*C19*COS(RADIANS(C15)))^2)","v":9.7969963649229719},"m/s^2"]
[]
["地表面地心半径ベクトル"]
["地理緯度","φD",35,"deg"]
["東経","λ",135,"deg"]
["地心緯度","φC＝Atan2{cosφD,(1-e^2)sinφD}",{"$f":"DEGREES(ATAN2(COS(RADIANS(C28)),(1-$C$9)*SIN(RADIANS(C28))))","v":34.819388701463829},"deg"]
["地表面地心半径ベクトル_x","x＝ a / √(1 - e^2 sin^2φD)cosφDcosλ",{"$f":"$C$3/SQRT(1-$C$9*SIN(RADIANS(C28))^2)*COS(RADIANS(C28))*COS(RADIANS(C29))","v":-3698470.2872257736},"m"]
["地表面地心半径ベクトル_y","y＝ a / √(1 - e^2 sin^2φD)cosφDsinλ",{"$f":"$C$3/SQRT(1-$C$9*SIN(RADIANS(C28))^2)*COS(RADIANS(C28))*SIN(RADIANS(C29))","v":3698470.2872257745},"m"]
["地表面地心半径ベクトル_z","z＝(1-e^2) a / √(1 - e^2 sin^2φD)sinφD",{"$f":"(1-$C$9)*$C$3/SQRT(1-$C$9*SIN(RADIANS(C28))^2)*SIN(RADIANS(C28))","v":3637866.9092777637},"m"]
["地表面地心半径","r＝√(x^2+y^2+z^2)",{"$f":"SQRT(C31^2+C32^2+C33^2)","v":6371141.23062752},"m"]
["地表面地心半径","r＝√[{(a^2cosφD)^2+(b^2sinφD)^2}/{a^2(1-e^2sin^2φD)}]",{"$f":"SQRT((($C$3^2*COS(RADIANS(C28)))^2+($C$4^2*SIN(RADIANS(C28)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(C28))^2)))","v":6371141.2306272872},"m",{"$f":"C35-C34","v":-2.3283064365386963E-7}]
["地表面地心半径ベクトル_x","x＝rcosφccosλ",{"$f":"C35*COS(RADIANS(C30))*COS(RADIANS(C29))","v":-3698470.287225639},"m",{"$f":"C36-C31","v":1.3457611203193665E-7}]
["地表面地心半径ベクトル_y","y＝rcosφcsinλ",{"$f":"C35*COS(RADIANS(C30))*SIN(RADIANS(C29))","v":3698470.2872256394},"m",{"$f":"C37-C32","v":-1.3504177331924438E-7}]
["地表面地心半径ベクトル_z","z＝rsinφc",{"$f":"C35*SIN(RADIANS(C30))","v":3637866.9092776314},"m",{"$f":"C38-C33","v":-1.3224780559539795E-7}]
[]
["軌道要素"]
["地理緯度","φD",{"$f":"C28","v":35},"deg"]
["東経","λ",{"$f":"C29","v":135},"deg"]
["高度","h",30000000,"m"]
["地心半径ベクトル_x","x=[{a/√(1-e^2sin^2φD)}+h]cosλ",{"$f":"(C$3/SQRT(1-$C$9*SIN(RADIANS(C41))^2)+C43)*COS(RADIANS(C41))*COS(RADIANS(C42))","v":-21075309.247412849},"m"]
["地心半径ベクトル_y","y=[{a/√(1-e^2sin^2φD)}+h]sinλ",{"$f":"(C$3/SQRT(1-$C$9*SIN(RADIANS(C41))^2)+C43)*COS(RADIANS(C41))*SIN(RADIANS(C42))","v":21075309.247412853},"m"]
["地心半径ベクトル_z","z=[(1-e^2){a/√(1-e^2sin^2φD)}+h]sinφD",{"$f":"(1-$C$9)*($C$3/SQRT(1-$C$9*SIN(RADIANS(C41))^2)+C43)*SIN(RADIANS(C41))","v":20729967.840695694},"m"]
["地心半径","r=√(x^2+y^2+z^2)",{"$f":"SQRT(C44^2+C45^2+C46^2)","v":36305218.446174495},"m"]
["地心緯度","φc=tan^-1{z/√(x^2+y^2)}",{"$f":"DEGREES(ATAN2(SQRT(C44^2+C45^2),C46))","v":34.819388701463829},"deg"]
["地理緯度","φD=tan^-1[z/{(1-e^2)√(x^2+y^2)}]",{"$f":"DEGREES(ATAN2((1-$C$9)*SQRT(C44^2+C45^2),C46))","v":35.000000000000007},"deg",{"$f":"C49-C41","v":0}]
["東経","λ=tan^-1(y/x)",{"$f":"DEGREES(ATAN2(C44,C45))","v":135},"deg",{"$f":"C50-C42","v":0}]
["高度","h=√[{√(x^2+y^2)-acosφD/√(1-e^2sin^2φD)}^2+{z-a(1-e^2)sinφD/√(1-e^2sin^2φD)}^2]",{"$f":"SQRT((SQRT(C44^2+C45^2)-$C$3*COS(RADIANS(C49))/SQRT(1-$C$9*SIN(RADIANS(C49))^2))^2+(C46-$C$3*(1-$C$9)*SIN(RADIANS(C49))/SQRT(1-$C$9*SIN(RADIANS(C49))^2))^2)","v":29934077.215546973},"m",{"$f":"C51-C43","v":-65922.78445302695}]
["慣性速度","v",1000,"m/s"]
["慣性速度方位角","μ",90,"deg"]
["慣性速度上下角","θ",30,"deg"]
["慣性速度ベクトル_x","vx",{"$f":"C$52*D55","v":-901.98641836558488},-0.90198641836558491,{"$f":"exe(\"v\",D55:D57=matrtn(matrtn(matrtn(rtnmat(C42,3),90-C41,2),180-C53,3),-C54,2))","v":"v"}]
["慣性速度ベクトル_y","vy",{"$f":"C$52*D56","v":-322.75845302599873},-0.32275845302599876]
["慣性速度ベクトル_z","vz",{"$f":"C$52*D57","v":286.78821817551756},0.28678821817551758]
["慣性速度","v",{"$f":"SQRT(C55^2+C56^2+C57^2)","v":1000},"m/s",{"$f":"C58-C52","v":0}]
["角運動量ベクトルx","hx＝yvz－zvy",{"$f":"C45*C57-C46*C56","v":12734922738.105186},"m^2/s"]
["角運動量ベクトルy","hy＝zvx－xvz",{"$f":"C46*C55-C44*C57","v":-12653999058.89933},"m^2/s"]
["角運動量ベクトルz","hz＝xvy－yvx",{"$f":"C44*C56-C45*C55","v":25811876913.760506},"m^2/s"]
["角運動量","h=√(hx^2+hy^2+hz^2)",{"$f":"SQRT(C59^2+C60^2+C61^2)","v":31441293534.765011},"m^2/s"]
["慣性速度方位角","μ= tan^-1(rhz/yhx-xhy)",{"$f":"DEGREES(ATAN2(C45*C59-C44*C60,C47*C61))","v":89.895724305994889},"deg",{"$f":"C63-C53","v":-0.10427569400511061}]
["慣性速度上下角","θ＝90－cos^-1{(xvx+yvy+zvz)/(rv)}",{"$f":"90-DEGREES(ACOS((C44*C55+C45*C56+C46*C57)/C47/C58))","v":29.99983564767421},"deg",{"$f":"C64-C54","v":-1.6435232578970727E-4}]
[]
["長半径","a=1/(2/r-v^2/GM)",{"$f":"1/(2/C47-C52^2/$C$6)","v":19018738.933868941},"m"]
["長半径","a=(ra+rp)/2",{"$f":"(E81+E80)/2","v":19018738.933868941},"m"]
["長半径","a=-GM/(2E)",{"$f":"-$C$6/(2*C89)","v":19018738.933868941},"m"]
["短半径","b=a√(1－e^2)",{"$f":"C67*SQRT(1-C76^2)","v":6867874.3989115283}]
["短半径","b=√(rarp)",{"$f":"SQRT(C80*C81)","v":6867874.3989115283}]
["半通径","p=h^2/GM",{"$f":"C62^2/$C$6","v":2480064.4734245343},"m"]
["半通径","p=a(1-e^2)",{"$f":"C66*(1-C74^2)","v":2480064.4734245352},"m"]
["半通径","p=rarp/a",{"$f":"C81*C80/C66","v":2480064.4734245352},"m"]
["離心率","e=√{1-h^2(2/r-v^2/GM)}",{"$f":"SQRT(1-C71*(2/C47-C52^2/$C$6))","v":0.93252286846971433}]
["離心率","e=√(1-p/a)",{"$f":"SQRT(1-C71/C66)","v":0.93252286846971433}]
["離心率","e=(ra-rp)/(ra+rp)",{"$f":"(E81-E80)/(E81+E80)","v":0.93252286846971433}]
["離心率","e=1+2rpE/GM",{"$f":"1+2*E80*C89/$C$6","v":0.93252286846971433}]
["軌道半径","r=p/(1+ecosν)",{"$f":"C71/(1+C75*COS(RADIANS(C96)))","v":36305218.446174502},"m",{"$f":"C78-C47","v":0}]
["速度","v=√{GM(2/r-1/a)}",{"$f":"SQRT($C$6*(2/C47-1/C66))","v":999.99999999999977},"m/s",{"$f":"C79-C52","v":0}]
["近地点半径","rp=a(1-e)",{"$f":"C66*(1-C75)","v":1283329.9485808397},"m",{"$f":"C80","v":1283329.9485808397}]
["遠地点半径","ra=a(1+e)",{"$f":"C66*(1+C75)","v":36754147.919157043},"m",{"$f":"C81","v":36754147.919157043}]
["近地点速度","vp=√[GM(1+e)/{a(1-e)}]",{"$f":"SQRT($C$6*(1+C75)/(C66*(1-C75)))","v":24499.773865274576},"m/s"]
["近地点速度","vp＝√[GM{2/rp－1/a}]",{"$f":"SQRT($C$6*(2/C80-1/C66))","v":24499.773865274572},"m/s"]
["近地点速度","vp＝√{(GM/a)(ra/rp)}",{"$f":"SQRT(($C$6/C66)*(C81/C80))","v":24499.773865274576},"m/s"]
["遠地点速度","va=√[GM(1-e)/{a(1+e)}]",{"$f":"SQRT($C$6*(1-C75)/(C66*(1+C75)))","v":855.44884903663205},"m/s"]
["遠地点速度","va＝√[GM{2/ra－1/a}]",{"$f":"SQRT($C$6*(2/C81-1/C66))","v":855.44884903663194},"m/s"]
["遠地点速度","va＝√{(GM/a)(rp/ra)}",{"$f":"SQRT(($C$6/C66)*(C80/C81))","v":855.44884903663205},"m/s"]
["軌道周期","T=2π√(a^3/GM)",{"$f":"2*PI()*SQRT(C66^3/$C$6)/3600","v":7.2507181495912052},"hr"]
["軌道エネルギー","E=-GM/(2a)",{"$f":"-$C$6/(2*C66)","v":-10479151.677353445},"m^2/s^2"]
["軌道エネルギー","E=-GM/r+v^2/2",{"$f":"-$C$6/C47+C52^2/2","v":-10479151.677353447},"m^2/s^2"]
["昇降点経度","Ω=tan^-2{hx/(-hy) }",{"$f":"DEGREES(ATAN2(-C60,C59))","v":45.18262175987168},"deg"]
["軌道傾斜角","i =tan^-1(√(hx^2+hz^2)/hz)",{"$f":"DEGREES(ATAN2(C61,SQRT(C59^2+C60^2)))","v":34.819525129306591},"deg"]
["緯度引数","u =tan^-1(zh/yhx-xhy) ",{"$f":"DEGREES(ATAN2(C45*C59-C44*C60,C46*C62))","v":89.85007564695789},"deg"]
["離心近点離角","E=tan^-1[{(xvx+yvy+zvz)/√(GMa)}/(1-r/a)]",{"$f":"DEGREES(ATAN2(1-C47/C66,(C44*C55+C45*C56+C46*C57)/SQRT($C$6*C66)))","v":167.08107251305768},"deg"]
["平均近点離角","M=E-tanE",{"$f":"C94-DEGREES(TAN(RADIANS(C94)))","v":180.22347963037211},"deg"]
["真近点離角","ν=tan^-1{h(xvx+yvy+zvz)/(h^2 - GMr)}",{"$f":"DEGREES(ATAN2(C62^2-$C$6*C47,C62*(C44*C55+C45*C56+C46*C57)))","v":177.57605304939455},"deg"]
["近地点引数","ω=u-ν",{"$f":"C93-C96","v":-87.725977402436655},"deg"]

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[]
["地球モデル定数"]
["長半径＝赤道半径","a",6378137,"m"]
["短半径＝極半径","b",6356752.3141400004,"m"]
["平均半径","Re＝ (2a+b)/3",{"$f":"(2*$C$3+$C$4)/3","v":6371008.7713799998},"m"]
["空気塊を含む地心重力定数","GM",398600500000000,"m^3/s^2"]
["自転角速度","ω",7.2921149999999999E-5,"s^-1"]
["扁平率","f＝ 1/298.257 222 101",{"$f":"1/298.257222101","v":3.3528106811823188E-3}]
["離心率の2乗","e^2 ＝f(2-f) ",{"$f":"$C$8*(2-$C$8)","v":6.6943800229007869E-3}]
["万有引力定数","G",6.6742799999999995E-11,"Nm^2/kg^2"]
["地球質量","M",5.9721872621466298E+24,"kg"]
[]
[]
["球面三角法"]
[null,"cosa=cosbcosc+sinbsinccosA",null,"A=Δλ","cosa=cosbcosc+sinbsinccosA"]
[null,"cosb=cosccosa+sincsinacosB",null,"b=90-φcq","       =sinφcqsinφcp+cosφcqcosφcpcosΔλ"]
[null,"cosc=cosacosb+sinasinbcosC",null,"c=90-φcp","cosθ=sinφcpsinφcq+cosφcpcosφcqcosΔλ"]
[null,"sina/sinA=sinb/sinB=sinc/sinC",null,null,"cosB=(cosbsinc-sinbcosccosA)/sina"]
[null,"sinacosB=cosbsinc-sinbcosccosA",null,"a=θ:地心角","sinB=sinbsinA/sina"]
[null,"sinacosC=coscsinb-sinccosbcosA",null,null,"tanB=sinbsinA/(cosbsinc-sinbcosccosA)"]
[null,"tan{(A+B)/2}/tan{(A-B)/2}=tan{(a+b)/2}/tan{(a-b)/2}",null,"P=μ:方位角","       =cosφcqsinΔλ/(sinφcqcosφcp-cosφcqsinφcpcosΔλ)"]
[null,"cotasinb=cosbcosC+cotAsinC",null,null,"tanμ=cosφcqsinΔλ/(cosφcpsinφcq-sinφcpcosφcqcosΔλ)"]
[]
["方位角、地表面距離"]
["点P測地緯度","φp",35,"deg"]
["点P東経","λp",135,"deg"]
["点P地心緯度","φcp＝tan^-1{(1-e^2)sinφp/cosφp}",{"$f":"DEGREES(ATAN2(COS(RADIANS(C25)),(1-$C$9)*SIN(RADIANS(C25))))","v":34.819388701463829},"deg"]
["点P地心半径","rp＝√[{(a^2cosφp)^2+(b^2sinφp)^2}/{a^2(1-e^2sin^2φp)}]",{"$f":"SQRT((($C$3^2*COS(RADIANS(C25)))^2+($C$4^2*SIN(RADIANS(C25)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(C25))^2)))","v":6371141.2306272872},"m"]
["点Q測地緯度","φq",40,"deg"]
["点Q東経","λq",140,"deg"]
["点Q地心緯度","φcq＝tan^-1{(1-e^2)sinφq/cosφq}",{"$f":"DEGREES(ATAN2(COS(RADIANS(C29)),(1-$C$9)*SIN(RADIANS(C29))))","v":39.81061055099908},"deg"]
["点Q地心半径","rq＝√[{(a^2cosφq)^2+(b^2sinφq)^2}/{a^2(1-e^2sin^2φq)}]",{"$f":"SQRT((($C$3^2*COS(RADIANS(C29)))^2+($C$4^2*SIN(RADIANS(C29)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(C29))^2)))","v":6369344.8631969597},"m"]
["PQ間の地心角","θ=cos^-1{sinφcpsinφcq+cosφcpcosφcqcos(λq-λp)}",{"$f":"DEGREES(ACOS(SIN(RADIANS(C27))*SIN(RADIANS(C31))+COS(RADIANS(C27))*COS(RADIANS(C31))*COS(RADIANS(C30-C26))))","v":6.379208778504645},"deg"]
["方位角","μ=tan^-1[cosφcqsin(λq-λp)/{cosφcpsinφcq-sinφcpcosφcqcos(λq-λp)}]",{"$f":"DEGREES(ATAN2(COS(RADIANS(C27))*SIN(RADIANS(C31))-SIN(RADIANS(C27))*COS(RADIANS(C31))*COS(RADIANS(C30-C26)),COS(RADIANS(C31))*SIN(RADIANS(C30-C26))))","v":37.05382976292703},"deg"]
["地表面距離","d=Recos^-1(sinφcpsinφcq+cosφcpcosφcqcos(λq-λp))",{"$f":"$C$5*ACOS(SIN(RADIANS(C27))*SIN(RADIANS(C31))+COS(RADIANS(C27))*COS(RADIANS(C31))*COS(RADIANS(C30-C26)))","v":709336.62876578222},"m",{"$f":"C35-GeoDes(C$25,C$26,C$29,C$30)","v":82.350506293936633}]
[null,"d=average(rp,rq)ecos^-1(sinφcpsinφcq+cosφcpcosφcqcos(λq-λp))",{"$f":"AVERAGE(C28,C32)*ACOS(SIN(RADIANS(C27))*SIN(RADIANS(C31))+COS(RADIANS(C27))*COS(RADIANS(C31))*COS(RADIANS(C30-C26)))","v":709251.37438423955},"m",{"$f":"C36-GeoDes(C$25,C$26,C$29,C$30)","v":-2.9038752487394959}]
[]
[]
["ある位置から見て方位角方向に地表面距離だけ離れた位置（緯度、経度）を求める"]
["点P測地緯度","φp",35,"deg",{"$f":"C40-C$25","v":0}]
["点P東経","λp",135,"deg",{"$f":"C41-C$26","v":0}]
["方位角","μ",{"$f":"C34","v":37.05382976292703},"deg",{"$f":"C42-C$34","v":0}]
["地表面距離","d",{"$f":"GeoDes(C$25,C$26,C$29,C$30)","v":709254.27825948829},"m",{"$f":"C43-C$35","v":-82.350506293936633}]
["点P地心緯度","φcp＝tan^-1{(1-e^2)sinφp/cosφp}",{"$f":"DEGREES(ATAN2(COS(RADIANS(C40)),(1-$C$9)*SIN(RADIANS(C40))))","v":34.819388701463829},"deg",{"$f":"C44-C$27","v":0}]
["点P地心半径","rp＝√[{(a^2cosφp)^2+(b^2sinφp)^2}/{a^2(1-e^2sin^2φp)}]",{"$f":"SQRT((($C$3^2*COS(RADIANS(C40)))^2+($C$4^2*SIN(RADIANS(C40)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(C40))^2)))","v":6371141.2306272872},"m",{"$f":"C45-C$28","v":0}]
["PQ間の地心角","θ＝d/rp",{"$f":"DEGREES(C43/C45)","v":6.3783355720502417},"deg",{"$f":"C46-C$33","v":-8.7320645440325251E-4}]
["点Q地心緯度","φcq=90-cos^-1(sinφcpcosθ+cosφcpsinθcosμ)",{"$f":"90-DEGREES(ACOS(SIN(RADIANS(C$44))*COS(RADIANS(C46))+COS(RADIANS(C$44))*SIN(RADIANS(C46))*COS(RADIANS(C$42))))","v":39.809942505513483},"deg",{"$f":"C47-C$31","v":-6.6804548559673549E-4}]
["点Q測地緯度","φq＝tan^-1{sinφcq/(1-e^2)cosφcq)",{"$f":"DEGREES(ATAN2((1-$C$9)*COS(RADIANS(C47)),SIN(RADIANS(C47))))","v":39.999331160195155},"deg",{"$f":"C48-C$29","v":-6.6883980484533367E-4}]
["点Q東経","λq=λp+tan^-1{(cosφcpsinθsinμ)/(cosθ-sinφcqsinφcp)}",{"$f":"C$41+DEGREES(ATAN2((COS(RADIANS(C46))-SIN(RADIANS(C47))*SIN(RADIANS(C$44))),(COS(RADIANS(C$44))*SIN(RADIANS(C46))*SIN(RADIANS(C$42)))))","v":139.99926797218964},"deg",{"$f":"IF(C49<0,C49+360,C49)-IF(C$30<0,C$30+360,C$30)","v":-7.3202781035774933E-4}]
["点Q地心半径","rq＝√[{(a^2cosφq)^2+(b^2sinφq)^2}/{a^2(1-e^2sin^2φq)}]",{"$f":"SQRT((($C$3^2*COS(RADIANS(C48)))^2+($C$4^2*SIN(RADIANS(C48)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(C48))^2)))","v":6369345.1086746305},"m",{"$f":"C50-C$32","v":0.24547767080366611}]
["方位角","μ=tan^-1[cosφcqsin(λq-λp)/{cosφcpsinφcq-sinφcpcosφcqcos(λq-λp)}]",{"$f":"DEGREES(ATAN2(COS(RADIANS(C$44))*SIN(RADIANS(C47))-SIN(RADIANS(C$44))*COS(RADIANS(C47))*COS(RADIANS(C49-C$41)),COS(RADIANS(C47))*SIN(RADIANS(C49-C$41))))","v":37.053829762927016},"deg",{"$f":"C51-C$34","v":0}]
["地表面距離","d=Reθ",{"$f":"$C$5*RADIANS(C46)","v":709239.53250446066},"m",{"$f":"C52-GeoDes(C$40,C$41,C$48,C$49)","v":82.325534839415923}]
[null,"d=average(rp,rq)θ",{"$f":"AVERAGE(C45,C50)*RADIANS(C46)","v":709154.30345645978},"m",{"$f":"C53-GeoDes(C$40,C$41,C$48,C$49)","v":-2.9035131614655256}]
[]
[]
["世界各地の成田から見た方位角と地表面距離",null,null,null,null,null,null,null,null,null,"方位角と地表面距離"]
[null,"成田","地理緯度",35.771337000000003,"国土地理院",null,"エクセル計算誤差"]
[null,null,"経度",140.383927,"[距離と方位角の計算]サイト",null,"誤差比率[%]",null,null,null,"地理緯度","経度","地心緯度","地心半径","国土地理院(基準)",null,"方位角誤差","距離誤差"]
[null,null,"地心緯度",{"$f":"DEGREES(ATAN2(COS(RADIANS(D57)),(1-$C$9)*SIN(RADIANS(D57))))","v":35.589005884740622},"方位角","距離","方位角","回転楕円体","球体",null,"[deg]","[deg]","[deg]","[m]","方位角","距離",null,"楕円体","地球平均半径","2点平均半径"]
[null,null,"地心半径",{"$f":"SQRT((($C$3^2*COS(RADIANS(D57)))^2+($C$4^2*SIN(RADIANS(D57)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(D57))^2)))","v":6370870.1659844248},"[deg]","[m]","[deg]","[m]","[m]","起点",35.771337000000003,140.383927,{"$f":"DEGREES(ATAN2(COS(RADIANS(K60)),(1-$C$9)*SIN(RADIANS(K60))))","v":35.589005884740622},{"$f":"SQRT((($C$3^2*COS(RADIANS(K60)))^2+($C$4^2*SIN(RADIANS(K60)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(K60))^2)))","v":6370870.1659844248},"[deg]","[m]","[deg]","[m]","[m]","[m]"]
[null,"ホノルル","地理緯度",21.312349999999999,null,null,null,null,null,null,0,0,0,6378137,305.44471666666698,14320269.987,{"$f":"IF(IF(ABS(DEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M61))-SIN(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L61-L$60)),COS(RADIANS(M61))*SIN(RADIANS(L61-L$60)))))<0.000000001,0,\nDEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M61))-SIN(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L61-L$60)),COS(RADIANS(M61))*SIN(RADIANS(L61-L$60)))))>=0,\nIF(ABS(DEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M61))-SIN(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L61-L$60)),COS(RADIANS(M61))*SIN(RADIANS(L61-L$60)))))<0.000000001,0,\nDEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M61))-SIN(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L61-L$60)),COS(RADIANS(M61))*SIN(RADIANS(L61-L$60))))),\nIF(ABS(DEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M61))-SIN(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L61-L$60)),COS(RADIANS(M61))*SIN(RADIANS(L61-L$60)))))<0.000000001,0,\nDEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M61))-SIN(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L61-L$60)),COS(RADIANS(M61))*SIN(RADIANS(L61-L$60)))))+360)-O61","v":-0.33460283277207736},{"$f":"GeoDes(K$60,L$60,K61,L61)-P61","v":11.19166911020875},{"$f":"$C$5*ACOS(SIN(RADIANS(M$60))*SIN(RADIANS(M61))+COS(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L$60-L61)))-P61","v":362.37182419002056},{"$f":"AVERAGE(N$60,N61)*ACOS(SIN(RADIANS(M$60))*SIN(RADIANS(M61))+COS(RADIANS(M$60))*COS(RADIANS(M61))*COS(RADIANS(L$60-L61)))-P61","v":8217.9429052844644}]
[null,null,"経度",-157.928404,87.365955555555502,6145510.1639999999,{"$f":"IF(DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D63))-SIN(RADIANS(D$59))*COS(RADIANS(D63))*COS(RADIANS(D62-D$58)),COS(RADIANS(D63))*SIN(RADIANS(D62-D$58))))>=0,DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D63))-SIN(RADIANS(D$59))*COS(RADIANS(D63))*COS(RADIANS(D62-D$58)),COS(RADIANS(D63))*SIN(RADIANS(D62-D$58)))),DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D63))-SIN(RADIANS(D$59))*COS(RADIANS(D63))*COS(RADIANS(D62-D$58)),COS(RADIANS(D63))*SIN(RADIANS(D62-D$58))))+360)-E62","v":8.958792510132696E-2},{"$f":"GeoDes(D$57,D$58,D61,D62)-F62","v":4.8364185998216271},{"$f":"$C$5*ACOS(SIN(RADIANS(D$59))*SIN(RADIANS(D63))+COS(RADIANS(D$59))*COS(RADIANS(D63))*COS(RADIANS(D62-D$58)))-F62","v":-1355.9655254008248},null,{"$f":"K61+45","v":45},{"$f":"L61","v":0},44.807576783073245,6367489.5438111397,333.20521388888898,10213761.868000001,-0.11956185117020368,{"$f":"GeoDes(K$60,L$60,K62,L62)-P62","v":8.1000330578535795},12495.189090909436,9559.5519329253584]
[null,null,"地心緯度",{"$f":"DEGREES(ATAN2(COS(RADIANS(D61)),(1-$C$9)*SIN(RADIANS(D61))))","v":21.182363249715696},null,null,{"$f":"G62/$E62","v":1.0254328992528275E-3},{"$f":"H62/$F62","v":7.8698406979343287E-7},{"$f":"I62/$F62","v":-2.2064328090188232E-4},null,{"$f":"K62+45","v":90},{"$f":"L62","v":0},90,6356752.3141396455,0,6041794.7939999998,0,4.7728932183235884,8440.0350535428151,1604.8922644173726]
[null,null,"地心半径",{"$f":"SQRT((($C$3^2*COS(RADIANS(D61)))^2+($C$4^2*SIN(RADIANS(D61)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(D61))^2)))","v":6375332.6575458311},null,null,null,null,null,null,-90,{"$f":"L63","v":0},-90,6356752.3141396455,180,13962136.666999999,0,10.656152466312051,2742.8560700006783,-13033.712653372437]
[null,"ニューヨーク","地理緯度",40.641179999999999,null,null,null,null,null,null,{"$f":"K64+45","v":-45},{"$f":"L64","v":0},-44.807576783073245,6367489.5438111397,240.50633888888899,16542986.741,8.2231625563167654E-2,12.816444873809814,-6823.4301078710705,-11570.443134725094]
[null,null,"経度",-73.778379000000001,25.418327777777801,10853736.012,{"$f":"IF(DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D67))-SIN(RADIANS(D$59))*COS(RADIANS(D67))*COS(RADIANS(D66-D$58)),COS(RADIANS(D67))*SIN(RADIANS(D66-D$58))))>=0,DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D67))-SIN(RADIANS(D$59))*COS(RADIANS(D67))*COS(RADIANS(D66-D$58)),COS(RADIANS(D67))*SIN(RADIANS(D66-D$58)))),DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D67))-SIN(RADIANS(D$59))*COS(RADIANS(D67))*COS(RADIANS(D66-D$58)),COS(RADIANS(D67))*SIN(RADIANS(D66-D$58))))+360)-E66","v":0.12701252410179009},{"$f":"GeoDes(D$57,D$58,D65,D66)-F66","v":8.5972284898161888},{"$f":"$C$5*ACOS(SIN(RADIANS(D$59))*SIN(RADIANS(D67))+COS(RADIANS(D$59))*COS(RADIANS(D67))*COS(RADIANS(D66-D$58)))-F66","v":13104.010677535087},null,0,{"$f":"L65+45","v":45},{"$f":"DEGREES(ATAN2(COS(RADIANS(K66)),(1-$C$9)*SIN(RADIANS(K66))))","v":0},{"$f":"SQRT((($C$3^2*COS(RADIANS(K66)))^2+($C$4^2*SIN(RADIANS(K66)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(K66))^2)))","v":6378137},273.297197222222,10499593.091,-0.15782040111207607,8.1927264761179686,-5436.3018782250583,320.25918189436197]
[null,null,"地心緯度",{"$f":"DEGREES(ATAN2(COS(RADIANS(D65)),(1-$C$9)*SIN(RADIANS(D65))))","v":40.451076546010796},null,null,{"$f":"G66/$E66","v":4.9968874904836157E-3},{"$f":"H66/$F66","v":7.9209854379275541E-7},{"$f":"I66/$F66","v":1.2073271971095631E-3},null,{"$f":"K66+45","v":45},{"$f":"L66","v":45},44.807576783073245,6367489.5438111397,311.015741666667,7683219.6169999996,-0.1167864314740541,6.0978206181898713,5438.9364804495126,3231.7641378566623]
[null,null,"地心半径",{"$f":"SQRT((($C$3^2*COS(RADIANS(D65)))^2+($C$4^2*SIN(RADIANS(D65)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(D65))^2)))","v":6369109.0701976186},null,null,null,null,null,null,{"$f":"K67+45","v":90},{"$f":"L67","v":45},90,6356752.3141396455,0,6041794.7929999996,0,4.7738931812345982,8440.0360535429791,1604.8932644175366]
[null,"ロンドン","地理緯度",51.470005,null,null,null,null,null,null,-90,{"$f":"L68","v":45},-90,6356752.3141396455,180,13962136.665999999,0,10.657152429223061,2742.8570700008422,-13033.711653372273]
[null,null,"経度",-0.45446399999999998,336.78599166666697,9614257.4600000009,{"$f":"IF(DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D71))-SIN(RADIANS(D$59))*COS(RADIANS(D71))*COS(RADIANS(D70-D$58)),COS(RADIANS(D71))*SIN(RADIANS(D70-D$58))))>=0,DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D71))-SIN(RADIANS(D$59))*COS(RADIANS(D71))*COS(RADIANS(D70-D$58)),COS(RADIANS(D71))*SIN(RADIANS(D70-D$58)))),DEGREES(ATAN2(COS(RADIANS(D$59))*SIN(RADIANS(D71))-SIN(RADIANS(D$59))*COS(RADIANS(D71))*COS(RADIANS(D70-D$58)),COS(RADIANS(D71))*SIN(RADIANS(D70-D$58))))+360)-E70","v":-9.5896799375736919E-2},{"$f":"GeoDes(D$57,D$58,D69,D70)-F70","v":7.6337598096579313},{"$f":"$C$5*ACOS(SIN(RADIANS(D$59))*SIN(RADIANS(D71))+COS(RADIANS(D$59))*COS(RADIANS(D71))*COS(RADIANS(D70-D$58)))-F70","v":12845.787201790139},null,{"$f":"K69+45","v":-45},{"$f":"L69","v":45},-44.807576783073245,6367489.5438111397,232.91436666666701,13090621.615,-2.1891543870736996E-2,{"$f":"GeoDes(K$60,L$60,K70,L70)-P70","v":10.049951493740082},-7122.0633752048016,-10877.925097221509]
[null,null,"地心緯度",{"$f":"DEGREES(ATAN2(COS(RADIANS(D69)),(1-$C$9)*SIN(RADIANS(D69))))","v":51.282327180618225},null,null,{"$f":"G70/$E70","v":-2.8474105737346262E-4},{"$f":"H70/$F70","v":7.9400409666769317E-7},{"$f":"I70/$F70","v":1.3361184943543355E-3},null,0,{"$f":"L70+45","v":90},0,6378137,244.34434722222201,6538891.8849999998,-6.5392909587131953E-2,5.0387910222634673,-4419.5284066516906,-835.0489794537425]
[null,null,"地心半径",{"$f":"SQRT((($C$3^2*COS(RADIANS(D69)))^2+($C$4^2*SIN(RADIANS(D69)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(D69))^2)))","v":6365092.9903924018},null,null,null,null,null,null,{"$f":"K71+45","v":45},{"$f":"L71","v":90},44.807576783073245,6367489.5438111397,299.61027777777798,4326063.1440000003,-6.247704992256331E-2,3.429736896418035,1702.1868671048433,459.82139111496508]
[null,"ベルリン","地理緯度",52.362482999999997,null,null,null,null,null,null,{"$f":"K72+45","v":90},{"$f":"L72","v":90},90,6356752.3141396455,0,6041794.7920000004,{"$f":"IF(IF(ABS(DEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M73))-SIN(RADIANS(M$60))*COS(RADIANS(M73))*COS(RADIANS(L73-L$60)),COS(RADIANS(M73))*SIN(RADIANS(L73-L$60)))))<0.000000001,0,\nDEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M73))-SIN(RADIANS(M$60))*COS(RADIANS(M73))*COS(RADIANS(L73-L$60)),COS(RADIANS(M73))*SIN(RADIANS(L73-L$60)))))>=0,\nIF(ABS(DEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M73))-SIN(RADIANS(M$60))*COS(RADIANS(M73))*COS(RADIANS(L73-L$60)),COS(RADIANS(M73))*SIN(RADIANS(L73-L$60)))))<0.000000001,0,\nDEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M73))-SIN(RADIANS(M$60))*COS(RADIANS(M73))*COS(RADIANS(L73-L$60)),COS(RADIANS(M73))*SIN(RADIANS(L73-L$60))))),\nIF(ABS(DEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M73))-SIN(RADIANS(M$60))*COS(RADIANS(M73))*COS(RADIANS(L73-L$60)),COS(RADIANS(M73))*SIN(RADIANS(L73-L$60)))))<0.000000001,0,\nDEGREES(ATAN2(COS(RADIANS(M$60))*SIN(RADIANS(M73))-SIN(RADIANS(M$60))*COS(RADIANS(M73))*COS(RADIANS(L73-L$60)),COS(RADIANS(M73))*SIN(RADIANS(L73-L$60)))))+360)-O73","v":0},4.7748931394889951,8440.0370535422117,1604.8942644167691]
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[null,null,"地心半径",{"$f":"SQRT((($C$3^2*COS(RADIANS(D85)))^2+($C$4^2*SIN(RADIANS(D85)))^2)/($C$3^2*(1-$C$9*SIN(RADIANS(D85))^2)))","v":6371509.2904763892},null,null,null,null,null,null,{"$f":"K87+45","v":90},{"$f":"L87","v":-180},90,6356752.3141396455,0,6041794.7920000004,0,4.7748931329697371,8440.0370535422117,1604.8942644167691]
[null,"ヨハネスブルグ","地理緯度",-26.136682,null,null,null,null,null,null,-90,{"$f":"L88","v":-180},-90,6356752.3141396455,180,13962136.664999999,0,10.6581523809582,2742.8580700010061,-13033.710653372109]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"最大",{"$f":"MAX(ABS(MIN(Q61:Q105)),MAX(Q61:Q105))","v":0.66975672215116333},{"$f":"MAX(ABS(MIN(R61:R105)),MAX(R61:R105))","v":14.593090239912271},{"$f":"MAX(ABS(MIN(S61:S105)),MAX(S61:S105))","v":16501.868440046906},{"$f":"MAX(ABS(MIN(T61:T105)),MAX(T61:T105))","v":22286.020566625521}]

{"sheet":"楕円体測地線距離","index":2,"n_rows":99,"n_cols":6,"rows_kept":99,"cut":false,"hidden":false,"merged":[]}
[null,"追加する必要がある定数"]
[null,null,"AXER=a",null,null,"：地球長半径（赤道半径）"]
[null,null,"EER2=e^2",null,null,"：地球離心率の2乗"]
[null,null,"CRDDG=π/180",null,null,"：ｄｅｇからｒａｄへの変換定数"]
[null,"手直し必要"]
[null,null," Artand(sy, cy)",null,null,"：ｄｅｇ単位で出力するアークタンジェント"]
[]
[]
[null,"Function GeoDes(lat1 As Double, lon1 As Double, lat2 As Double, lon2 As Double) As Double"]
[]
[null,"'測地線に沿った距離の計算"]
[]
[null,"' lat1　：入力、第1地点の測地緯度（北緯）　[度]"]
[null,"' lon1　：入力、第1地点の経度（東経）　[度]"]
[null,"' lat2　：入力、第2地点の測地緯度（北緯）　[度]"]
[null,"' lon2　：入力、第2地点の経度（東経）　[度]"]
[null,"' GeoDes：出力、2地点間の距離　[m]"]
[]
[null,"    Dim glat1 As Double, glon1 As Double"]
[null,"    Dim glat2 As Double, glon2 As Double"]
[null,"    Dim tu1 As Double, tu2 As Double"]
[null,"    Dim cu1 As Double, su1 As Double, cu2 As Double"]
[null,"    Dim s1 As Double, b1 As Double, f1 As Double"]
[null,"    Dim x As Double, sx As Double, cx As Double"]
[null,"    Dim y As Double, sy As Double, cy As Double"]
[null,"    Dim sa As Double, c2a As Double, cz As Double"]
[null,"    Dim e As Double, s As Double, c As Double, r As Double, d As Double"]
[null,"    Dim a As Double, f As Double"]
[null,"    Dim iter As Integer, flag As Boolean"]
[]
[null,"    Const EPS As Double = 0.00000000005"]
[null,"    Const MAXITER As Integer = 100"]
[null,"    iter = 0"]
[null,"    flag = False"]
[null,"    "]
[null,"    a = AXER"]
[null,"    f = 1# - Sqrt(1# - EER2)"]
[]
[null,"    If (lat1 + lat2 = 0# And Abs(lon1 - lon2) >= 179.4) Then"]
[null,"        lat2 = 0.5 * (lat1 + lat2)"]
[null,"        lon2 = 0.5 * (lon1 + lon2)"]
[null,"        flag = True"]
[null,"    End If"]
[null,"    "]
[null,"    glat1 = CRDDG * lat1"]
[null,"    glon1 = CRDDG * lon1"]
[null,"    glat2 = CRDDG * lat2"]
[null,"    glon2 = CRDDG * lon2"]
[]
[null,"    r = 1# - f"]
[null,"    tu1 = r * Tan(glat1)"]
[null,"    tu2 = r * Tan(glat2)"]
[null,"    cu1 = 1# / Sqrt(1# + tu1 * tu1)"]
[null,"    su1 = cu1 * tu1"]
[null,"    cu2 = 1# / Sqrt(1# + tu2 * tu2)"]
[null,"    s1 = cu1 * cu2"]
[null,"    b1 = s1 * tu2"]
[null,"    f1 = b1 * tu1"]
[null,"    x = glon2 - glon1"]
[null,"    d = x + 1#"]
[]
[null,"    Do While ((Abs(d - x) > EPS) And (iter <= MAXITER))"]
[null,"        iter = iter + 1"]
[null,"        sx = Sin(x)"]
[null,"        cx = Cos(x)"]
[null,"        tu1 = cu2 * sx"]
[null,"        tu2 = b1 - su1 * cu2 * cx"]
[null,"        sy = Sqrt(tu1 * tu1 + tu2 * tu2)"]
[null,"        cy = s1 * cx + f1"]
[null,"        y = CRDDG * Artand(sy, cy)"]
[null,"        sa = s1 * sx / sy"]
[null,"        c2a = 1# - sa * sa"]
[null,"        cz = f1 + f1"]
[null,"        If (c2a > 0#) Then"]
[null,"            cz = cy - cz / c2a"]
[null,"        End If"]
[null,"        e = cz * cz * 2# - 1#"]
[null,"        c = ((-3# * c2a + 4#) * f + 4#) * c2a * f / 16#"]
[null,"        d = x"]
[null,"        x = ((e * cy * c + cz) * sy * c + y) * sa"]
[null,"        x = (1# - c) * x * f + glon2 - glon1"]
[null,"    Loop"]
[]
[null,"    x = Sqrt((1# / (r * r) - 1#) * c2a + 1#)"]
[null,"    x = (x - 1#) / (x + 1#)"]
[null,"    c = (x * x / 4# + 1#) / (1# - x)"]
[null,"    d = (0.375 * x * x - 1#) * x"]
[null,"    x = e * cy"]
[null,"    s = ((((sy * sy * 4# - 3#) * (1# - e - e) * cz * d / 6# - x) * d / 4# + cz) * sy * d + y) * c * a * r"]
[null,"    If flag Then"]
[null,"        s = 2# * s"]
[null,"    End If"]
[null,"    If (iter >= MAXITER) Then"]
[null,"        s = vbInf   '計算できなかった"]
[null,"    End If"]
[]
[null,"    GeoDes = s"]
[]
[null,"End Function"]

{"sheet":"お問合せ","index":3,"n_rows":125,"n_cols":5,"rows_kept":125,"cut":false,"hidden":false,"merged":[[3,2,3,6]]}
[]
[null,"技術的なご質問のみお受けします。"]
[]
[null,null,"sxsijk@Gmail.com","sxsijk@Gmail.com"]
[]
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