由於最近剛好准備用lua腳本去寫一個軟件，需要用到非常精確的節氣計算時間，壽星萬年歷是我在網上見到的一份極高高精度的萬年歷，其采用先進的算法實現，其精度堪比劉安國教授為中國科學院國家授時中心制作的日梭萬年歷。但網絡上只有javascript版本。於是自己將其翻譯為lua腳本程序，並公布於此，方便大家使用。
僅保留了節氣計算部分，省略了一些塑望月計算、陰歷計算的內容。
我之前的一篇文章：壽星萬年歷---java算法實現，是我用java實現的一個版本。
壽星萬年歷相關信息：http://www.fjptsz.com/xxjs/xjw/rj/113.htm 設計:許劍偉
日梭萬年歷相關信息：http://www.time.ac.cn/calendar/calendar.htm 作者：劉安國
關於壽星萬年歷相關簡要描述如下：
壽星萬年歷是一款采用現代天文算法制作的農歷歷算程序，含有公歷與回歷信息，可以很方便的進行公、農、回三歷之間的轉換。提供公元-4712年到公元9999年的日期查詢功能。其中1500年到1940農歷數據已經與陳垣的《二十史朔閏表》核對；含有從公420元(南北朝/宋武帝元年)到今的基本年號。在過去幾百年中，壽星萬年歷的誤差是非常小的，節氣時刻計算及日月合朔時刻的平均誤差小於1秒，太陽坐標的最大可能誤差為0.2角秒，月亮坐標的最大可能誤差為3角秒，平均誤差為誤差的1/6。萬年歷中含有幾百個國內城市的經緯度，並且用戶可根據自已的需要擴展經緯度數據。
以下是本人用lua實現的代碼：
--*******農歷節氣計算部分 --========角度變換=============== local rad = 180*3600/math.pi --每弧度的角秒數 local RAD = 180/math.pi --每弧度的角度數 function int2(v) --取整數部分 v=math.floor(v) if v<0 then return v+1 else return v end end function rad2mrad(v) --對超過0-2PI的角度轉為0-2PI v=math.fmod(v ,2*math.pi) if v<0 then return v+2*math.pi else return v end end function rad2str(d,tim) --將弧度轉為字串 ---tim=0輸出格式示例: -23°59' 48.23" ---tim=1輸出格式示例: 18h 29m 44.52s local s="+" local w1="°" w2="’" w3="”" if d<0 then d=-d s='-'end if tim~= 0 then d=d*12/math.pi w1="h " w2="m " w3="s " else d=d*180/math.pi end local a=math.floor(d) d=(d-a)*60 local b=math.floor(d) d=(d-b)*60 local c=math.floor(d) d=(d-c)*100 d=math.floor(d+0.5) if d>=100 then d=d-100 c=c+1 end if c>=60 then c=c-60 b=b+1 end if b>=60 then b=b-60 a=a+1 end a=" "+a b="0"+b c="0"+c d="0"+d local alen = string.len(a) local blen = string.len(b) local clen = string.len(c) local dlen = string.len(d) s = s .. string.sub(a, alen-3,alen)+w1 s = s .. string.sub(b, blen-2,blen)+w2 s = s .. string.sub(c, clen-2,clen)+"." s = s .. string.sub(d, dlen-2,dlen)+w3 return s end --================日歷計算=============== local J2000=2451545 --2000年前儒略日數(2000-1-1 12:00:00格林威治平時) local JDate={ --日期元件 Y=2000, M=1, D=1, h=12, m=0, s=0, dts = { --世界時與原子時之差計算表 -4000,108371.7,-13036.80,392.000, 0.0000, -500, 17201.0, -627.82, 16.170,-0.3413, -150, 12200.6, -346.41, 5.403,-0.1593, 150, 9113.8, -328.13, -1.647, 0.0377, 500, 5707.5, -391.41, 0.915, 0.3145, 900, 2203.4, -283.45, 13.034,-0.1778, 1300, 490.1, -57.35, 2.085,-0.0072, 1600, 120.0, -9.81, -1.532, 0.1403, 1700, 10.2, -0.91, 0.510,-0.0370, 1800, 13.4, -0.72, 0.202,-0.0193, 1830, 7.8, -1.81, 0.416,-0.0247, 1860, 8.3, -0.13, -0.406, 0.0292, 1880, -5.4, 0.32, -0.183, 0.0173, 1900, -2.3, 2.06, 0.169,-0.0135, 1920, 21.2, 1.69, -0.304, 0.0167, 1940, 24.2, 1.22, -0.064, 0.0031, 1960, 33.2, 0.51, 0.231,-0.0109, 1980, 51.0, 1.29, -0.026, 0.0032, 2000, 64.7, -1.66, 5.224,-0.2905, 2150, 279.4, 732.95,429.579, 0.0158, 6000}, deltatT = function(JDate, y) --計算世界時與原子時之差,傳入年 local i local d=JDate.dts for x=1,100, 5 do if y<d[x+5] or x==96 then i=x break end end local t1=(y-d[i])/(d[i+5]-d[i])*10 local t2=t1*t1 local t3=t2*t1 return d[i+1] +d[i+2]*t1 +d[i+3]*t2 +d[i+4]*t3 end, deltatT2 = function(JDate,jd) --傳入儒略日(J2000起算),計算UTC與原子時的差(單位:日) return JDate:deltatT(jd/365.2425+2000)/86400.0 end, toJD = function(JDate, UTC) --公歷轉儒略日,UTC=1表示原日期是UTC local y=JDate.Y m=JDate.M n=0 --取出年月 if m<=2 then m=m+12 y=y-1 end if JDate.Y*372+JDate.M*31+JDate.D>=588829 then --判斷是否為格里高利歷日1582*372+10*31+15 n =int2(y/100) n =2-n+int2(n/4)--加百年閏 end n = n + int2(365.2500001*(y+4716)) --加上年引起的偏移日數 n = n + int2(30.6*(m+1))+JDate.D --加上月引起的偏移日數及日偏移數 n = n + ((JDate.s/60+JDate.m)/60+JDate.h)/24 - 1524.5 if(UTC == 1) then return n+JDate.deltatT2(n-J2000) end return n end, setFromJD = function(JDate, jd,UTC) --儒略日數轉公歷,UTC=1表示目標公歷是UTC if UTC==1 then jd= jd - JDate:deltatT2(jd-J2000) end jd =jd+0.5 local A=int2(jd) F=jd-A, D --取得日數的整數部份A及小數部分F if A>2299161 then D=int2((A-1867216.25)/36524.25) A=A+1+D-int2(D/4) end A = A + 1524 --向前移4年零2個月 JDate.Y =int2((A-122.1)/365.25)--年 D =A-int2(365.25*JDate.Y) --去除整年日數后余下日數 JDate.M =int2(D/30.6001) --月數 JDate.D =D-int2(JDate.M*30.6001)--去除整月日數后余下日數 JDate.Y=JDate.Y-4716 JDate.M=JDate.M-1 if JDate.M>12 then JDate.M=JDate.M - 12 end if JDate.M<=2 then JDate.Y = JDate.Y+1 end --日的小數轉為時分秒 F=F*24 JDate.h=int2(F) F=F - JDate.h F=F*60 JDate.m=int2(F) F=F - JDate.m F=F*60 JDate.s=F end, setFromStr = function(JDate, s) --設置時間,參數例:"20000101 120000"或"20000101" JDate.Y=string.sub(s, 1,4) JDate.M=string.sub(s, 5, 6) JDate.D=string.sub(s,7, 8) JDate.h=string.sub(s, 10, 11) JDate.m=string.sub(s, 12,13) JDate.s=string.sub(s, 14,18) end, toStr = function(JDate) --日期轉為串 local Y=" " .. JDate.Y local M="0" .. JDate.M local D="0" .. JDate.D local h=JDate.h local m=JDate.m local s=math.floor(JDate.s+.5) if s>=60 then s=s-60 m=m+1 end if m>=60 then m=m-60 h=h+1 end h="0".. h m="0" .. m s="0" .. s local Ylen = string.len(Y) local Mlen = string.len(M) local Dlen = string.len(D) local hlen = string.len(h) local mlen = string.len(m) local slen = string.len(s) Y=string.sub(Y, Ylen -4,Ylen) M=string.sub(M, Mlen-1,Mlen) D=string.sub(D,Dlen-1, Dlen) h=string.sub(h, hlen-1, hlen) m=string.sub(m, mlen-1,mlen) s=string.sub(s, slen-1,slen) return Y .. "-" .. M .. "-" .. D .. " " .. h .. ":" .. m .. ":" .. s end, JQ = function(JDate) --輸出節氣日期的秒數 local t = {} t.year=JDate.Y t.month=JDate.M t.day=JDate.D t.hour=JDate.h t.min=JDate.m t.sec=math.floor(JDate.s+.5) if t.sec>=60 then t.sec=t.sec-60 t.min=t.min+1 end if t.min>=60 then t.min=t.min-60 t.hour=t.hour+1 end return os.time(t) end, Dint_dec = function(JDate, jd,shiqu,int_dec) --算出:jd轉到當地UTC后,UTC日數的整數部分或小數部分 --基於J2000力學時jd的起算點是12:00:00時,所以跳日時刻發生在12:00:00,這與日歷計算發生矛盾 --把jd改正為00:00:00起算,這樣儒略日的跳日動作就與日期的跳日同步 --改正方法為jd=jd+0.5-deltatT+shiqu/24 --把儒略日的起點移動-0.5(即前移12小時) --式中shiqu是時區,北京的起算點是-8小時,shiqu取8 local u=jd+0.5-JDate.deltatT2(jd)+shiqu/24 if int_dec~= 0 then return math.floor(u) --返回整數部分 else return u-math.floor(u) --返回小數部分 end end, d1_d2 = function(JDate, d1,d2) --計算兩個日期的相差的天數,輸入字串格式日期,如:"20080101" local Y=JDate.Y M=JDate.M D=JDate.D h=JDate.h m=JDate.m s=JDate.s --備份原來的數據 JDate.setFromStr(string.sub(d1,1,8)+" 120000") local jd1=JDate.toJD(0) JDate.setFromStr(string.sub(d2,1,8)+" 120000") local jd2=JDate.toJD(0) JDate.Y=Y JDate.M=M JDate.D=D JDate.h=h JDate.m=m JDate.s=s --還原 if jd1>jd2 then return math.floor(jd1-jd2+.0001) else return -Math.floor(jd2-jd1+.0001) end end, } --=========黃赤交角及黃赤坐標變換=========== local hcjjB = {84381.448, -46.8150, -0.00059, 0.001813}--黃赤交角系數表 local preceB= {0,50287.92262,111.24406,0.07699,-0.23479,-0.00178,0.00018,0.00001}--Date黃道上的歲差p function hcjj1 (t) --返回黃赤交角(常規精度),短期精度很高 local t1=t/36525 t2=t1*t1 t3=t2*t1 return (hcjjB[1] +hcjjB[2]*t1 +hcjjB[3]*t2 +hcjjB[4]*t3)/rad end function HCconv(JW,E) --黃赤轉換(黃赤坐標旋轉) --黃道赤道坐標變換,赤到黃E取負 local HJ=rad2mrad(JW[1]) HW=JW[2] local sinE =math.sin(E) cosE =math.cos(E) local sinW=cosE*math.sin(HW)+sinE*math.cos(HW)*math.sin(HJ) local J=math.atan2( math.sin(HJ)*cosE-math.tan(HW)*sinE, math.cos(HJ) ) JW[1]=rad2mrad(J) JW[2]=math.asin(sinW) end function addPrece(jd,zb) --補歲差 local i t=1 v=0 t1=jd/365250 for i=2,8 do t=t*t1 v=v+preceB[i]*t end zb[1]=rad2mrad(zb[1]+(v+2.9965*t1)/rad) end --===============光行差================== local GXC_e={0.016708634, -0.000042037,-0.0000001267} --離心率 local GXC_p={102.93735/RAD,1.71946/RAD, 0.00046/RAD} --近點 local GXC_l={280.4664567/RAD,36000.76982779/RAD,0.0003032028/RAD,1/49931000/RAD,-1/153000000/RAD} --太平黃經 local GXC_k=20.49552/rad --光行差常數 function addGxc(t,zb)--恆星周年光行差計算(黃道坐標中) local t1=t/36525 local t2=t1*t1 local t3=t2*t1 local t4=t3*t1 local L=GXC_l[1] +GXC_l[2]*t1 +GXC_l[3]*t2 +GXC_l[4]*t3 +GXC_l[5]*t4 local p=GXC_p[1] +GXC_p[2]*t1 +GXC_p[3]*t2 local e=GXC_e[1] +GXC_e[2]*t1 +GXC_e[3]*t2 local dL=L-zb[1] local dP=p-zb[1] zb[1]=zb[1] - (GXC_k * (math.cos(dL)-e*math.cos(dP)) / math.cos(zb[2])) zb[2]=zb[2] - (GXC_k * math.sin(zb[2]) * (math.sin(dL)-e*math.sin(dP))) --print('aa', L,p,e,dL,dP,zb[1], zb[2]) zb[1]=rad2mrad(zb[1]) end --===============章動計算================== local nutB={--章動表 2.1824391966, -33.757045954, 0.0000362262, 3.7340E-08,-2.8793E-10,-171996,-1742,92025, 89, 3.5069406862, 1256.663930738, 0.0000105845, 6.9813E-10,-2.2815E-10, -13187, -16, 5736,-31, 1.3375032491, 16799.418221925,-0.0000511866, 6.4626E-08,-5.3543E-10, -2274, -2, 977, -5, 4.3648783932, -67.514091907, 0.0000724525, 7.4681E-08,-5.7586E-10, 2062, 2, -895, 5, 0.0431251803, -628.301955171, 0.0000026820, 6.5935E-10, 5.5705E-11, -1426, 34, 54, -1, 2.3555557435, 8328.691425719, 0.0001545547, 2.5033E-07,-1.1863E-09, 712, 1, -7, 0, 3.4638155059, 1884.965885909, 0.0000079025, 3.8785E-11,-2.8386E-10, -517, 12, 224, -6, 5.4382493597, 16833.175267879,-0.0000874129, 2.7285E-08,-2.4750E-10, -386, -4, 200, 0, 3.6930589926, 25128.109647645, 0.0001033681, 3.1496E-07,-1.7218E-09, -301, 0, 129, -1, 3.5500658664, 628.361975567, 0.0000132664, 1.3575E-09,-1.7245E-10, 217, -5, -95, 3} function nutation(t) --計算黃經章動及交角章動 local d={} d.Lon=0 d.Obl=0 t=t/36525 local i,c local t1=t local t2=t1*t1 local t3=t2*t1 local t4=t3*t1 local t5=t4*t1 for i=1,#nutB,9 do c=nutB[i] +nutB[i+1]*t1 +nutB[i+2]*t2 +nutB[i+3]*t3 +nutB[i+4]*t4 d.Lon=d.Lon + (nutB[i+5]+nutB[i+6]*t/10)*math.sin(c) --黃經章動 d.Obl=d.Obl + (nutB[i+7]+nutB[i+8]*t/10)*math.cos(c) --交角章動 end d.Lon=d.Lon/(rad*10000) --黃經章動 d.Obl=d.Obl/(rad*10000) --交角章動 return d end function nutationRaDec(t,zb) --本函數計算赤經章動及赤緯章動 local Ra=zb[1] local Dec=zb[2] local E=hcjj1(t) local sinE=math.sin(E) local cosE=math.cos(E) --計算黃赤交角 local d=nutation(t) --計算黃經章動及交角章動 local cosRa=math.cos(Ra) local sinRa=math.sin(Ra) local tanDec=math.tan(Dec) zb[1]=zb[1] + (cosE+sinE*sinRa*tanDec)*d.Lon-cosRa*tanDec*d.Obl --赤經章動 zb[2]= zb[2] + sinE*cosRa*d.Lon+sinRa*d.Obl --赤緯章動 zb[1]=rad2mrad(zb[1]) end --=================以下是月球及地球運動參數表=================== --[[*************************************** * 如果用記事本查看此代碼,請在"格式"菜單中去除"自動換行" * E10是關於地球的,格式如下: * 它是一個數組,每3個數看作一條記錄,每條記錄的3個數記為A,B,C * rec=A*cos(B+C*t) 式中t是J2000起算的儒略千年數 * 每條記錄的計算結果(即rec)取和即得地球的日心黃經的周期量L0 * E11格式如下: rec = A*cos*(B+C*t) *t, 取和后得泊松量L1 * E12格式如下: rec = A*cos*(B+C*t) *t*t, 取和后得泊松量L2 * E13格式如下: rec = A*cos*(B+C*t) *t*t*t, 取和后得泊松量L3 * 最后地球的地心黃經:L = L0+L1+L2+L3+... * E20,E21,E22,E23...用於計算黃緯 * M10,M11等是關於月球的,參數的用法請閱讀Mnn()函數 ***************************************** --]] --地球運動VSOP87參數 local E10={ --黃經周期項 1.75347045673, 0.00000000000, 0.0000000000, 0.03341656456, 4.66925680417, 6283.0758499914, 0.00034894275, 4.62610241759, 12566.1516999828, 0.00003417571, 2.82886579606, 3.5231183490, 0.00003497056, 2.74411800971, 5753.3848848968, 0.00003135896, 3.62767041758, 77713.7714681205, 0.00002676218, 4.41808351397, 7860.4193924392, 0.00002342687, 6.13516237631, 3930.2096962196, 0.00001273166, 2.03709655772, 529.6909650946, 0.00001324292, 0.74246356352, 11506.7697697936, 0.00000901855, 2.04505443513, 26.2983197998, 0.00001199167, 1.10962944315, 1577.3435424478, 0.00000857223, 3.50849156957, 398.1490034082, 0.00000779786, 1.17882652114, 5223.6939198022, 0.00000990250, 5.23268129594, 5884.9268465832, 0.00000753141, 2.53339053818, 5507.5532386674, 0.00000505264, 4.58292563052, 18849.2275499742, 0.00000492379, 4.20506639861, 775.5226113240, 0.00000356655, 2.91954116867, 0.0673103028, 0.00000284125, 1.89869034186, 796.2980068164, 0.00000242810, 0.34481140906, 5486.7778431750, 0.00000317087, 5.84901952218, 11790.6290886588, 0.00000271039, 0.31488607649, 10977.0788046990, 0.00000206160, 4.80646606059, 2544.3144198834, 0.00000205385, 1.86947813692, 5573.1428014331, 0.00000202261, 2.45767795458, 6069.7767545534, 0.00000126184, 1.08302630210, 20.7753954924, 0.00000155516, 0.83306073807, 213.2990954380, 0.00000115132, 0.64544911683, 0.9803210682, 0.00000102851, 0.63599846727, 4694.0029547076, 0.00000101724, 4.26679821365, 7.1135470008, 0.00000099206, 6.20992940258, 2146.1654164752, 0.00000132212, 3.41118275555, 2942.4634232916, 0.00000097607, 0.68101272270, 155.4203994342, 0.00000085128, 1.29870743025, 6275.9623029906, 0.00000074651, 1.75508916159, 5088.6288397668, 0.00000101895, 0.97569221824, 15720.8387848784, 0.00000084711, 3.67080093025, 71430.6956181291, 0.00000073547, 4.67926565481, 801.8209311238, 0.00000073874, 3.50319443167, 3154.6870848956, 0.00000078756, 3.03698313141, 12036.4607348882, 0.00000079637, 1.80791330700, 17260.1546546904, 0.00000085803, 5.98322631256,161000.6857376741, 0.00000056963, 2.78430398043, 6286.5989683404, 0.00000061148, 1.81839811024, 7084.8967811152, 0.00000069627, 0.83297596966, 9437.7629348870, 0.00000056116, 4.38694880779, 14143.4952424306, 0.00000062449, 3.97763880587, 8827.3902698748, 0.00000051145, 0.28306864501, 5856.4776591154, 0.00000055577, 3.47006009062, 6279.5527316424, 0.00000041036, 5.36817351402, 8429.2412664666, 0.00000051605, 1.33282746983, 1748.0164130670, 0.00000051992, 0.18914945834, 12139.5535091068, 0.00000049000, 0.48735065033, 1194.4470102246, 0.00000039200, 6.16832995016, 10447.3878396044, 0.00000035566, 1.77597314691, 6812.7668150860, 0.00000036770, 6.04133859347, 10213.2855462110, 0.00000036596, 2.56955238628, 1059.3819301892, 0.00000033291, 0.59309499459, 17789.8456197850, 0.00000035954, 1.70876111898, 2352.8661537718} local E11={ --黃經泊松1項 6283.31966747491,0.00000000000, 0.0000000000, 0.00206058863, 2.67823455584, 6283.0758499914, 0.00004303430, 2.63512650414, 12566.1516999828, 0.00000425264, 1.59046980729, 3.5231183490, 0.00000108977, 2.96618001993, 1577.3435424478, 0.00000093478, 2.59212835365, 18849.2275499742, 0.00000119261, 5.79557487799, 26.2983197998, 0.00000072122, 1.13846158196, 529.6909650946, 0.00000067768, 1.87472304791, 398.1490034082, 0.00000067327, 4.40918235168, 5507.5532386674, 0.00000059027, 2.88797038460, 5223.6939198022, 0.00000055976, 2.17471680261, 155.4203994342, 0.00000045407, 0.39803079805, 796.2980068164, 0.00000036369, 0.46624739835, 775.5226113240, 0.00000028958, 2.64707383882, 7.1135470008, 0.00000019097, 1.84628332577, 5486.7778431750, 0.00000020844, 5.34138275149, 0.9803210682, 0.00000018508, 4.96855124577, 213.2990954380, 0.00000016233, 0.03216483047, 2544.3144198834, 0.00000017293, 2.99116864949, 6275.9623029906} local E12={ --黃經泊松2項 0.00052918870, 0.00000000000, 0.0000000000, 0.00008719837, 1.07209665242, 6283.0758499914, 0.00000309125, 0.86728818832, 12566.1516999828, 0.00000027339, 0.05297871691, 3.5231183490, 0.00000016334, 5.18826691036, 26.2983197998, 0.00000015752, 3.68457889430, 155.4203994342, 0.00000009541, 0.75742297675, 18849.2275499742, 0.00000008937, 2.05705419118, 77713.7714681205, 0.00000006952, 0.82673305410, 775.5226113240, 0.00000005064, 4.66284525271, 1577.3435424478} local E13={ 0.00000289226, 5.84384198723, 6283.0758499914, 0.00000034955, 0.00000000000, 0.0000000000, 0.00000016819, 5.48766912348, 12566.1516999828} local E14={ 0.00000114084, 3.14159265359, 0.0000000000, 0.00000007717, 4.13446589358, 6283.0758499914, 0.00000000765, 3.83803776214, 12566.1516999828} local E15={ 0.00000000878, 3.14159265359, 0.0000000000 } local E20={ --黃緯周期項 0.00000279620, 3.19870156017, 84334.6615813083, 0.00000101643, 5.42248619256, 5507.5532386674, 0.00000080445, 3.88013204458, 5223.6939198022, 0.00000043806, 3.70444689758, 2352.8661537718, 0.00000031933, 4.00026369781, 1577.3435424478, 0.00000022724, 3.98473831560, 1047.7473117547, 0.00000016392, 3.56456119782, 5856.4776591154, 0.00000018141, 4.98367470263, 6283.0758499914, 0.00000014443, 3.70275614914, 9437.7629348870, 0.00000014304, 3.41117857525, 10213.2855462110} local E21={ 0.00000009030, 3.89729061890, 5507.5532386674, 0.00000006177, 1.73038850355, 5223.6939198022} local E30={ --距離周期項 1.00013988799, 0.00000000000, 0.0000000000, 0.01670699626, 3.09846350771, 6283.0758499914, 0.00013956023, 3.05524609620, 12566.1516999828, 0.00003083720, 5.19846674381, 77713.7714681205, 0.00001628461, 1.17387749012, 5753.3848848968, 0.00001575568, 2.84685245825, 7860.4193924392, 0.00000924799, 5.45292234084, 11506.7697697936, 0.00000542444, 4.56409149777, 3930.2096962196} local E31={ 0.00103018608, 1.10748969588, 6283.0758499914, 0.00001721238, 1.06442301418, 12566.1516999828, 0.00000702215, 3.14159265359, 0.0000000000} local E32={ 0.00004359385, 5.78455133738, 6283.0758499914 } local E33={ 0.00000144595, 4.27319435148, 6283.0758499914 } --月球運動參數 local M10={ 22639.5858800, 2.3555545723, 8328.6914247251, 1.5231275E-04, 2.5041111E-07,-1.1863391E-09, 4586.4383203, 8.0413790709, 7214.0628654588,-2.1850087E-04,-1.8646419E-07, 8.7760973E-10, 2369.9139357, 10.3969336431, 15542.7542901840,-6.6188121E-05, 6.3946925E-08,-3.0872935E-10, 769.0257187, 4.7111091445, 16657.3828494503, 3.0462550E-04, 5.0082223E-07,-2.3726782E-09, -666.4175399, -0.0431256817, 628.3019552485,-2.6638815E-06, 6.1639211E-10,-5.4439728E-11, -411.5957339, 3.2558104895, 16866.9323152810,-1.2804259E-04,-9.8998954E-09, 4.0433461E-11, 211.6555524, 5.6858244986, -1114.6285592663,-3.7081362E-04,-4.3687530E-07, 2.0639488E-09, 205.4359530, 8.0845047526, 6585.7609102104,-2.1583699E-04,-1.8708058E-07, 9.3204945E-10, 191.9561973, 12.7524882154, 23871.4457149091, 8.6124629E-05, 3.1435804E-07,-1.4950684E-09, 164.7286185, 10.4400593249, 14914.4523349355,-6.3524240E-05, 6.3330532E-08,-2.5428962E-10, -147.3213842, -2.3986802540, -7700.3894694766,-1.5497663E-04,-2.4979472E-07, 1.1318993E-09, -124.9881185, 5.1984668216, 7771.3771450920,-3.3094061E-05, 3.1973462E-08,-1.5436468E-10, -109.3803637, 2.3124288905, 8956.9933799736, 1.4964887E-04, 2.5102751E-07,-1.2407788E-09, 55.1770578, 7.1411231536, -1324.1780250970, 6.1854469E-05, 7.3846820E-08,-3.4916281E-10, -45.0996092, 5.6113650618, 25195.6237400061, 2.4270161E-05, 2.4051122E-07,-1.1459056E-09, 39.5333010, -0.9002559173, -8538.2408905558, 2.8035534E-04, 2.6031101E-07,-1.2267725E-09, 38.4298346, 18.4383127140, 22756.8171556428,-2.8468899E-04,-1.2251727E-07, 5.6888037E-10, 36.1238141, 7.0666637168, 24986.0742741754, 4.5693825E-04, 7.5123334E-07,-3.5590172E-09, 30.7725751, 16.0827581417, 14428.1257309177,-4.3700174E-04,-3.7292838E-07, 1.7552195E-09, -28.3971008, 7.9982533891, 7842.3648207073,-2.2116475E-04,-1.8584780E-07, 8.2317000E-10, -24.3582283, 10.3538079614, 16171.0562454324,-6.8852003E-05, 6.4563317E-08,-3.6316908E-10, -18.5847068, 2.8429122493, -557.3142796331,-1.8540681E-04,-2.1843765E-07, 1.0319744E-09, 17.9544674, 5.1553411398, 8399.6791003405,-3.5757942E-05, 3.2589854E-08,-2.0880440E-10, 14.5302779, 12.7956138971, 23243.1437596606, 8.8788511E-05, 3.1374165E-07,-1.4406287E-09, 14.3796974, 15.1080427876, 32200.1371396342, 2.3843738E-04, 5.6476915E-07,-2.6814075E-09, 14.2514576,-24.0810366320, -2.3011998397, 1.5231275E-04, 2.5041111E-07,-1.1863391E-09, 13.8990596, 20.7938672862, 31085.5085803679,-1.3237624E-04, 1.2789385E-07,-6.1745870E-10, 13.1940636, 3.3302699264, -9443.3199839914,-5.2312637E-04,-6.8728642E-07, 3.2502879E-09, -9.6790568, -4.7542348263,-16029.0808942018,-3.0728938E-04,-5.0020584E-07, 2.3182384E-09, -9.3658635, 11.2971895604, 24080.9951807398,-3.4654346E-04,-1.9636409E-07, 9.1804319E-10, 8.6055318, 5.7289501804, -1742.9305145148,-3.6814974E-04,-4.3749170E-07, 2.1183885E-09, -8.4530982, 7.5540213938, 16100.0685698171, 1.1921869E-04, 2.8238458E-07,-1.3407038E-09, 8.0501724, 10.4831850066, 14286.1503796870,-6.0860358E-05, 6.2714140E-08,-1.9984990E-10, -7.6301553, 4.6679834628, 17285.6848046987, 3.0196162E-04, 5.0143862E-07,-2.4271179E-09, -7.4474952, -0.0862513635, 1256.6039104970,-5.3277630E-06, 1.2327842E-09,-1.0887946E-10, 7.3712011, 8.1276304344, 5957.4589549619,-2.1317311E-04,-1.8769697E-07, 9.8648918E-10, 7.0629900, 0.9591375719, 33.7570471374,-3.0829302E-05,-3.6967043E-08, 1.7385419E-10, -6.3831491, 9.4966777258, 7004.5133996281, 2.1416722E-04, 3.2425793E-07,-1.5355019E-09, -5.7416071, 13.6527441326, 32409.6866054649,-1.9423071E-04, 5.4047029E-08,-2.6829589E-10, 4.3740095, 18.4814383957, 22128.5152003943,-2.8202511E-04,-1.2313366E-07, 6.2332010E-10, -3.9976134, 7.9669196340, 33524.3151647312, 1.7658291E-04, 4.9092233E-07,-2.3322447E-09, -3.2096876, 13.2398458924, 14985.4400105508,-2.5159493E-04,-1.5449073E-07, 7.2324505E-10, -2.9145404, 12.7093625336, 24499.7476701576, 8.3460748E-05, 3.1497443E-07,-1.5495082E-09, 2.7318890, 16.1258838235, 13799.8237756692,-4.3433786E-04,-3.7354477E-07, 1.8096592E-09, -2.5679459, -2.4418059357, -7072.0875142282,-1.5764051E-04,-2.4917833E-07, 1.0774596E-09, -2.5211990, 7.9551277074, 8470.6667759558,-2.2382863E-04,-1.8523141E-07, 7.6873027E-10, 2.4888871, 5.6426988169, -486.3266040178,-3.7347750E-04,-4.3625891E-07, 2.0095091E-09, 2.1460741, 7.1842488353, -1952.4799803455, 6.4518350E-05, 7.3230428E-08,-2.9472308E-10, 1.9777270, 23.1494218585, 39414.2000050930, 1.9936508E-05, 3.7830496E-07,-1.8037978E-09, 1.9336825, 9.4222182890, 33314.7656989005, 6.0925100E-04, 1.0016445E-06,-4.7453563E-09, 1.8707647, 20.8369929680, 30457.2066251194,-1.2971236E-04, 1.2727746E-07,-5.6301898E-10, -1.7529659, 0.4873576771, -8886.0057043583,-3.3771956E-04,-4.6884877E-07, 2.2183135E-09, -1.4371624, 7.0979974718, -695.8760698485, 5.9190587E-05, 7.4463212E-08,-4.0360254E-10, -1.3725701, 1.4552986550, -209.5494658307, 4.3266809E-04, 5.1072212E-07,-2.4131116E-09, 1.2618162, 7.5108957121, 16728.3705250656, 1.1655481E-04, 2.8300097E-07,-1.3951435E-09 } local M11={ 1.6768000, -0.0431256817, 628.3019552485,-2.6638815E-06, 6.1639211E-10,-5.4439728E-11, 0.5164200, 11.2260974062, 6585.7609102104,-2.1583699E-04,-1.8708058E-07, 9.3204945E-10, 0.4138300, 13.5816519784, 14914.4523349355,-6.3524240E-05, 6.3330532E-08,-2.5428962E-10, 0.3711500, 5.5402729076, 7700.3894694766, 1.5497663E-04, 2.4979472E-07,-1.1318993E-09, 0.2756000, 2.3124288905, 8956.9933799736, 1.4964887E-04, 2.5102751E-07,-1.2407788E-09, 0.2459863,-25.6198212459, -2.3011998397, 1.5231275E-04, 2.5041111E-07,-1.1863391E-09, 0.0711800, 7.9982533891, 7842.3648207073,-2.2116475E-04,-1.8584780E-07, 8.2317000E-10, 0.0612800, 10.3538079614, 16171.0562454324,-6.8852003E-05, 6.4563317E-08,-3.6316908E-10 } local M12={ 0.0048700, -0.0431256817, 628.3019552485,-2.6638815E-06, 6.1639211E-10,-5.4439728E-11, 0.0022800,-27.1705318325, -2.3011998397, 1.5231275E-04, 2.5041111E-07,-1.1863391E-09, 0.0015000, 11.2260974062, 6585.7609102104,-2.1583699E-04,-1.8708058E-07, 9.3204945E-10 } local M20={ 18461.2400600, 1.6279052448, 8433.4661576405,-6.4021295E-05,-4.9499477E-09, 2.0216731E-11, 1010.1671484, 3.9834598170, 16762.1575823656, 8.8291456E-05, 2.4546117E-07,-1.1661223E-09, 999.6936555, 0.7276493275, -104.7747329154, 2.1633405E-04, 2.5536106E-07,-1.2065558E-09, 623.6524746, 8.7690283983, 7109.2881325435,-2.1668263E-06, 6.8896872E-08,-3.2894608E-10, 199.4837596, 9.6692843156, 15647.5290230993,-2.8252217E-04,-1.9141414E-07, 8.9782646E-10, 166.5741153, 6.4134738261, -1219.4032921817,-1.5447958E-04,-1.8151424E-07, 8.5739300E-10, 117.2606951, 12.0248388879, 23976.2204478244,-1.3020942E-04, 5.8996977E-08,-2.8851262E-10, 61.9119504, 6.3390143893, 25090.8490070907, 2.4060421E-04, 4.9587228E-07,-2.3524614E-09, 33.3572027, 11.1245829706, 15437.9795572686, 1.5014592E-04, 3.1930799E-07,-1.5152852E-09, 31.7596709, 3.0832038997, 8223.9166918098, 3.6864680E-04, 5.0577218E-07,-2.3928949E-09, 29.5766003, 8.8121540801, 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25300.3984729215,-1.9206388E-04,-1.4849843E-08, 6.0650192E-11, -5.6323538, -0.7707750092, 733.0766881638,-2.1899793E-04,-2.5474467E-07, 1.1521161E-09, -5.3683961, 6.8263720663, 16204.8433027325,-9.7115356E-05, 2.7023515E-08,-1.3414795E-10, -5.3112784, 3.9403341353, 17390.4595376141, 8.5627574E-05, 2.4607756E-07,-1.2205621E-09, -5.0759179, 0.6845236457, 523.5272223331, 2.1367016E-04, 2.5597745E-07,-1.2609955E-09, -4.8396143, -1.6710309265, -7805.1642023920, 6.1357413E-05, 5.5663398E-09,-7.4656459E-11, -4.8057401, 3.5705615768, -662.0890125485, 3.0927234E-05, 3.6923410E-08,-1.7458141E-10, 3.9840545, 8.6945689615, 33419.5404318159, 3.9291696E-04, 7.4628340E-07,-3.5388005E-09, 3.6744619, 19.1659620415, 22652.0424227274,-6.8354947E-05, 1.3284380E-07,-6.3767543E-10, 2.9984815, 20.0662179587, 31190.2833132833,-3.4871029E-04,-1.2746721E-07, 5.8909710E-10, 2.7986413, -2.5281611620,-16971.7070481963, 3.4437664E-04, 2.6526096E-07,-1.2469893E-09, 2.4138774, 17.7106633865, 22861.5918885581,-5.0102304E-04,-3.7787833E-07, 1.7754362E-09, 2.1863132, 5.5132179088, -9757.6441827375, 1.2587576E-04, 7.8796768E-08,-3.6937954E-10, 2.1461692, 13.4801375428, 23766.6709819937, 3.0245868E-04, 5.6971910E-07,-2.7016242E-09, 1.7659832, 11.1677086523, 14809.6776020201, 1.5280981E-04, 3.1869159E-07,-1.4608454E-09, -1.6244212, 7.3137297434, 7318.8375983742,-4.3483492E-04,-4.4182525E-07, 2.0841655E-09, 1.5813036, 5.4387584720, 16552.6081165349, 5.2095955E-04, 7.5618329E-07,-3.5792340E-09, 1.5197528, 16.7359480324, 40633.6032972747, 1.7441609E-04, 5.5981921E-07,-2.6611908E-09, 1.5156341, 1.7023646816,-17876.7861416319,-4.5910508E-04,-6.8233647E-07, 3.2300712E-09, 1.5102092, 5.4977296450, 8399.6847301375,-3.3094061E-05, 3.1973462E-08,-1.5436468E-10, -1.3178223, 9.6261586339, 16275.8309783478,-2.8518605E-04,-1.9079775E-07, 8.4338673E-10, -1.2642739, 11.9817132061, 24604.5224030729,-1.3287330E-04, 5.9613369E-08,-3.4295235E-10, 1.1918723, 22.4217725310, 39518.9747380084,-1.9639754E-04, 1.2294390E-07,-5.9724197E-10, 1.1346110, 14.4235191419, 31676.6099173011, 2.4767216E-05, 3.0879170E-07,-1.4204120E-09, 1.0857810, 8.8552797618, 5852.6842220465, 3.1609367E-06, 6.7664088E-08,-2.2006663E-10, -1.0193852, 7.2392703065, 33629.0898976466,-3.9751134E-05, 2.3556127E-07,-1.1256889E-09, -0.8227141, 11.0814572888, 16066.2815125171, 1.4748204E-04, 3.1992438E-07,-1.5697249E-09, 0.8042238, 3.5274358950, -33.7870573000, 2.8263353E-05, 3.7539802E-08,-2.2902113E-10, 0.8025939, 6.7832463846, 16833.1452579809,-9.9779237E-05, 2.7639907E-08,-1.8858767E-10, -0.7931866, -6.3821400710,-24462.5470518423,-2.4326809E-04,-4.9525589E-07, 2.2980217E-09, -0.7910153, 6.3703481443, -591.1013369332,-1.5714346E-04,-1.8089785E-07, 8.0295327E-10, -0.6674056, 9.1819266386, 24533.5347274576, 5.5197395E-05, 2.7743463E-07,-1.3204870E-09, 0.6502226, 4.1010449356,-10176.3966721553,-3.0412845E-04,-4.3254175E-07, 2.0981718E-09, -0.6388131, 6.2958887075, 25719.1509623392, 2.3794032E-04, 4.9648867E-07,-2.4069012E-09 } local M21={ 0.0743000, 11.9537467337, 6480.9861772950, 4.9705523E-07, 6.8280480E-08,-2.7450635E-10, 0.0304300, 8.7259027166, 7737.5900877920,-4.8307078E-06, 6.9513264E-08,-3.8338581E-10, 0.0222900, 12.8540026510, 15019.2270678508,-2.7985829E-04,-1.9203053E-07, 9.5226618E-10, 0.0199900, 15.2095572232, 23347.9184925760,-1.2754553E-04, 5.8380585E-08,-2.3407289E-10, 0.0186900, 9.5981921614, -1847.7052474301,-1.5181570E-04,-1.8213063E-07, 9.1183272E-10, 0.0169600, 7.1681781524, 16133.8556271171, 9.0955337E-05, 2.4484477E-07,-1.1116826E-09, 0.0162300, 1.5847795630, 9061.7681128890,-6.6685176E-05,-4.3335556E-09,-3.4222998E-11, 0.0141900, -0.7707750092, 733.0766881638,-2.1899793E-04,-2.5474467E-07, 1.1521161E-09 } local M30={ 385000.5290396, 1.5707963268, 0.0000000000, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00,-20905.3551378, 3.9263508990, 8328.6914247251, 1.5231275E-04, 2.5041111E-07,-1.1863391E-09,-3699.1109330, 9.6121753977, 7214.0628654588,-2.1850087E-04,-1.8646419E-07, 8.7760973E-10,-2955.9675626, 11.9677299699, 15542.7542901840,-6.6188121E-05, 6.3946925E-08,-3.0872935E-10, -569.9251264, 6.2819054713, 16657.3828494503, 3.0462550E-04, 5.0082223E-07,-2.3726782E-09, 246.1584797, 7.2566208254, -1114.6285592663,-3.7081362E-04,-4.3687530E-07, 2.0639488E-09, -204.5861179, 12.0108556517, 14914.4523349355,-6.3524240E-05, 6.3330532E-08,-2.5428962E-10, -170.7330791, 14.3232845422, 23871.4457149091, 8.6124629E-05, 3.1435804E-07,-1.4950684E-09, -152.1378118, 9.6553010794, 6585.7609102104,-2.1583699E-04,-1.8708058E-07, 9.3204945E-10, -129.6202242, -0.8278839272, -7700.3894694766,-1.5497663E-04,-2.4979472E-07, 1.1318993E-09, 108.7427014, 6.7692631483, 7771.3771450920,-3.3094061E-05, 3.1973462E-08,-1.5436468E-10, 104.7552944, 3.8832252173, 8956.9933799736, 1.4964887E-04, 2.5102751E-07,-1.2407788E-09, 79.6605685, 0.6705404095, -8538.2408905558, 2.8035534E-04, 2.6031101E-07,-1.2267725E-09, 48.8883284, 1.5276706450, 628.3019552485,-2.6638815E-06, 6.1639211E-10,-5.4439728E-11, -34.7825237, 20.0091090408, 22756.8171556428,-2.8468899E-04,-1.2251727E-07, 5.6888037E-10, 30.8238599, 11.9246042882, 16171.0562454324,-6.8852003E-05, 6.4563317E-08,-3.6316908E-10, 24.2084985, 9.5690497159, 7842.3648207073,-2.2116475E-04,-1.8584780E-07, 8.2317000E-10, -23.2104305, 8.6374600436, 24986.0742741754, 4.5693825E-04, 7.5123334E-07,-3.5590172E-09, -21.6363439, 17.6535544685, 14428.1257309177,-4.3700174E-04,-3.7292838E-07, 1.7552195E-09, -16.6747239, 6.7261374666, 8399.6791003405,-3.5757942E-05, 3.2589854E-08,-2.0880440E-10, 14.4026890, 4.9010662531, -9443.3199839914,-5.2312637E-04,-6.8728642E-07, 3.2502879E-09, -12.8314035, 14.3664102239, 23243.1437596606, 8.8788511E-05, 3.1374165E-07,-1.4406287E-09, -11.6499478, 22.3646636130, 31085.5085803679,-1.3237624E-04, 1.2789385E-07,-6.1745870E-10, -10.4447578, 16.6788391144, 32200.1371396342, 2.3843738E-04, 5.6476915E-07,-2.6814075E-09, 10.3211071, 8.7119194804, -1324.1780250970, 6.1854469E-05, 7.3846820E-08,-3.4916281E-10, 10.0562033, 7.2997465071, -1742.9305145148,-3.6814974E-04,-4.3749170E-07, 2.1183885E-09, -9.8844667, 12.0539813334, 14286.1503796870,-6.0860358E-05, 6.2714140E-08,-1.9984990E-10, 8.7515625, 6.3563649081, -9652.8694498221,-9.0458282E-05,-1.7656429E-07, 8.3717626E-10, -8.3791067, 4.4137085761, -557.3142796331,-1.8540681E-04,-2.1843765E-07, 1.0319744E-09, -7.0026961, -3.1834384995,-16029.0808942018,-3.0728938E-04,-5.0020584E-07, 2.3182384E-09, 6.3220032, 9.1248177206, 16100.0685698171, 1.1921869E-04, 2.8238458E-07,-1.3407038E-09, 5.7508579, 6.2387797896, 17285.6848046987, 3.0196162E-04, 5.0143862E-07,-2.4271179E-09, -4.9501349, 9.6984267611, 5957.4589549619,-2.1317311E-04,-1.8769697E-07, 9.8648918E-10, -4.4211770, 3.0260949818, -209.5494658307, 4.3266809E-04, 5.1072212E-07,-2.4131116E-09, 4.1311145, 11.0674740526, 7004.5133996281, 2.1416722E-04, 3.2425793E-07,-1.5355019E-09, -3.9579827, 20.0522347225, 22128.5152003943,-2.8202511E-04,-1.2313366E-07, 6.2332010E-10, 3.2582371, 14.8106422192, 14985.4400105508,-2.5159493E-04,-1.5449073E-07, 7.2324505E-10, -3.1483020, 4.8266068163, 16866.9323152810,-1.2804259E-04,-9.8998954E-09, 4.0433461E-11, 2.6164092, 14.2801588604, 24499.7476701576, 8.3460748E-05, 3.1497443E-07,-1.5495082E-09, 2.3536310, 9.5259240342, 8470.6667759558,-2.2382863E-04,-1.8523141E-07, 7.6873027E-10, -2.1171283, -0.8710096090, -7072.0875142282,-1.5764051E-04,-2.4917833E-07, 1.0774596E-09, -1.8970368, 17.6966801503, 13799.8237756692,-4.3433786E-04,-3.7354477E-07, 1.8096592E-09, -1.7385258, 2.0581540038, -8886.0057043583,-3.3771956E-04,-4.6884877E-07, 2.2183135E-09, -1.5713944, 22.4077892948, 30457.2066251194,-1.2971236E-04, 1.2727746E-07,-5.6301898E-10, -1.4225541, 24.7202181853, 39414.2000050930, 1.9936508E-05, 3.7830496E-07,-1.8037978E-09, -1.4189284, 17.1661967915, 23314.1314352759,-9.9282182E-05, 9.5920387E-08,-4.6309403E-10, 1.1655364, 3.8400995356, 9585.2953352221, 1.4698499E-04, 2.5164390E-07,-1.2952185E-09, -1.1169371, 10.9930146158, 33314.7656989005, 6.0925100E-04, 1.0016445E-06,-4.7453563E-09, 1.0656723, 1.4845449633, 1256.6039104970,-5.3277630E-06, 1.2327842E-09,-1.0887946E-10, 1.0586190, 11.9220903668, 8364.7398411275,-2.1850087E-04,-1.8646419E-07, 8.7760973E-10, -0.9333176, 9.0816920389, 16728.3705250656, 1.1655481E-04, 2.8300097E-07,-1.3951435E-09, 0.8624328, 12.4550876470, 6656.7485858257,-4.0390768E-04,-4.0490184E-07, 1.9095841E-09, 0.8512404, 4.3705828944, 70.9876756153,-1.8807069E-04,-2.1782126E-07, 9.7753467E-10, -0.8488018, 16.7219647962, 31571.8351843857, 2.4110126E-04, 5.6415276E-07,-2.6269678E-09, -0.7956264, 3.5134526588, -9095.5551701890, 9.4948529E-05, 4.1873358E-08,-1.9479814E-10 } local M31={ 0.5139500, 12.0108556517, 14914.4523349355,-6.3524240E-05, 6.3330532E-08,-2.5428962E-10, 0.3824500, 9.6553010794, 6585.7609102104,-2.1583699E-04,-1.8708058E-07, 9.3204945E-10, 0.3265400, 3.9694765808, 7700.3894694766, 1.5497663E-04, 2.4979472E-07,-1.1318993E-09, 0.2639600, 0.7416325637, 8956.9933799736, 1.4964887E-04, 2.5102751E-07,-1.2407788E-09, 0.1230200, -1.6139220085, 628.3019552485,-2.6638815E-06, 6.1639211E-10,-5.4439728E-11, 0.0775400, 8.7830116346, 16171.0562454324,-6.8852003E-05, 6.4563317E-08,-3.6316908E-10, 0.0606800, 6.4274570623, 7842.3648207073,-2.2116475E-04,-1.8584780E-07, 8.2317000E-10, 0.0497000, 12.0539813334, 14286.1503796870,-6.0860358E-05, 6.2714140E-08,-1.9984990E-10 } local M1n={3.81034392032, 8.39968473021E+03,-3.31919929753E-05, --月球平黃經系數 3.20170955005E-08,-1.53637455544E-10 } --==================日位置計算=================== local EnnT=0 --調用Enn前先設置EnnT時間變量 function Enn(F) --計算E10,E11,E20等,即:某一組周期項或泊松項算出,計算前先設置EnnT時間 local i local v=0 for i=1,#F,3 do v=v+F[i]*math.cos(F[i+1]+EnnT*F[i+2]) --print('Fsize=' .. #F, 'i=' .. i, 'v='..v, 'F[i]='..F[i], 'm='..math.cos(F[i+1]+EnnT*F[i+2])) end return v end function earCal(jd)--返回地球位置,日心Date黃道分點坐標 EnnT=jd/365250 --print('EnnT=' .. EnnT) local llr={} local t1=EnnT local t2=t1*t1 local t3=t2*t1 local t4=t3*t1 local t5=t4*t1 --print('t1='..t1, 't2='..t2, 't3='..t3, 't4='..t4, 't5='..t5) llr[1] =Enn(E10) +Enn(E11)*t1 +Enn(E12)*t2 +Enn(E13)*t3 +Enn(E14)*t4 +Enn(E15)*t5 --print('sppp') llr[2] =Enn(E20) +Enn(E21)*t1 --print('eppp') llr[3] =Enn(E30) +Enn(E31)*t1 +Enn(E32)*t2 +Enn(E33)*t3 llr[1]=rad2mrad(llr[1]) --print('llr[0]='..llr[1], 'llr[1]='..llr[2], 'llr[2]='..llr[3]) return llr end function sunCal2(jd) --傳回jd時刻太陽的地心視黃經及黃緯 local sun=earCal(jd) sun[1]=sun[1] + math.pi sun[2]=-sun[2] --計算太陽真位置 local d=nutation(jd) sun[1]=rad2mrad(sun[1]+d.Lon) --補章動 addGxc(jd,sun) --補周年黃經光行差 return sun --返回太陽視位置 end --==================月位置計算=================== local MnnT=0 --調用Mnn前先設置MnnT時間變量 function Mnn(F) --計算M10,M11,M20等,計算前先設置MnnT時間 local i local v=0 local t1=MnnT local t2=t1*t1 local t3=t2*t1 local t4=t3*t1 for i=1,#F,6 do v=v+F[i]*math.sin(F[i+1] +t1*F[i+2] +t2*F[i+3] +t3*F[i+4] +t4*F[i+5]) end return v end function moonCal(jd)--返回月球位置,返回地心Date黃道坐標 MnnT=jd/36525 local t1=MnnT local t2=t1*t1 local t3=t2*t1 local t4=t3*t1 local llr={} llr[1] =(Mnn(M10) +Mnn(M11)*t1 +Mnn(M12)*t2)/rad llr[2] =(Mnn(M20) +Mnn(M21)*t1)/rad llr[3] =(Mnn(M30) +Mnn(M31)*t1)*0.999999949827 llr[1] =llr[1] +M1n[1] +M1n[2]*t1 +M1n[3]*t2 +M1n[4]*t3 +M1n[5]*t4 llr[1] =rad2mrad(llr[1]) --地心Date黃道原點坐標(不含歲差) addPrece(jd,llr) --補歲差 return llr end function moonCal2(jd) --傳回月球的地心視黃經及視黃緯 local moon=moonCal(jd) local d=nutation(jd) moon[1]=rad2mrad(moon[1]+d.Lon) --補章動 return moon end function moonCal3(jd) --傳回月球的地心視赤經及視赤緯 local moon=moonCal(jd) HCconv(moon,hcjj1(jd)) nutationRaDec(jd,moon) --補赤經及赤緯章動 --如果黃赤轉換前補了黃經章動及交章動,就不能再補赤經赤緯章動 return moon end --==================地心坐標中的日月位置計算=================== function jiaoCai(lx,t,jiao) --lx=1時計算t時刻日月角距與jiao的差, lx=0計算t時刻太陽黃經與jiao的差 local sun=earCal(t) --計算太陽真位置(先算出日心坐標中地球的位置) sun[1]=sun[1] + math.pi sun[2]=-sun[2] --轉為地心坐標 addGxc(t,sun) --補周年光行差 --print('sun[1]=' .. sun[1], 'sun[2]=' .. sun[2]) if lx==0 then local d=nutation(t) sun[1]=sun[1] + d.Lon --補黃經章動 return rad2mrad(jiao-sun[1]) end local moon=moonCal(t) --日月角差與章動無關 return rad2mrad(jiao-(moon[1]-sun[1])) end --==================已知位置反求時間=================== function jiaoCal(t1,jiao,lx) --t1是J2000起算儒略日數 --已知角度(jiao)求時間(t) --lx=0是太陽黃經達某角度的時刻計算(用於節氣計算) --lx=1是日月角距達某角度的時刻計算(用於定朔望等) --傳入的t1是指定角度對應真時刻t的前一些天 --對於節氣計算,應滿足t在t1到t1+360天之間,對於Y年第n個節氣(n=0是春分),t1可取值Y*365.2422+n*15.2 --對於朔望計算,應滿足t在t1到t1+25天之間,在此范圍之外,求右邊的根 local t2=t1 local t=0 local v if lx==0 then t2=t2+360 --在t1到t2范圍內求解(范氣360天范圍),結果置於t else t2=t2+25 end jiao=jiao*math.pi/180 --待搜索目標角 --利用截弦法計算 --print('lx=' .. lx .. ', t1=' .. t1 .. ', t2=' .. t2 .. ', jiao=' .. jiao) local v1=jiaoCai(lx,t1,jiao) --v1,v2為t1,t2時對應的黃經 local v2=jiaoCai(lx,t2,jiao) --print('v1=' .. v1 .. ', v2=' ..v2) if v1<v2 then v2=v2 - 2*math.pi end --減2pi作用是將周期性角度轉為連續角度 local k=1,k2,i --k是截弦的斜率 for i=1,10 do --快速截弦求根,通常截弦三四次就已達所需精度 k2=(v2-v1)/(t2-t1) --算出斜率 if math.abs(k2)>1e-15 then k=k2 end --差商可能為零,應排除 t=t1-v1/k v=jiaoCai(lx,t,jiao)--直線逼近法求根(直線方程的根) if v>1 then v=v-2*math.pi end --一次逼近后,v1就已接近0,如果很大,則應減1周 if math.abs(v)<1e-8 then break end --已達精度 t1=t2 v1=v2 t2=t v2=v --下一次截弦 end return t end --==================節氣計算=================== local jqB={ --節氣表 "春分","清明","谷雨","立夏","小滿","芒種","夏至","小暑","大暑","立秋","處暑","白露", "秋分","寒露","霜降","立冬","小雪","大雪","冬至","小寒","大寒","立春","雨水","驚蟄"} function JQtest(y) --節氣使計算范例,y是年分,這是個測試函數 local i local jd=365.2422*(y-2000) local q,s1,s2 print("節氣:世界時 原子時") for i=0,23 do q=jiaoCal(jd+i*15.2,i*15,0)+J2000+8/24 --計算第i個節氣(i=0是春風),結果轉為北京時 print('q=' .. q) JDate:setFromJD(q,1) s1=JDate:toStr() --將儒略日轉成世界時 JDate:setFromJD(q,0) s2=JDate:toStr() --將儒略日轉成日期格式(輸出日期形式的力學時) print(jqB[i+1] .. " : " .. s1 .. " " .. s2 ) --顯示 end end function getJQ(y) --返回一年中各個節氣的時間表，從春分開始 local i local jd=365.2422*(y-2000) local q local jq = {} for i=0,23 do q=jiaoCal(jd+i*15.2,i*15,0)+J2000+8/24 --計算第i個節氣(i=0是春風),結果轉為北京時 JDate:setFromJD(q,1) jq[i+1] = JDate:JQ() --將儒略日轉成世界時 end return jq end --返回一年的二十四個節氣,從立春開始 function getYearJQ(y) local jq1 = getJQ(y-1) --上一年 local jq2 = getJQ(y) -- 當年 local jq = {} for i=1,3 do jq[i] = jq1[i+21] end for i=1,21 do jq[i+3] = jq2[i] end return jq end --=================定朔弦望計算======================== function dingSuo(y,arc) --這是個測試函數 local i,jd=365.2422*(y-2000),q,s1,s2 print("月份:世界時 原子時<br>") for i=0,11 do q=jiaoCal(jd+29.5*i,arc,1)+J2000+8/24 --計算第i個節氣(i=0是春風),結果轉為北京時 JDate.setFromJD(q,1) s1=JDate:toStr() --將儒略日轉成世界時 JDate.setFromJD(q,0) s2=JDate:toStr() --將儒略日轉成日期格式(輸出日期形式的力學時) print((i+1) .. "月 : ".. s1 .. " " .. s2 ) --顯示 end end --=================農歷計算======================== --[[***** 1.冬至所在的UTC日期保存在A[0],根據"規定1"得知在A[0]之前(含A[0])的那個UTC朔日定為年首日期 冬至之后的中氣分保存在A[1],A[2],A[3]...A[13],其中A[12]又回到了冬至,共計算13次中氣 2.連續計算冬至后14個朔日,即起算時間時A[0]+1 14個朔日編號為0,1...12,保存在C[0],C[1]...C[13] 這14個朔日表示編號為0月,1月,...12月0月的各月終止日期,但要注意實際終止日是新月初一,不屬本月 這14個朔日同樣表示編號為1月,2月...的開始日期 設某月編號為n,那么開始日期為C[n-1],結束日期為C[n],如果每月都含中氣,該月所含的中氣為A[n] 注:為了全總計算出13個月的大小月情況,須算出14個朔日。 3.閏年判斷:含有13個月的年份是閏年 當第13月(月編號12月)終止日期大於冬至日, 即C[12]〉A[12], 那么該月是新年,本年沒月12月,本年共12個月 當第13月(月編號12月)終止日期小等於冬至日,即C[12]≤A[12],那么該月是本年的有效月份,本年共13個月 4.閏年中處理閏月: 13個月中至少1個月份無中氣,首個無中氣的月置閏,在n=1...12月中找到閏月,即C[n]≤A[n] 從農歷年首的定義知道,0月一定含有中氣冬至,所以不可能是閏月。 首月有時很貪心,除冬至外還可能再吃掉本年或前年的另一個中氣 定出閏月后,該月及以后的月編號減1 5.以上所述的月編號不是日常生活中說的"正月","二月"等月名稱: 如果"建子",0月為首月,如果"建寅",2月的月名"正月",3月是"二月",其余類推 *****--]] --local yueMing={"正","二","三","四","五","六","七","八","九","十","冬","臘"} -- --function paiYue(inYear) --農歷排月序計算,可定出農歷 -- --y=in1.value-0 -- local y = inYear-0 -- local zq={},jq={}, hs={} --中氣表,節氣表,日月合朔表 -- -- --從冬至開始,連續計算14個中氣時刻 -- local i,t1=365.2422*(y-2000)-50 --農歷年首始於前一年的冬至,為了節氣中氣一起算,取前年大雪之前 -- for i=0,13 do --計算節氣(從冬至開始),注意:返回的是力學時 -- zq[i+1]=jiaoCal(t1+i*30.4,i*30-90, 0) --中氣計算,冬至的太陽黃經是270度(或-90度) -- jq[i+1]=jiaoCal(t1+i*30.4,i*30-105,0) --順便計算節氣,它不是農歷定朔計算所必需的 --end --... --end JQtest(2000) --測試函數