寿星万年历Lua实现

    由于最近刚好准备用lua脚本去写一个软件，需要用到非常精确的节气计算时间，寿星万年历是我在网上见到的一份极高高精度的万年历，其采用先进的算法实现，其精度堪比刘安国教授为中国科学院国家授时中心制作的日梭万年历。但网络上只有javascript版本。于是自己将其翻译为lua脚本程序，并公布于此，方便大家使用。

    仅保留了节气计算部分，省略了一些塑望月计算、阴历计算的内容。

    我之前的一篇文章：寿星万年历---java算法实现，是我用java实现的一个版本。

    寿星万年历相关信息：http://www.fjptsz.com/xxjs/xjw/rj/113.htm  设计:许剑伟

    日梭万年历相关信息：http://www.time.ac.cn/calendar/calendar.htm 作者：刘安国

 关于寿星万年历相关简要描述如下：

寿星万年历是一款采用现代天文算法制作的农历历算程序，含有公历与回历信息，可以很方便的进行公、农、回三历之间的转换。提供公元-4712年到公元9999年的日期查询功能。其中1500年到1940农历数据已经与陈垣的《二十史朔闰表》核对；含有从公420元(南北朝/宋武帝元年)到今的基本年号。在过去几百年中，寿星万年历的误差是非常小的，节气时刻计算及日月合朔时刻的平均误差小于1秒，太阳坐标的最大可能误差为0.2角秒，月亮坐标的最大可能误差为3角秒，平均误差为误差的1/6。万年历中含有几百个国内城市的经纬度，并且用户可根据自已的需要扩展经纬度数据。

以下是本人用lua实现的代码：

--*******农历节气计算部分
--========角度变换===============
local rad = 180*3600/math.pi --每弧度的角秒数
local RAD = 180/math.pi      --每弧度的角度数
function int2(v) --取整数部分
    v=math.floor(v)
    if v<0 then return v+1
    else return v
    end
end

function rad2mrad(v)   --对超过0-2PI的角度转为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) --将弧度转为字串
    ---tim=0输出格式示例: -23°59' 48.23"
    ---tim=1输出格式示例:  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
--================日历计算===============
local J2000=2451545 --2000年前儒略日数(2000-1-1 12:00:00格林威治平时)

local JDate={ --日期元件
Y=2000, M=1, D=1, h=12, m=0, s=0,
dts = { --世界时与原子时之差计算表
-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) --计算世界时与原子时之差,传入年
    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) --传入儒略日(J2000起算),计算UTC与原子时的差(单位:日)
    return JDate:deltatT(jd/365.2425+2000)/86400.0
end,
toJD = function(JDate, UTC) --公历转儒略日,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 --判断是否为格里高利历日1582*372+10*31+15
        n =int2(y/100) n =2-n+int2(n/4)--加百年闰
    end
    n = n + int2(365.2500001*(y+4716))    --加上年引起的偏移日数
    n = n + int2(30.6*(m+1))+JDate.D       --加上月引起的偏移日数及日偏移数
    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) --儒略日数转公历,UTC=1表示目标公历是UTC
    if UTC==1 then  jd= jd - JDate:deltatT2(jd-J2000) end
    jd =jd+0.5
    local A=int2(jd) F=jd-A, D  --取得日数的整数部份A及小数部分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个月
    JDate.Y =int2((A-122.1)/365.25)--年
    D =A-int2(365.25*JDate.Y) --去除整年日数后余下日数
    JDate.M =int2(D/30.6001)       --月数
    JDate.D =D-int2(JDate.M*30.6001)--去除整月日数后余下日数
    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
    --日的小数转为时分秒
    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) --设置时间,参数例:"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) --日期转为串
    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) --输出节气日期的秒数
    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转到当地UTC后,UTC日数的整数部分或小数部分
    --基于J2000力学时jd的起算点是12:00:00时,所以跳日时刻发生在12:00:00,这与日历计算发生矛盾
    --把jd改正为00:00:00起算,这样儒略日的跳日动作就与日期的跳日同步
    --改正方法为jd=jd+0.5-deltatT+shiqu/24
    --把儒略日的起点移动-0.5(即前移12小时)
    --式中shiqu是时区,北京的起算点是-8小时,shiqu取8
    local u=jd+0.5-JDate.deltatT2(jd)+shiqu/24
    if int_dec~= 0 then  return math.floor(u) --返回整数部分
    else return u-math.floor(u)      --返回小数部分
    end
end,

d1_d2 = function(JDate, d1,d2) --计算两个日期的相差的天数,输入字串格式日期,如:"20080101"
    local Y=JDate.Y M=JDate.M D=JDate.D h=JDate.h m=JDate.m s=JDate.s --备份原来的数据
    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 --还原
    if jd1>jd2 then  return  math.floor(jd1-jd2+.0001)
    else        return -Math.floor(jd2-jd1+.0001)
    end
end,
}
--=========黄赤交角及黄赤坐标变换===========
local hcjjB = {84381.448, -46.8150, -0.00059, 0.001813}--黄赤交角系数表
local preceB= {0,50287.92262,111.24406,0.07699,-0.23479,-0.00178,0.00018,0.00001}--Date黄道上的岁差p

function hcjj1 (t) --返回黄赤交角(常规精度),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) --黄赤转换(黄赤坐标旋转)
    --黄道赤道坐标变换,赤到黄E取负
    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) --补岁差
    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} --离心率
local GXC_p={102.93735/RAD,1.71946/RAD, 0.00046/RAD}  --近点
local GXC_l={280.4664567/RAD,36000.76982779/RAD,0.0003032028/RAD,1/49931000/RAD,-1/153000000/RAD} --太平黄经
local GXC_k=20.49552/rad --光行差常数
function addGxc(t,zb)--恒星周年光行差计算(黄道坐标中)
    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

--===============章动计算==================
local nutB={--章动表
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) --计算黄经章动及交角章动
    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) --黄经章动
        d.Obl=d.Obl + (nutB[i+7]+nutB[i+8]*t/10)*math.cos(c) --交角章动
    end
    d.Lon=d.Lon/(rad*10000) --黄经章动
    d.Obl=d.Obl/(rad*10000) --交角章动
    return d
end

function nutationRaDec(t,zb) --本函数计算赤经章动及赤纬章动
    local Ra=zb[1]
    local Dec=zb[2]
    local E=hcjj1(t)
    local sinE=math.sin(E)
    local cosE=math.cos(E) --计算黄赤交角
    local d=nutation(t)                                  --计算黄经章动及交角章动
    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 --赤经章动
    zb[2]= zb[2] + sinE*cosRa*d.Lon+sinRa*d.Obl   --赤纬章动
    zb[1]=rad2mrad(zb[1])
end

--=================以下是月球及地球运动参数表===================
--[[***************************************
* 如果用记事本查看此代码,请在"格式"菜单中去除"自动换行"
* E10是关于地球的,格式如下:
*    它是一个数组,每3个数看作一条记录,每条记录的3个数记为A,B,C
*    rec=A*cos(B+C*t)  式中t是J2000起算的儒略千年数
*    每条记录的计算结果(即rec)取和即得地球的日心黄经的周期量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
* 最后地球的地心黄经:L = L0+L1+L2+L3+...
* E20,E21,E22,E23...用于计算黄纬
* M10,M11等是关于月球的,参数的用法请阅读Mnn()函数
***************************************** --]]
--地球运动VSOP87参数
local E10={ --黄经周期项
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={ --黄经泊松1项
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={ --黄经泊松2项
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={ --黄纬周期项
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={ --距离周期项
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 }
--月球运动参数
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,  6480.9861772950, 4.9705523E-07, 6.8280480E-08,-2.7450635E-10,   15.5662654,  4.0579192538, -9548.0947169068,-3.0679233E-04,-4.3192536E-07, 2.0437321E-09,
    15.1215543, 14.3803934601, 32304.9118725496, 2.2103334E-05, 3.0940809E-07,-1.4748517E-09,  -12.0941511,  8.7259027166,  7737.5900877920,-4.8307078E-06, 6.9513264E-08,-3.8338581E-10,    8.8681426,  9.7124099974, 15019.2270678508,-2.7985829E-04,-1.9203053E-07, 9.5226618E-10,    8.0450400,  0.6687636586,  8399.7091105030,-3.3191993E-05, 3.2017096E-08,-1.5363746E-10,
    7.9585542, 12.0679645696, 23347.9184925760,-1.2754553E-04, 5.8380585E-08,-2.3407289E-10,    7.4345550,  6.4565995078, -1847.7052474301,-1.5181570E-04,-1.8213063E-07, 9.1183272E-10,   -6.7314363, -4.0265854988,-16133.8556271171,-9.0955337E-05,-2.4484477E-07, 1.1116826E-09,    6.5795750, 16.8104074692, 14323.3509980023,-2.2066770E-04,-1.1756732E-07, 5.4866364E-10,
    -6.4600721,  1.5847795630,  9061.7681128890,-6.6685176E-05,-4.3335556E-09,-3.4222998E-11,   -6.2964773,  4.8837157343, 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, --月球平黄经系数
3.20170955005E-08,-1.53637455544E-10 }

--==================日位置计算===================
local EnnT=0 --调用Enn前先设置EnnT时间变量
function Enn(F) --计算E10,E11,E20等,即:某一组周期项或泊松项算出,计算前先设置EnnT时间
    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黄道分点坐标
    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) --传回jd时刻太阳的地心视黄经及黄纬
    local sun=earCal(jd)  sun[1]=sun[1] + math.pi sun[2]=-sun[2] --计算太阳真位置
    local d=nutation(jd)  sun[1]=rad2mrad(sun[1]+d.Lon)   --补章动
    addGxc(jd,sun)  --补周年黄经光行差
    return sun      --返回太阳视位置
end

--==================月位置计算===================
local MnnT=0 --调用Mnn前先设置MnnT时间变量
function Mnn(F) --计算M10,M11,M20等,计算前先设置MnnT时间
    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黄道坐标
    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黄道原点坐标(不含岁差)
    addPrece(jd,llr) --补岁差
    return llr
end

function moonCal2(jd) --传回月球的地心视黄经及视黄纬
    local moon=moonCal(jd)
    local d=nutation(jd)
    moon[1]=rad2mrad(moon[1]+d.Lon) --补章动
    return moon
end

function moonCal3(jd) --传回月球的地心视赤经及视赤纬
    local moon=moonCal(jd)
    HCconv(moon,hcjj1(jd))
    nutationRaDec(jd,moon) --补赤经及赤纬章动
    --如果黄赤转换前补了黄经章动及交章动,就不能再补赤经赤纬章动
    return moon
end

--==================地心坐标中的日月位置计算===================
function jiaoCai(lx,t,jiao)
    --lx=1时计算t时刻日月角距与jiao的差, lx=0计算t时刻太阳黄经与jiao的差
    local sun=earCal(t)  --计算太阳真位置(先算出日心坐标中地球的位置)
    sun[1]=sun[1] + math.pi sun[2]=-sun[2] --转为地心坐标
    addGxc(t,sun)      --补周年光行差
    --print('sun[1]=' .. sun[1], 'sun[2]=' .. sun[2])
    if lx==0 then
        local d=nutation(t)
        sun[1]=sun[1] + d.Lon --补黄经章动
        return rad2mrad(jiao-sun[1])
    end
    local moon=moonCal(t) --日月角差与章动无关
    return rad2mrad(jiao-(moon[1]-sun[1]))
end

--==================已知位置反求时间===================
function jiaoCal(t1,jiao,lx) --t1是J2000起算儒略日数
    --已知角度(jiao)求时间(t)
    --lx=0是太阳黄经达某角度的时刻计算(用于节气计算)
    --lx=1是日月角距达某角度的时刻计算(用于定朔望等)
    --传入的t1是指定角度对应真时刻t的前一些天
    --对于节气计算,应满足t在t1到t1+360天之间,对于Y年第n个节气(n=0是春分),t1可取值Y*365.2422+n*15.2
    --对于朔望计算,应满足t在t1到t1+25天之间,在此范围之外,求右边的根
    local t2=t1
    local t=0
    local v
    if lx==0 then  t2=t2+360  --在t1到t2范围内求解(范气360天范围),结果置于t
    else t2=t2+25
    end
    jiao=jiao*math.pi/180  --待搜索目标角
    --利用截弦法计算
    --print('lx=' .. lx .. ', t1=' .. t1 .. ', t2=' .. t2 .. ', jiao=' .. jiao)
    local v1=jiaoCai(lx,t1,jiao)           --v1,v2为t1,t2时对应的黄经
    local v2=jiaoCai(lx,t2,jiao)
    --print('v1=' .. v1 .. ', v2=' ..v2)
    if v1<v2 then v2=v2 - 2*math.pi end  --减2pi作用是将周期性角度转为连续角度
    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达所需精度
        k2=(v2-v1)/(t2-t1)    --算出斜率
        if math.abs(k2)>1e-15 then k=k2  end   --差商可能为零,应排除
        t=t1-v1/k  v=jiaoCai(lx,t,jiao)--直线逼近法求根(直线方程的根)
        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,则应减1周
        if math.abs(v)<1e-8 then  break  end     --已达精度
        t1=t2 v1=v2 t2=t v2=v          --下一次截弦
    end
    return t
end

--==================节气计算===================
local jqB={ --节气表
"春分","清明","谷雨","立夏","小满","芒种","夏至","小暑","大暑","立秋","处暑","白露",
"秋分","寒露","霜降","立冬","小雪","大雪","冬至","小寒","大寒","立春","雨水","惊蛰"}

function JQtest(y) --节气使计算范例,y是年分,这是个测试函数
    local i
    local jd=365.2422*(y-2000)
    local q,s1,s2
    print("节气:世界时  原子时")
    for i=0,23 do
        q=jiaoCal(jd+i*15.2,i*15,0)+J2000+8/24  --计算第i个节气(i=0是春风),结果转为北京时
        print('q=' .. q)
        JDate:setFromJD(q,1)  s1=JDate:toStr()  --将儒略日转成世界时
        JDate:setFromJD(q,0)  s2=JDate:toStr()  --将儒略日转成日期格式(输出日期形式的力学时)
        print(jqB[i+1] .. " : " .. s1 .. " " .. s2 ) --显示
    end
end

function getJQ(y) --返回一年中各个节气的时间表，从春分开始
    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  --计算第i个节气(i=0是春风),结果转为北京时
        JDate:setFromJD(q,1)  jq[i+1] = JDate:JQ()  --将儒略日转成世界时
    end
    return jq
end

--返回一年的二十四个节气,从立春开始
function getYearJQ(y)
    local jq1 = getJQ(y-1) --上一年
    local jq2 = getJQ(y) -- 当年
    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


--=================定朔弦望计算========================
function dingSuo(y,arc) --这是个测试函数
    local i,jd=365.2422*(y-2000),q,s1,s2
    print("月份:世界时  原子时<br>")
    for i=0,11 do
        q=jiaoCal(jd+29.5*i,arc,1)+J2000+8/24    --计算第i个节气(i=0是春风),结果转为北京时
        JDate.setFromJD(q,1)  s1=JDate:toStr()  --将儒略日转成世界时
        JDate.setFromJD(q,0)  s2=JDate:toStr()  --将儒略日转成日期格式(输出日期形式的力学时)
        print((i+1) .. "月 : ".. s1 .. " " .. s2 ) --显示
    end
end

--=================农历计算========================
--[[*****
1.冬至所在的UTC日期保存在A[0],根据"规定1"得知在A[0]之前(含A[0])的那个UTC朔日定为年首日期
冬至之后的中气分保存在A[1],A[2],A[3]...A[13],其中A[12]又回到了冬至,共计算13次中气
2.连续计算冬至后14个朔日,即起算时间时A[0]+1
14个朔日编号为0,1...12,保存在C[0],C[1]...C[13]
这14个朔日表示编号为0月,1月,...12月0月的各月终止日期,但要注意实际终止日是新月初一,不属本月
这14个朔日同样表示编号为1月,2月...的开始日期
设某月编号为n,那么开始日期为C[n-1],结束日期为C[n],如果每月都含中气,该月所含的中气为A[n]
注:为了全总计算出13个月的大小月情况,须算出14个朔日。
3.闰年判断:含有13个月的年份是闰年
当第13月(月编号12月)终止日期大于冬至日,  即C[12]〉A[12], 那么该月是新年,本年没月12月,本年共12个月
当第13月(月编号12月)终止日期小等于冬至日,即C[12]≤A[12],那么该月是本年的有效月份,本年共13个月
4.闰年中处理闰月:
13个月中至少1个月份无中气,首个无中气的月置闰,在n=1...12月中找到闰月,即C[n]≤A[n]
从农历年首的定义知道,0月一定含有中气冬至,所以不可能是闰月。
首月有时很贪心,除冬至外还可能再吃掉本年或前年的另一个中气
定出闰月后,该月及以后的月编号减1
5.以上所述的月编号不是日常生活中说的"正月","二月"等月名称:
如果"建子",0月为首月,如果"建寅",2月的月名"正月",3月是"二月",其余类推
*****--]]


--local yueMing={"正","二","三","四","五","六","七","八","九","十","冬","腊"}
--
--function paiYue(inYear) --农历排月序计算,可定出农历
--  --y=in1.value-0
--  local y = inYear-0
--  local zq={},jq={}, hs={}  --中气表,节气表,日月合朔表
--
--  --从冬至开始,连续计算14个中气时刻
--  local i,t1=365.2422*(y-2000)-50 --农历年首始于前一年的冬至,为了节气中气一起算,取前年大雪之前
--  for i=0,13 do   --计算节气(从冬至开始),注意:返回的是力学时
--    zq[i+1]=jiaoCal(t1+i*30.4,i*30-90, 0) --中气计算,冬至的太阳黄经是270度(或-90度)
--    jq[i+1]=jiaoCal(t1+i*30.4,i*30-105,0) --顺便计算节气,它不是农历定朔计算所必需的
--end
--...
--end

JQtest(2000) --测试函数