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  发帖心情 Post By:2008/5/29 22:09:00

第8贴算法测试程序——地球、太阳

这是精简的超高速的算法

<script language=javascript>
rad = 180*3600/Math.PI;
function rad2mrad(v){   //对超过0-2PI的角度转为0-2PI
  v=v % (2*Math.PI);
  if(v<0) return v+2*Math.PI;
  return v;
}
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
 var s="+";
 var w1="°",w2="’",w3="”";
 if(d<0)  d=-d,s='-';
 if(tim){ d*=12/Math.PI; w1="h ",w2="m ",w3="s "; }
 else     d*=180/Math.PI;
 var a=Math.floor(d); d=(d-a)*60;
 var b=Math.floor(d); d=(d-b)*60;
 var c=Math.floor(d); d=(d-c)*100;
 d=Math.floor(d+0.5);
 if(d>=100) d-=100, c++;
 if(c>=60)  c-=60,  b++;
 if(b>=60)  b-=60,  a++;
 a="   "+a, b="0"+b, c="0"+c, d="0"+d;
 s+=a.substr(a.length-3,3)+w1;
 s+=b.substr(b.length-2,2)+w2;
 s+=c.substr(c.length-2,2)+".";
 s+=d.substr(d.length-2,2)+w3;
 return s;
}

//以下是地球黄经数据,最大误差0.25"
var E_L0=new Array(
33416565,4.6692568,6283.07584999,
348943,4.626102,12566.1517,34971,2.74412,5753.38488,34176,2.82887,3.52312,31359,3.62767,77713.77147,
26762,4.41808,7860.41939,23427,6.13516,3930.2097,13243,0.74246,11506.76977,12732,2.0371,529.69097,
11992,1.10963,1577.34354,9903,5.2327,5884.9268,9019,2.0451,26.2983,8572,3.5085,398.149,
7798,1.1788,5223.6939,7531,2.5334,5507.5532,5053,4.5829,18849.2275,4924,4.2051,775.5226,
3567,2.9195,0.0673,3171,5.849,11790.6291,2841,1.8987,796.298,2710,0.3149,10977.0788,
2428,0.3448,5486.7778,2062,4.8065,2544.3144,2054,1.8695,5573.1428,2023,2.4577,6069.7768,
1555,0.8331,213.2991,1322,3.4112,2942.4634,1262,1.083,20.7754,1151,0.6454,0.9803,
1029,0.636,4694.003,1019,0.9757,15720.8388,1017,4.2668,7.1135,992,6.21,2146.165,
976,0.681,155.42,858,5.983,161000.686,851,1.299,6275.962,847,3.671,71430.696,
796,1.808,17260.155,788,3.037,12036.461,747,1.755,5088.629,739,3.503,3154.687,
735,4.679,801.821,696,0.833,9437.763,624,3.978,8827.39,611,1.818,7084.897,
570,2.784,6286.599,561,4.387,14143.495,556,3.47,6279.553,520,0.189,12139.554,
516,1.333,1748.016,511,0.283,5856.478,490,0.487,1194.447,410,5.368,8429.241,
409,2.399,19651.048,392,6.168,10447.388,368,6.041,10213.286,366,2.57,1059.382,
360,1.709,2352.866,356,1.776,6812.767,333,0.593,17789.846,304,0.443,83996.847,
300,2.74,1349.867,254,3.165,4690.48,247,0.215,3.59,237,0.485,8031.092,
236,2.065,3340.612,228,5.222,4705.732,219,5.556,553.569,214,1.426,16730.464,
211,4.148,951.718,203,0.371,283.859,199,5.222,12168.003,199,5.775,6309.374,
191,3.822,23581.258,189,5.386,149854.4,179,2.215,13367.973,175,4.561,135.065,
162,5.988,11769.854,151,4.196,6256.778,144,4.193,242.729,143,3.724,38.028,
140,4.401,6681.225,136,1.889,7632.943,125,1.131,5.523,121,2.622,955.6,
120,1.004,632.784,113,0.177,4164.312,108,0.327,103.093,105,0.939,11926.254,
105,5.359,1592.596,103,6.2,6438.496,100,6.029,5746.271,98,1,11371.7,
98,5.24,27511.47,94,2.62,5760.5,92,0.48,522.58,92,4.57,4292.33,
90,5.34,6386.17,86,4.17,7058.6,84,3.3,7234.79,84,4.54,25132.3,
81,6.11,4732.03,81,6.27,426.6,80,5.82,28.45,79,1,5643.18,
78,2.96,23013.54,77,3.12,7238.68,76,3.97,11499.66,73,4.39,316.39,
73,0.61,11513.88,72,4,74.78,71,0.32,263.08,68,5.91,90955.55,
66,3.66,17298.18,65,5.79,18073.7,63,4.72,6836.65,62,1.46,233141.31,
61,1.07,19804.83,60,3.32,6283.01,60,2.88,6283.14,55,2.45,12352.85);

var E_L1=new Array(
2060589,2.6782346,6283.07585,43034,2.63513,12566.1517,4253,1.5905,3.5231,1193,5.7956,26.2983,
1090,2.9662,1577.3435,935,2.592,18849.228,721,1.138,529.691,678,1.875,398.149,
673,4.409,5507.553,590,2.888,5223.694,560,2.175,155.42,454,0.398,796.298,
364,0.466,775.523,290,2.647,7.114,208,5.341,0.98,191,1.846,5486.778,
185,4.969,213.299,173,2.991,6275.962,162,0.032,2544.314,158,1.43,2146.165,
146,1.205,10977.079,125,2.834,1748.016,119,3.258,5088.629,118,5.274,1194.447,
115,2.075,4694.003,106,0.766,553.569,100,1.303,6286.599,97,4.24,1349.87,
95,2.7,242.73,86,5.64,951.72,76,5.3,2352.87,64,2.65,9437.76,
61,4.67,4690.48,58,1.77,1059.38,53,0.91,3154.69,52,5.66,71430.7,
52,1.85,801.82,50,1.42,6438.5,43,0.24,6812.77,43,0.77,10447.39,
41,5.24,7084.9,37,2,8031.09,36,2.43,14143.5,35,4.8,6279.55,
34,0.89,12036.46,34,3.86,1592.6,33,3.4,7632.94,32,0.62,8429.24,
32,3.19,4705.73,30,6.07,4292.33,30,1.43,5746.27,29,2.32,20.36,
27,0.93,5760.5,27,4.8,7234.79,25,6.22,6836.65,23,5,17789.85,
23,5.67,11499.66,21,5.2,11513.88,21,3.96,10213.29,21,2.27,522.58,
21,2.22,5856.48,21,2.55,25132.3,20,0.91,6256.78,19,0.53,3340.61,
19,4.74,83996.85,18,1.47,4164.31,18,3.02,5.52,18,3.03,5753.38,
16,4.64,3.29,16,6.12,5216.58,16,3.08,6681.22,15,4.2,13367.97,
14,1.19,3894.18,14,3.09,135.07,14,4.25,426.6,13,5.77,6040.35,
13,3.09,5643.18,13,2.09,6290.19,13,3.08,11926.25,12,3.45,536.8);

var E_L2=new Array(
87198,1.0721,6283.07585,3091,0.8673,12566.1517,273,0.053,3.523,163,5.188,26.298,
158,3.685,155.42,95,0.76,18849.23,89,2.06,77713.77,70,0.83,775.52,
51,4.66,1577.34,41,1.03,7.11,38,3.44,5573.14,35,5.14,796.3,
32,6.05,5507.55,30,1.19,242.73,29,6.12,529.69,27,0.31,398.15,
25,2.28,553.57,24,4.38,5223.69,21,3.75,0.98,17,0.9,951.72,
15,5.76,1349.87,14,4.36,1748.02,13,3.72,1194.45,13,2.95,6438.5,
12,2.97,2146.17,11,1.27,161000.69,10,0.6,3154.69,10,5.99,6286.6,
9,4.8,5088.63,9,5.23,7084.9,8,3.31,213.3,8,3.42,5486.78,
7,6.19,4690.48,7,3.43,4694,6,1.6,2544.31,6,1.98,801.82,
6,2.48,10977.08,5,1.44,6836.65,5,2.34,1592.6,5,1.31,4292.33,
5,3.81,149854.4,4,0.04,7234.79,4,4.94,7632.94,4,1.57,71430.7,
4,3.17,6309.37,3,0.99,6040.35,3,0.67,1059.38,3,3.18,2352.87,
3,3.55,8031.09,3,1.92,10447.39,3,2.52,6127.66,3,4.42,9437.76,
3,2.71,3894.18,3,0.67,25132.3,3,5.27,6812.77,3,0.55,6279.55);

var E_L3=new Array(
2892,5.8438,6283.0758,168,5.488,12566.152,30,5.2,155.42,
13,4.72,3.52,7,5.3,18849.23,6,5.97,242.73,4,3.79,553.57,1,4.3,6286.6,1,0.91,6127.66);

var E_L4=new Array(77,4.13,6283.08,8,3.84,12566.15,4,0.42,155.42);
var E_L5=new Array(2,2.77,6283.08,1,2.01,155.42);

//地球黄纬数据,误差0.2"
var E_B0=new Array(
2796,3.1987,84334.6616,1016,5.4225,5507.5532,804,3.88,5223.694,438,3.704,2352.866,
319,4,1577.344,227,3.985,1047.747);

var E_B1=new Array(90,3.9,5507.55,62,1.73,5223.69);
var E_B2=new Array(17,1.63,84334.66);

//地球向径数据,误差0.00001AU
var E_R0=new Array(
1000139888,0,0,16706996,3.09846351,6283.07584999,
139560,3.055246,12566.1517,30837,5.19847,77713.77147,
16285,1.17388,5753.38488,15756,2.84685,7860.41939,
9248,5.4529,11506.7698,5424,4.5641,3930.2097,
4721,3.661,5884.9268,3460,0.9637,5507.5532,
3288,5.8998,5223.6939,3068,0.2987,5573.1428,
2432,4.2735,11790.6291,2118,5.8471,1577.3435,
1858,5.0219,10977.0788,1748,3.0119,18849.2275);

var E_R1=new Array(1030186,1.1074897,6283.07585,17212,1.06442,12566.1517,7022,3.1416,0);
var E_R2=new Array(43594,5.78455,6283.07585,1236,5.5793,12566.1517,123,3.142,0,88,3.63,77713.77);
var E_R3=new Array(1446,4.2732,6283.0758,67,3.92,12566.15);
var E_R4=new Array(39,2.56,6283.08,3,2.27,12566.15);
var E_R5=new Array(1,1.22,6283.08);

 

function Enn(F,t,n){ //计算E_L0或E_L1或E_L2等
  n=Math.floor(n*F.length+0.5); //按百分比取项数
  var i,v=0;
  for(i=0;i<n;i+=3) v+=F[i]*Math.cos(F[i+1] +t*F[i+2]);
  return v;
}
function earthLon(t,n){ //地球经度计算,返回Date分点黄经,传入千年数
  if(n<0) n=1; else n = 3*n/E_L0.length;
  var t2=t*t, t3=t2*t, t4=t3*t, t5=t4*t;
  var v  = 1753469512 + 6283319653318*t + 529674*t2 + 432*t3 - 1157*t4 - 9*t5; //地球平黄经(已拟合DE406)
      v += 630 * Math.cos(6+3*t); //拟合DE406
      v += Enn( E_L0, t, n );
      v += Enn( E_L1, t, n )*t;
      v += Enn( E_L2, t, n )*t2;
      v += Enn( E_L3, t, n )*t3;
      v += Enn( E_L4, t, n )*t4;
      v += Enn( E_L5, t, n )*t5;
  return v/1000000000;
}
function earthCoor(t,re,n){ //返回地球坐标
  var t2=t*t, t3=t2*t, t4=t3*t, t5=t4*t;
  re[0] = earthLon(t,n);
  re[1] = Enn( E_B0, t, 1 )
        + Enn( E_B1, t, 1 )*t
        + Enn( E_B2, t, 1 )*t2;
  re[2] = Enn( E_R0, t, 1 )
        + Enn( E_R1, t, 1 )*t
        + Enn( E_R2, t, 1 )*t2
        + Enn( E_R3, t, 1 )*t3
        + Enn( E_R4, t, 1 )*t4
        + Enn( E_R5, t, 1 )*t5;
  re[1]/=1000000000;
  re[2]/=1000000000;
}
function earthV(t){ //地球速度,t是千年数,误差小于万分3
 var f=6283.07585*t;
 return v = 6283.32
  +210 *Math.sin(1.527+f)
  +4.4 *Math.sin(1.48+f*2)
  +12.9*Math.sin(5.82+f)*t
  +0.55*Math.sin(4.21+f)*t*t;
}
function earth_t(W){ //已知黄经求时间
  var t,dW,v= 6283.319653318;
  t  = ( W - 1.75347       )/v; v=earthV(t,1);   //v的精度0.03%,详见原文
  t += ( W - earthLon(t,10))/v;
  t += ( W - earthLon(t,-1))/v;
  return t;
}

//迭代算法测试
t=1;
L=earthLon(t,-1);
t2=earth_t(L);
document.write("迭代算法测试<br>");
document.write("输入时间(千年):"+t+"<br>");
document.write("地球黄经(弧度):"+L+"<br>");
document.write("返算时间(千年):"+t2+"<br>");
document.write("迭代误差(秒):"+(t2-t)*365250*86400+"<br><br>");

 

 

//=======================
// 以下是视位置计算
//=======================
var nutB=new Array(
  2.1824,  -33.75705, 36e-6,-1720,920,
  3.5069, 1256.66393, 11e-6,-132, 57,
  1.3375,16799.4182, -51e-6, -23, 10,
  4.3649,  -67.5141,  72e-6,  21, -9,
  0.04,   -628.302,   0,     -14,  0,
  2.36,   8328.691,   0,       7,  0,
  3.46,   1884.966,   0,      -5,  2,
  5.44,  16833.175,   0,      -4,  2,
  3.69,  25128.110,   0,      -3,  0,
  3.55,    628.362,   0,       2,  0);
function nutation(t){ //章动计算
 var i,c,a, t2=t*t,dL=0,dE=0;
 for(i=0;i<nutB.length;i+=5){
  c = nutB[i]+nutB[i+1]*t+nutB[i+2]*t2;
  if(i==0) a=-1.742*t; else a=0;
  dL+=(nutB[i+3]+a)*Math.sin(c);
  dE+= nutB[i+4]   *Math.cos(c);
 }
 this.dL=dL/100;  //黄经章动
 this.dE=dE/100;  //交角章动
}
function gxc_sun(t,L){ //太阳光行差(黄经),L为太阳黄经,t是千年数
 var v = L-(282.93735+17.1946*t+ 0.046*t*t)/180*Math.PI; //真近点角
 var e = 0.016708634-0.00042037*t-0.00001267*t*t;
 return -20.49552 * (1+e*Math.cos(v));
}
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
  var HJ=rad2mrad(JW[0]), HW=JW[1];
  var sinE =Math.sin(E),cosE =Math.cos(E);
  var sinW=cosE*Math.sin(HW)+sinE*Math.cos(HW)*Math.sin(HJ);
  var J=Math.atan2( Math.sin(HJ)*cosE-Math.tan(HW)*sinE, Math.cos(HJ) );
  JW[0]=rad2mrad(J);
  JW[1]=Math.asin(sinW);
}

function hcjj (t){ //返回黄赤交角,t是千年数
 var t2=t*t, t3=t2*t,t4=t3*t;
 return (84381.4088 -468.36051*t -0.01667*t2 -1.99911*t3-0.00523*t4)/rad;
}

 

z=new Array();
da=1;
testT=0.008+(da-1.5)/365250;    //世纪数
earthCoor(testT,z,-1);         //地球黄经
z[0]+=Math.PI,z[1]=-z[1];      //太阳黄经黄纬

//L=z[0]-50287.9*(testT-0.008)/rad;
//L=rad2mrad(L);
//document.write(rad2str(L,0)+"<br>");

gx= gxc_sun(testT,z[0]);       //太阳光行差
nu= new nutation(testT*10);    //章动计算
z[0] += (nu.dL+gx)/rad;        //补章动与光行差
E = hcjj(testT)+nu.dE/rad;     //得到真黄赤交角
HCconv(z,E); //转到赤道坐标

document.write("坐标精度测试<br>");
document.write("testT:" + testT+"<br>");
document.write("视赤经:" + rad2str(z[0],1)+"<br>");
document.write("视赤纬:" + rad2str(z[1],0)+"<br>");
document.write("距离:" + z[2]+"<br>");
document.write("请与《2008中国天文年历》太阳视赤经赤纬比对。该年的第 "+da+" 天0h TD。注意:几乎分秒不差!<br>");
document.write("本程序中VSOP87地球数据序列以做了长期项拟合到DE405/406<br>");

</script>

[此贴子已经被作者于2008-5-30 8:05:57编辑过]

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