📄 eph.js
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/****************************************
以下是天文计算部分,包含有：
常数 rad : 每弧度的角秒数
常数 J2000 : 2000年1月1日 12:00:00 的儒略日数
常数 pi2 : 圆周率的2倍,即2*3.14159...
trim() : 去除字串首尾的空格
rad2str() : 弧度转为"度分秒"或"时分秒"
rad2str2() : 弧度转为"度分"
rad2mrad() : 将超出0到360度的角度转为0到360度的解度
mod2(a,b) : 临界余数(a与最近的整倍数b相差的距离)
int2(a) : 取小等于a的最大整数
物件 JD : 公历——儒略日——时间物件
物件 ZB : 坐标变换物件，包含坐标旋转、章动、日月光行差(时)、视差、大气折射、恒星时的计算
物件 XL : 日月黄道平分点坐标、视坐标、速度、已知经度反求时间等方面的计算
物件 SZJ : 用来计算日月的升起、中天、降落
注意，上述函数或物件是纯天文学的，根据实际需要组合使用可以得到所需要的各种日月坐标，计算精度及计算速度也是可以根据需要有效控制的。
*****************************************/
rad = 180*3600/Math.PI,
J2000= 2451545;
pi2 = Math.PI*2;
function trim(s){ return s.replace(/(^\s*)|(\s*$)/g, ""); }
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;
}
function rad2str2(d){ //将弧度转为字串,精确到分
//输出格式示例: -23°59'
var s="+";
var w1="°",w2="'",w3='"';
if(d<0) d=-d,s='-';
d*=180/Math.PI;
var a=Math.floor(d);
var b=Math.floor((d-a)*60+0.5);
if(b>=60) b-=60, a++;
a=" "+a, b="0"+b;
s+=a.substr(a.length-3,3)+w1;
s+=b.substr(b.length-2,2)+w2;
return s;
}
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 mod2(a,b){ //临界余数(a与最近的整倍数b相差的距离)
var c=a/b;
c -= Math.floor(c);
if(c>0.5) c-=1;
return c*b;
}
function int2(v){ return Math.floor(v); } //取整数部分
var JD={ //日期元件
Y:2000, M:1, D:1, h:12, m:0, s:0,
dts:new Array( // TD - UT1 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, 63.87, 0.1, 0, 0, 2005),
deltatExt:function(y,jsd){ var dy=(y-1820)/100; return -20+jsd*dy*dy; }, //二次曲线外推
deltatT:function(y){ //计算世界时与原子时之差,传入年
if(y>=2005){
//sd是2005年之后几年（一值到y1年）的速度估计。
//sjd是y1年之后的加速度估计。瑞士星历表jsd=31,NASA网站jsd=32,skmap的jsd=29
var y1=2014, sd=0.4, jsd=31;
if(y<=y1) return 64.7 + (y-2005) *sd; //直线外推
var v = this.deltatExt(y,jsd); //二次曲线外推
var dv= this.deltatExt(y1,jsd) - ( 64.7+(y1-2005)*sd ); //y1年的二次外推与直线外推的差
if(y<y1+100 ) v -= dv*(y1+100-y)/100;
return v;
}
var i,d=this.dts;
for(i=0;i<d.length;i+=5) if(y<d[i+5]) break;
var t1=(y-d[i])/(d[i+5]-d[i])*10, t2=t1*t1, t3=t2*t1;
return d[i+1] +d[i+2]*t1 +d[i+3]*t2 +d[i+4]*t3;
},
deltatT2:function(t){ //传入儒略日(J2000起算),计算TD-UT(单位:日)
return this.deltatT(t/365.2425+2000)/86400.0;
},
toJD:function(){ //公历转儒略日
var y=this.Y, m=this.M, n=0; //取出年月
if(m<=2) m+=12,y--;
if(this.Y*372+this.M*31+this.D>=588829)//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
n +=int2(365.25*(y+4716)+0.01); //加上年引起的偏移日数
n +=int2(30.6*(m+1))+this.D; //加上月引起的偏移日数及日偏移数
n +=((this.s/60+this.m)/60+this.h)/24 - 1524.5;
return n;
},
setFromJD:function(jd){ //儒略日数转公历
jd+=0.5;
var 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) D=int2((A-1867216.25)/36524.25),A+=1+D-int2(D/4);
A +=1524; //向前移4年零2个月
this.Y =int2((A-122.1)/365.25);//年
D =A-int2(365.25*this.Y); //去除整年日数后余下日数
this.M =int2(D/30.6001); //月数
this.D =D-int2(this.M*30.6001);//去除整月日数后余下日数
this.Y-=4716; this.M--;
if(this.M>12) this.M-=12;
if(this.M<=2) this.Y++;
//日的小数转为时分秒
F*=24; this.h=int2(F); F-=this.h;
F*=60; this.m=int2(F); F-=this.m;
F*=60; this.s=F;
},
toStr:function(){ //日期转为串
var Y=" "+this.Y,M="0"+this.M, D="0"+this.D;
var h=this.h,m=this.m,s=int2(this.s+.5);
if(s>=60) s-=60,m++;
if(m>=60) m-=60,h++;
h="0"+h; m="0"+m; s="0"+s;
Y=Y.substr(Y.length-5,5); M=M.substr(M.length-2,2); D=D.substr(D.length-2,2);
h=h.substr(h.length-2,2); m=m.substr(m.length-2,2); s=s.substr(s.length-2,2);
return Y+"-"+M+"-"+D+" "+h+":"+m+":"+s;
},
setFromJD_str:function(jd){ this.setFromJD(jd); return this.toStr(); },
timeStr:function(jd){ //提取jd中的时间(去除日期)
var h,m,s;
jd+=0.5; jd = (jd - int2(jd));
jd*=24; h = int2(jd); jd-=h;
jd*=60; m = int2(jd); jd-=m;
jd*=60; s = int2(jd+0.5);
if(s>=60) s-=60,m++;
if(m>=60) m-=60,h++;
h="0"+h; m="0"+m; s="0"+s;
return h.substr(h.length-2,2)+':'+m.substr(m.length-2,2)+':'+s.substr(s.length-2,2);
}
};
var ZB={ //坐标类
llrConv:function(JW,E){ //球面坐标旋转
//黄道赤道坐标变换,赤到黄E取负
var sinE =Math.sin(E), cosE =Math.cos(E);
var sinJ =Math.sin(JW[0]),cosJ =Math.cos(JW[0]);
var sinW =Math.sin(JW[1]),cosW =Math.cos(JW[1]), tanW=Math.tan(JW[1]);
JW[0]=Math.atan2( sinJ*cosE - tanW*sinE, cosJ );
JW[1]=Math.asin ( cosE*sinW + sinE*cosW*sinJ );
JW[0]=rad2mrad(JW[0]);
},
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),
nutation:function(t){ //章动计算,t是世纪数
var i,c,a, t2=t*t, B=this.nutB, dL=0,dE=0;
for(i=0;i<B.length;i+=5){
c = B[i]+B[i+1]*t+B[i+2]*t2;
if(i==0) a=-1.742*t; else a=0;
dL+=(B[i+3]+a)*Math.sin(c);
dE+= B[i+4] *Math.cos(c);
}
this.dL=dL/100/rad; //黄经章动
this.dE=dE/100/rad; //交角章动
},
nutationLon:function(t){ //只计算黄经章动
var i,a, t2=t*t, dL=0, B=this.nutB;
for(i=0;i<B.length;i+=5){
if(i==0) a=-1.742*t; else a=0;
dL += (B[i+3]+a) * Math.sin( B[i]+B[i+1]*t+B[i+2]*t2 );
}
return dL/100/rad;
},
hcjj:function(t){ //返回黄赤交角,t是世纪数
var t2=t*t, t3=t2*t,t4=t3*t;
return (84381.4088 -46.836051*t -0.0001667*t2 -0.00199911*t3-0.000000523*t4)/rad;
},
gst:function(T,dt){ //传入T是2000年首起算的日数(UT),dt是deltatT(日),精度要求不高时dt可取值为0
//返回格林尼治恒星时(不含赤经章动及非多项式部分),即格林尼治子午圈的平春风点起算的赤经
var t=(T+dt)/36525,t2=t*t, t3=t2*t, t4=t3*t;
return pi2*(0.7790572732640 + 1.00273781191135448*T) //严格说这里的T是UT,下一行的t是力学时(世纪数)
+ (0.014506 + 4612.15739966*t + 1.39667721*t2 - 0.00009344*t3 + 0.00001882*t4)/rad;
},
gxc_sunLon:function(t){ //太阳光行差,t是世纪数
var v =-0.043126+ 628.301955*t -0.000002732*t*t; //平近点角
var e = 0.016708634-0.000042037*t-0.0000001267*t*t;
return ( -20.49552 * (1+e*Math.cos(v)) )/rad; //黄经光行差
},
gxc_sunLat:function(t) { return 0; }, //黄纬光行差
gxc_moonLon:function(t){ return -3.4E-6; }, //月球经度光行差,误差0.07"
gxc_moonLat:function(t){ //月球纬度光行差,误差0.006"
return 0.063*Math.sin(0.057+8433.4662*t+0.000064*t*t)/rad;
},
AR:function(ho){ return -0.0002909/Math.tan( ho+0.002227/(ho+0.07679) ); }, //大气折射,ho是视高度
AR2:function(h){ return 0.0002967/Math.tan( h +0.003138/( h+0.08919) ); }, //大气折射,h是真高度
parallax:function(z,H,fa,high){ //视差修正
//z赤道坐标,fa地理纬度,H时角,high海拔(千米)
var sinP = 8.794/rad/z[2]; //赤道地平视差,z[2]应以AU为单位
var ba = 0.99664719;
var u = Math.atan(ba*Math.tan(fa));
var sinD = -sinP*(Math.sin(u)*ba+ high*Math.sin(fa)/6378.14);
var cosD = -sinP*(Math.cos(u) + high*Math.cos(fa)/6378.14);
var sinH = Math.sin(H), cosH = Math.cos(H);
var sinW = Math.sin(z[1]), cosW = Math.cos(z[1]);
var a = Math.atan( cosD*sinH / (cosW+cosD*cosH) );
z[1] = Math.atan( (sinW+sinD) / (cosW+cosD*cosH) * Math.cos(a) );
z[0] = rad2mrad( z[0]+a );
}
};
var XL={ //星历类
//==========================
EL:new Array(//以下是地球黄经数据,最大误差0.25"
new Array(//EL0
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),
new Array(//EL1
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,
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