function rev(angle){return angle-Math.floor(angle/360.0)*360.0;}

function sind(angle){return Math.sin((angle*Math.PI)/180.0);}

function cosd(angle){return Math.cos((angle*Math.PI)/180.0);}

function tand(angle){return Math.tan((angle*Math.PI)/180.0);}

function asind(c){return (180.0/Math.PI)*Math.asin(c);}

function acosd(c){return (180.0/Math.PI)*Math.acos(c);}

function atan2d(y,x){return (180.0/Math.PI)*Math.atan(y/x)-180.0*(x<0);}



function anglestring(a,circle)
 {
  var ar=Math.round(a*60)/60;
  var deg=Math.abs(ar);
  var min=Math.round(60.0*(deg-Math.floor(deg)));
  if (min >= 60) { deg+=1; min=0; }
  var anglestr="";
  if (!circle) anglestr+=(ar < 0 ? "-" : "+");
  if (circle) anglestr+=((Math.floor(deg) < 100) ? "0" : "" );
  anglestr+=((Math.floor(deg) < 10) ? "0" : "" )+Math.floor(deg);
  anglestr+=((min < 10) ? ":0" : ":" )+(min);

  return anglestr;
 }



function getFullYear(now)
 {
  var year = now.getYear();
  if (year==0) {year=2000};
  if (year<1900) {year=year+1900};

  return year;
 }



function datestring(year,month,day)
 {
  var datestr = "";
  datestr += ((day < 10) ? "0" : "") + day;
  datestr += ((month < 10) ? ".0" : ".") + month;
  datestr += "." + year;

  return datestr;
 }



function hmstring(t)// takes hours and returns hh:mm
 {
  var hours=t;
  while (hours >= 24) {hours-=24;}
  while (hours < 0) {hours+=24;}
  var minutes=Math.round(60.0*(hours-Math.floor(hours)));
  hours=Math.floor(hours);
  if (minutes >= 60) {hours+=1; minutes-=60;}
  if (hours >= 24) {hours-=24;}
  var hmstr=(t < 0) ? "-" : "";
  hmstr=((hours < 10) ? "0" : "")+hours;
  hmstr+=((minutes < 10) ? ":0" : ":")+minutes;

  return hmstr;
 }



function hmsstring(t)   // takes hours and returns hh:mm:ss
 {
  var hours = Math.abs(t);
  var minutes = 60.0*(hours-Math.floor(hours));
  hours=Math.floor(hours);
  var seconds = Math.round(60.0*(minutes-Math.floor(minutes)));
  minutes=Math.floor(minutes);
  if (seconds >= 60) { minutes+=1; seconds-=60; }
  if (minutes >= 60) { hour+=1; minutes-=60; }
  if (hours >= 24) { hours-=24; }
  var hmsstr=(t < 0) ? "-" : "";
  hmsstr=((hours < 10) ? "0" : "" )+hours;
  hmsstr+=((minutes < 10) ? ":0" : ":" )+minutes;
  hmsstr+=((seconds < 10) ? ":0" : ":" )+seconds;
  return hmsstr;
}


function dayno (year,month,day,hours)
 {
  var d= 367*year-Math.floor(7*(year+Math.floor((month+9)/12))/4)
         +Math.floor((275*month)/9)+day-730530+hours/24;
  return d;
 }



function julian(year,month,day,hours)
 {
  return  dayno(year,month,day,hours)+2451543.5
 }



function jdtocd(jd)
 {
  // The calendar date from julian date
  // Returns year, month, day, day of week, hours, minutes, seconds
  var Z=Math.floor(jd+0.5);
  var F=jd+0.5-Z;
  var A=Z;
  if (Z >= 2299161)
   {
    var alpha=Math.floor((Z-1867216.25)/36524.25);
    A=Z+1+alpha-Math.floor(alpha/4);
   }
  var B=A+1524;
  var C=Math.floor((B-122.1)/365.25);
  var D=Math.floor(365.25*C);
  var E=Math.floor((B-D)/30.6001);
  var d=B-D-Math.floor(30.6001*E)+F;
  var month=E-1;
  if (E > 13) {month=month-12;}
  var year=C-4715;
  if ( month>2) {year=year-1;}
  var day=Math.floor(d);
  var h=(d-day)*24;
  var hours=Math.floor(h);
  var m=(h-hours)*60;
  var minutes=Math.floor(m);
  var seconds=Math.round((m-minutes)*60);
  if (seconds >= 60) {minutes=minutes+1;seconds=seconds-60;}
  if (minutes >= 60) {hours=hours+1;minutes=0;}
  var dw=Math.floor(jd+1.5)-7*Math.floor((jd+1.5)/7);

  return new Array(year,month,day,dw,hours,minutes,seconds);
 }



function local_sidereal(year,month,day,hours,lon) {
  // Compute local siderial time in degrees
  // year, month, day and hours are the Greenwich date and time
  // lon is the observers longitude
  var d=dayno(year,month,day,hours);
  var lst=(98.9818+0.985647352*d+hours*15+lon);
  return rev(lst)/15;
}



function radtoaa(ra,dec,year,month,day,hours,lat,lon) {
  // convert ra and dec to altitude and azimuth
  // year, month, day and hours are the Greenwich date and time
  // lat and lon are the observers latitude and longitude
  var lst=local_sidereal(year,month,day,hours,lon);
  var x=cosd(15.0*(lst-ra))*cosd(dec);
  var y=sind(15.0*(lst-ra))*cosd(dec);
  var z=sind(dec);
  // rotate so z is the local zenith
  var xhor=x*sind(lat)-z*cosd(lat);
  var yhor=y;
  var zhor=x*cosd(lat)+z*sind(lat);
  var azimuth=rev(atan2d(yhor,xhor)+180.0); // so 0 degrees is north
  var altitude=atan2d(zhor,Math.sqrt(xhor*xhor+yhor*yhor));
  return new Array(altitude,azimuth);
}



function SunRiseSet (year,month,day,latitude,longitude)
 {
  var d=dayno(year,month,day,12.0-longitude/15);
  var oblecl=23.4393-3.563E-7*d;
  var w=282.9404+4.70935E-5*d;
  var M=356.0470+0.9856002585*d;
  var e=0.016709-1.151E-9*d;
  var E=M+e*(180/Math.PI)*sind(M)*(1.0+e*cosd(M));
  var A=cosd(E)-e;
  var B=Math.sqrt(1-e*e)*sind(E);
  var slon=w+atan2d(B,A);
  var sRA=atan2d(sind(slon)*cosd(oblecl),cosd(slon));
  while(sRA<0)sRA+=360; while(sRA>360)sRA-=360; sRA=sRA/15;
  var sDec=asind(sind(oblecl)*sind(slon));
  var lst=local_sidereal(year,month,day,12-longitude/15,longitude);
  var MT=12.0-longitude/15+sRA-lst;
  while(MT<0)MT+=24; while(MT>24)MT-=24;
  var cHA0=(sind(-0.833)-sind(latitude)*sind(sDec))/(cosd(latitude)*cosd(sDec));
  var HA0=acosd(cHA0);
  HA0 = rev(HA0)/15;

  return new Array((MT-HA0),(MT+HA0));
}




   var T45AD = new Array(0, 2, 2, 0, 0, 0, 2, 2, 2, 2,
                         0, 1, 0, 2, 0, 0, 4, 0, 4, 2,
                         2, 1, 1, 2, 2, 4, 2, 0, 2, 2,
                         1, 2, 0, 0, 2, 2, 2, 4, 0, 3,
                         2, 4, 0, 2, 2, 2, 4, 0, 4, 1,
                         2, 0, 1, 3, 4, 2, 0, 1, 2, 2);

   var T45AM = new Array(0,  0,  0,  0,  1,  0,  0, -1,  0, -1,
                         1,  0,  1,  0,  0,  0,  0,  0,  0,  1,
                         1,  0,  1, -1,  0,  0,  0,  1,  0, -1,
                         0, -2,  1,  2, -2,  0,  0, -1,  0,  0,
                         1, -1,  2,  2,  1, -1,  0,  0, -1,  0,
                         1,  0,  1,  0,  0, -1,  2,  1,  0,  0);

   var T45AMP = new Array( 1, -1,  0,  2,  0,  0, -2, -1,  1,  0,
                          -1,  0,  1,  0,  1,  1, -1,  3, -2, -1,
                           0, -1,  0,  1,  2,  0, -3, -2, -1, -2,
                           1,  0,  2,  0, -1,  1,  0, -1,  2, -1,
                           1, -2, -1, -1, -2,  0,  1,  4,  0, -2,
                           0,  2,  1, -2, -3,  2,  1, -1,  3, -1);

   var T45AF  = new Array( 0,  0,  0,  0,  0,  2,  0,  0,  0,  0,
                           0,  0,  0, -2,  2, -2,  0,  0,  0,  0,
                           0,  0,  0,  0,  0,  0,  0,  0,  2,  0,
                           0,  0,  0,  0,  0, -2,  2,  0,  2,  0,
                           0,  0,  0,  0,  0, -2,  0,  0,  0,  0,
                          -2, -2,  0,  0,  0,  0,  0,  0,  0, -2);

   var T45AL = new Array(6288774, 1274027, 658314, 213618, -185116,
                         -114332,   58793,  57066,  53322,   45758,
                          -40923,  -34720, -30383,  15327,  -12528,
                           10980,   10675,  10034,   8548,   -7888,
                           -6766,   -5163,   4987,   4036,    3994,
                            3861,    3665,  -2689,  -2602,    2390,
                           -2348,    2236,  -2120,  -2069,    2048,
                           -1773,   -1595,   1215,  -1110,    -892,
                            -810,     759,   -713,   -700,     691,
                             596,     549,    537,    520,    -487,
                            -399,    -381,    351,   -340,     330,
                             327,    -323,    299,    294,       0);

   var T45AR = new Array(-20905355, -3699111, -2955968, -569925,   48888,
                             -3149,   246158,  -152138, -170733, -204586,
                           -129620,   108743,   104755,   10321,       0,
                             79661,   -34782,   -23210,  -21636,   24208,
                             30824,    -8379,   -16675,  -12831,  -10445,
                            -11650,    14403,    -7003,       0,   10056,
                              6322,    -9884,     5751,       0,   -4950,
                              4130,        0,    -3958,       0,    3258,
                              2616,    -1897,    -2117,    2354,       0,
                                 0,    -1423,    -1117,   -1571,   -1739,
                                 0,    -4421,        0,       0,       0,
                                 0,     1165,        0,       0,    8752);

// Meeus table 45B latitude of the moon

   var T45BD = new Array(0, 0, 0, 2, 2, 2, 2, 0, 2, 0,
                         2, 2, 2, 2, 2, 2, 2, 0, 4, 0,
                         0, 0, 1, 0, 0, 0, 1, 0, 4, 4,
                         0, 4, 2, 2, 2, 2, 0, 2, 2, 2,
                         2, 4, 2, 2, 0, 2, 1, 1, 0, 2,
                         1, 2, 0, 4, 4, 1, 4, 1, 4, 2);

   var T45BM = new Array( 0,  0,  0,  0,  0,  0,  0, 0,  0,  0,
                         -1,  0,  0,  1, -1, -1, -1, 1,  0,  1,
                          0,  1,  0,  1,  1,  1,  0, 0,  0,  0,
                          0,  0,  0,  0, -1,  0,  0, 0,  0,  1,
                          1,  0, -1, -2,  0,  1,  1, 1,  1,  1,
                          0, -1,  1,  0, -1,  0,  0, 0, -1, -2);

   var T45BMP = new Array(0,  1, 1,  0, -1, -1,  0,  2,  1,  2,
                          0, -2, 1,  0, -1,  0, -1, -1, -1,  0,
                          0, -1, 0,  1,  1,  0,  0,  3,  0, -1,
                          1, -2, 0,  2,  1, -2,  3,  2, -3, -1,
                          0,  0, 1,  0,  1,  1,  0,  0, -2, -1,
                          1, -2, 2, -2, -1,  1,  1, -1,  0,  0);

   var T45BF = new Array( 1,  1, -1, -1,  1, -1,  1,  1, -1, -1,
                         -1, -1,  1, -1,  1,  1, -1, -1, -1,  1,
                          3,  1,  1,  1, -1, -1, -1,  1, -1,  1,
                         -3,  1, -3, -1, -1,  1, -1,  1, -1,  1,
                          1,  1,  1, -1,  3, -1, -1,  1, -1, -1,
                          1, -1,  1, -1, -1, -1, -1, -1, -1,  1);

   var T45BL = new Array(5128122, 280602, 277693, 173237, 55413,
                           46271,  32573,  17198,   9266,  8822,
                            8216,   4324,   4200,  -3359,  2463,
                            2211,   2065,  -1870,   1828, -1794,
                           -1749,  -1565,  -1491,  -1475, -1410,
                           -1344,  -1335,   1107,   1021,   833,
                             777,    671,    607,    596,   491,
                            -451,    439,    422,    421,  -366,
                            -351,    331,    315,    302,  -283,
                            -229,    223,    223,   -220,  -220,
                            -185,    181,   -177,    176,   166,
                            -164,    132,   -119,    115,   107);



// MoonPos calculates the Moon position, based on Meeus chapter 45

function MoonPos(year,month,day,hours)
 {
  var jd=julian(year,month,day,hours);
  var T=(jd-2451545.0)/36525;
  var T2=T*T;
  var T3=T2*T;
  var T4=T3*T;

  var LP=218.3164477+481267.88123421*T-0.0015786*T2+T3/538841.0-T4/65194000.0;
  var D=297.8501921+445267.1114034*T-0.0018819*T2+T3/545868.0-T4/113065000.0;
  var M=357.5291092+35999.0502909*T-0.0001536*T2+T3/24490000.0;
  var MP=134.9633964+477198.8675055*T+0.0087414*T2+T3/69699.0-T4/14712000.0;
  var F=93.2720950+483202.0175233*T-0.0036539*T2-T3/3526000.0+T4/863310000.0;

  var A1=119.75+131.849*T;
  var A2=53.09+479264.290*T;
  var A3=313.45+481266.484*T;
  var E=1-0.002516*T-0.0000074*T2;
  var E2=E*E;

  var Sl=0.0;
  var Sr=0.0;
  var i, Eterm;

  for (i=0; i<60; i++)
   {
    Eterm=1;
    if (Math.abs(T45AM[i])==1) Eterm=E;
    if (Math.abs(T45AM[i])==2) Eterm=E2;
    Sl+=T45AL[i]*Eterm*sind(rev(T45AD[i]*D+T45AM[i]*M+T45AMP[i]*MP+T45AF[i]*F));
    Sr+=T45AR[i]*Eterm*cosd(rev(T45AD[i]*D+T45AM[i]*M+T45AMP[i]*MP+T45AF[i]*F));
   }

  var Sb=0.0;
  for (i=0; i<60; i++) {
    Eterm=1;
    if (Math.abs(T45BM[i])==1) Eterm=E;
    if (Math.abs(T45BM[i])==2) Eterm=E2;
    Sb+=T45BL[i]*Eterm*sind(rev(T45BD[i]*D+T45BM[i]*M+T45BMP[i]*MP+T45BF[i]*F));
  }
  // Additional additive terms
  Sl=Sl+3958*sind(rev(A1))+1962*sind(rev(LP-F))+318*sind(rev(A2));
  Sb=Sb-2235*sind(rev(LP))+382*sind(rev(A3))+175*sind(rev(A1-F))+
     175*sind(rev(A1+F))+127*sind(rev(LP-MP))-115*sind(rev(LP+MP));
  // geocentric longitude, latitude and distance
  var mglong=rev(LP+Sl/1000000.0);
  var mglat=rev(Sb/1000000.0);
  if (mglat > 180.0) mglat=mglat-360;
  var mr=Math.round(385000.56+Sr/1000.0);
  // Obliquity of Ecliptic
  var obl=23.4393-3.563E-9*(jd-2451543.5);
  // RA and dec
  var ra=rev(atan2d(sind(mglong)*cosd(obl)-tand(mglat)*sind(obl),
                    cosd(mglong)))/15.0;
  var dec=rev(asind(sind(mglat)*cosd(obl)+cosd(mglat)*sind(obl)*sind(mglong)));
  if (dec > 180.0) dec=dec-360;
  return new Array(ra,dec,mr);
}



function MoonRise(year,month,day,latitude,longitude)
 {
  var i;
  // returns an array containing rise and set times (-1 if does not occur).
  var hours=0;
  // array to return -1 means not found
  var riseset=new Array(-1,-1);
  // elh is the elevation at the hour elhdone is true if elh calculated
  var elh=new Array();
  var elhdone=new Array();
  for (i=0; i<=24; i++) {elhdone[i]=false;}
  // Compute the moon elevation at start and end of day
  // store elevation at the hours in an array elh to save search time
  var rad=MoonPos(year,month,day,hours);
  var altaz=radtoaa(rad[0],rad[1],year,month,day,hours,latitude,longitude);
  elh[0]=altaz[0]; elhdone[0]=true;
  hours=24;
  rad=MoonPos(year,month,day,hours);
  altaz=radtoaa(rad[0],rad[1],year,month,day,hours,latitude,longitude);
  elh[24]=altaz[0]; elhdone[24]=true;
  // search for moonrise and set
  for (var rise=0; rise<2; rise++) {
     var found=false;
     var hfirst=0;
     var hmid=0;
     var hlast=24;
     // Try a binary chop on the hours to speed the search
     while (Math.ceil((hlast-hfirst)/2) > 1) {
       hmid=hfirst+Math.round((hlast-hfirst)/2);
       if (!elhdone[hmid]) {
         hours=hmid;
         rad=MoonPos(year,month,day,hours);
         altaz=radtoaa(rad[0],rad[1],year,month,day,hours,latitude,longitude);
         elh[hmid]=altaz[0]; elhdone[hmid]=true;
       }
       if (((rise == 0) && (elh[hfirst] <= 0.0) && (elh[hmid] >= 0.0)) ||
           ((rise == 1) && (elh[hfirst] >= 0.0) && (elh[hmid] <= 0.0))) {
         hlast=hmid; found=true; continue;
       }
       if (((rise == 0) && (elh[hmid] <= 0.0) && (elh[hlast] >= 0.0)) ||
           ((rise == 1) && (elh[hmid] >= 0.0) && (elh[hlast] <= 0.0))) {
         hfirst=hmid; found=true; continue;
       }
       break;
     }
     // If the binary chop did not find a 1 hour interval
     if ((hlast-hfirst) > 1) {
       for (i=hfirst; i<hlast; i++) {
         found=false;
         if (!elhdone[i+1]) {
           hours=i+1;
           rad=MoonPos(year,month,day,hours);
           altaz=radtoaa(rad[0],rad[1],year,month,day,hours,latitude,longitude);
           elh[hours]=altaz[0]; elhdone[hours]=true;
         }
         if (((rise == 0) && (elh[i] <= 0.0) && (elh[i+1] >= 0.0)) ||
             ((rise == 1) && (elh[i] >= 0.0) && (elh[i+1] <= 0.0))) {
           hfirst=i; hlast=i+1; found=true; break;
         }
       }
     }
     // simple linear interpolation for the minutes
     if (found) {
       var elfirst=elh[hfirst]; var ellast=elh[hlast];
       hours=hfirst+0.5;
       rad=MoonPos(year,month,day,hours);
       altaz=radtoaa(rad[0],rad[1],year,month,day,hours,latitude,longitude);
       if ((rise == 0) && (altaz[0] <= 0.0)) {hfirst=hours; elfirst=altaz[0];}
       if ((rise == 0) && (altaz[0] > 0.0)) {hlast=hours; ellast=altaz[0];}
       if ((rise == 1) && (altaz[0] <= 0.0)) {hlast=hours; ellast=altaz[0];}
       if ((rise == 1) && (altaz[0] > 0.0)) {hfirst=hours; elfirst=altaz[0];}
       var eld=Math.abs(elfirst)+Math.abs(ellast);
       riseset[rise]=hfirst+(hlast-hfirst)*Math.abs(elfirst)/eld;
     }
  } // End of rise/set loop
  return(riseset);
}



function MoonPhase(year,month,day)
 {
  // the illuminated percentage from Meeus chapter 46
  var j=dayno(year,month,day,12)+2451543.5;
  var T=(j-2451545.0)/36525;
  var T2=T*T;
  var T3=T2*T;
  var T4=T3*T;
  // Moons mean elongation Meeus first edition
  // var D=297.8502042+445267.1115168*T-0.0016300*T2+T3/545868.0-T4/113065000.0;
  // Moons mean elongation Meeus second edition
  var D=297.8501921+445267.1114034*T-0.0018819*T2+T3/545868.0-T4/113065000.0;
  // Moons mean anomaly M' Meeus first edition
  // var MP=134.9634114+477198.8676313*T+0.0089970*T2+T3/69699.0-T4/14712000.0;
  // Moons mean anomaly M' Meeus second edition
  var MP=134.9633964+477198.8675055*T+0.0087414*T2+T3/69699.0-T4/14712000.0;
  // Suns mean anomaly
  var M=357.5291092+35999.0502909*T-0.0001536*T2+T3/24490000.0;
  // phase angle
  var pa=180.0-D-6.289*sind(MP)+2.1*sind(M)-1.274*sind(2*D-MP)
         -0.658*sind(2*D)-0.214*sind(2*MP)-0.11*sind(D);
  return(rev(pa));
}



function moons(year)
 {
  // Returns the dates for New and Full Moons.
  // Converted from Basic Sky & Telescope, March, 1985
  var moondates=new Array();
  var R1=Math.PI/180;
  var U=false;
  var Y=year;
  var K0=Math.floor((Y-1900)*12.3685);
  var T=(Y-1899.5)/100;
  var T2=T*T;
  var T3=T*T*T;
  var J0=2415020+29*K0;
  var F0=0.0001178*T2-0.000000155*T3;
  F0=F0+0.75933+0.53058868*K0;
  F0=F0-0.000837*T-0.000335*T2;
  var M0=K0*0.08084821133;
  M0=360*(M0-Math.floor(M0))+359.2242;
  M0=M0-0.0000333*T2;
  M0=M0-0.00000347*T3;
  var M1=K0*0.07171366128;
  M1=360*(M1-Math.floor(M1))+306.0253;
  M1=M1+0.0107306*T2;
  M1=M1+0.00001236*T3;
  var B1=K0*0.08519585128;
  B1=360*(B1-Math.floor(B1))+21.2964;
  B1=B1-0.0016528*T2;
  B1=B1-0.00000239*T3;
  for (var K9=0; K9<=28; K9+=1) {
    var J=J0+14*K9;
    var F=F0+0.765294*K9;
    var K=K9/2;
    var M5=(M0+K*29.10535608)*R1;
    var M6=(M1+K*385.81691806)*R1;
    var B6=(B1+K*390.67050646)*R1;
    F=F-0.4068*Math.sin(M6);
    F=F+(0.1734-0.000393*T)*Math.sin(M5);
    F=F+0.0161*Math.sin(2*M6);
    F=F+0.0104*Math.sin(2*B6);
    F=F-0.0074*Math.sin(M5-M6);
    F=F-0.0051*Math.sin(M5+M6);
    F=F+0.0021*Math.sin(2*M5);
    F=F+0.0010*Math.sin(2*B6-M6);
    J=J+F;
    moondates[K9]=J;
    U=!U;
  }
  return moondates;
}