It looks like those figures come from a model rather than empirical
measurements.
Follow the Javascript functions.
update references AutoCalculateAngles, which references CalculateAngles,
which references moon_angles.
function moon_angles(d,SiteLon,SiteLat){ var
SunSouth,HourAngle,SIDEREALTIME,SatAz,SunSat,Tst,SatelliteAzimuth,pi,NewRA
var
w,a,e,M,L,N,oblecl,E,x,y,r,v,sunlon,z,xequat,yequat,zequat,RA,Decl,GMST0,UT ,SIDTIME,HA
var
SunElevation,xhor,yhor,zhor,SunSatElevationDifference,SatElevation,Geometri cElevation
pi=Math.PI; var angles= new Array(); var sunangles=new Array(); var
E0,E1,xeclip,yeclip,zeclip,Lm,Ls,Ms,Mm,D,F var
P_lon1,P_lon2,P_lon3,P_lon4,P_lon5,P_lon6,P_lon7,P_lon8,P_lon9,P_lon10,P_lo n11,P_lon12
var
P_lat1,P_lat2,P_lat3,P_lat4,P_lat5,P_lat,P_lon,P_moondistance,Moon_RA,Moon_ Decl
var
xh,yh,zh,MoonAzimuth,MoonElevation,Iterations,E_error,Ebeforeit,Eafterit,E_ ErrorBefore
//*********CALCULATE Moon DATA *********************
N=125.1228-0.0529538083*d; i=5.1454; w=318.0634 + 0.1643573223 * d ; //OK
a=60.2666; //a=6.6107940559473451507806351067866; //a=0; //a=149476000;
//km average distance e= 0.054900; M= 115.3654 + 13.0649929509 * d;
w=Rev(w); M=Rev(M); N=Rev(N); // ok so far //alert('N='+N+'\n i='+i+'\n
w='+w+'\n a='+a+'\n e='+e+'\n M='+M); E=M+
(180/pi)*e*Math.sin(Radians(M))*( 1+e * Math.cos(Radians(M)) ); E=Rev(E);
// OK Ebeforeit=E; // now iterate until difference between E0 and E1 is
less than 0.005_deg // use E0, calculate E1 Iterations=0; E_error=9; while
((E_error>0.0005) && (Iterations<20)) // ok - itererer korrekt {
Iterations=Iterations+1; E0=E; E1= E0- (E0-
(180/pi)*e*Math.sin(Radians(E0)) -M ) /( 1-e * Math.cos(Radians(E0))) ;
//alert('1 E0='+E0+'\nNew E1='+E1+'\nE='+E+'\Diff='+Rev(E0-E1)); E=Rev(E1);
//alert(Math.abs(E-E0)); Eafterit=E; if (E<E0) E_error=E0-E else
E_error=E-E0; if (E<Ebeforeit) E_ErrorBefore=Ebeforeit-E else
E_ErrorBefore=E-Ebeforeit; window.status="Iterations="+Iterations+" Moon
eccentric anomaly error before
iterations="+formatvalue(E_ErrorBefore,7)+"_deg after
iterations="+E_error+"_deg"; if (Iterations>10) window.status="Number of
Iterations more than 10="+Iterations+" Ebefore="+Ebeforeit+"
Eafter="+Eafterit+" E_errorbefore="+formatvalue(E_ErrorBefore,7)+"
E_errorafter"+E_error; } //alert(E); x= a*(Math.cos(Radians(E)) -e) ; y=
a*Math.sin(Radians(Rev(E)))*Math.sqrt(1-e*e); r=Math.sqrt(x*x+y*y);
v=Deg(Math.atan2(y,x)); //alert('E='+E); // ok så langt sunlon=Rev(v+w); //
trolig ok x=r*Math.cos(Radians(sunlon)); y=r*Math.sin(Radians(sunlon));
z=0; xeclip=r*( Math.cos(Radians(N))*Math.cos(Radians(v+w)) -
Math.sin(Radians(N)) * Math.sin(Radians(v+w))*Math.cos(Radians(i)) );
yeclip=r*( Math.sin(Radians(N))*Math.cos(Radians(v+w)) +
Math.cos(Radians(N)) * Math.sin(Radians(v+w))*Math.cos(Radians(i)) );
zeclip=r*Math.sin(Radians(v+w))*Math.sin(Radians(i));
//alert('xeclip='+xeclip+'\nyeclip='+yeclip+'\nzeclip='+zeclip+'\Long='+Rev (v+w));
//ok so far moon_longitude=Rev(Deg(Math.atan2(yeclip,xeclip))); // OK
moon_latitude=Deg(Math.atan2(zeclip,Math.sqrt(xeclip*xeclip +yeclip*yeclip
) )); // trolig OK // Now add Perbutations, we actually need Sun mean
longitude and Suns mean anomaly
//alert('moon_longitude='+moon_longitude+'\nmoon_latitude='+moon_latitude+' \nr='+r);
sunangles=sun_angles(d,SiteLon,SiteLat); Ls=sunangles[11]; // Suns mean
longitude er feil Ms=sunangles[6]; // Suns mean anomaly Mm=Rev(M); // Moons
mean anomaly Lm=Rev(N+w+M) ; // moon mean longitude D=Rev(Lm-Ls); //Moons
mean elongation F=Rev(Lm-N); //Moons argument of latitude
//alert('Ms='+Ms+'\nMm='+Mm+'\nLs='+Ls+'\nLm='+Lm+'\nD='+D+'\nF='+F); // ok
so far // Perbutations Moons Longitude P_lon1= -1.274 * Math.sin(Radians(Mm
- 2*D)); // (Evection) P_lon2= +0.658 * Math.sin(Radians(2*D)); //
(Variation) P_lon3= -0.186 * Math.sin(Radians(Ms) ) ; // (Yearly equation)
P_lon4= -0.059 * Math.sin(Radians(2*Mm - 2*D)); P_lon5= -0.057 *
Math.sin(Radians(Mm - 2*D + Ms)); P_lon6= +0.053 * Math.sin(Radians(Mm +
2*D)); P_lon7= +0.046 * Math.sin(Radians(2*D - Ms)); P_lon8= +0.041 *
Math.sin(Radians(Mm - Ms)); P_lon9= -0.035 * Math.sin(Radians(D) ); //
(Parallactic equation) P_lon10= -0.031 * Math.sin(Radians(Mm + Ms));
P_lon11= -0.015 * Math.sin(Radians(2*F - 2*D)); P_lon12= +0.011 *
Math.sin(Radians(Mm - 4*D)); // Perbutations Moons Latitude P_lat1=-0.173 *
Math.sin(Radians(F - 2*D)); P_lat2=-0.055 * Math.sin(Radians(Mm - F -
2*D)); P_lat3=-0.046 * Math.sin(Radians(Mm + F - 2*D)); P_lat4=+0.033 *
Math.sin(Radians(F + 2*D)); P_lat5=+0.017 * Math.sin(Radians(2*Mm + F));
P_lon=P_lon1+P_lon2+P_lon3+P_lon4+P_lon5+P_lon6+P_lon7+P_lon8+P_lon9+P_lon1 0+P_lon11+P_lon12;
P_lat=P_lat1+P_lat2+P_lat3+P_lat4+P_lat5; P_moondistance=-0.58 *
Math.cos(Radians(Mm - 2*D)) -0.46 * Math.cos(Radians(2*D));
//alert('P_lon='+P_lon+'\nP_lat='+P_lat+'\nP_moondistance='+P_moondistance) ;
moon_longitude=moon_longitude+P_lon; moon_latitude=moon_latitude+P_lat;
r=r+P_moondistance;
//alert('moon_longitude='+moon_longitude+'\nmoon_latitude='+moon_latitude+' \nmoondistance='+r);
// OK so far // now calculate RA & Decl // get the Eliptic coordinates
xh=r*Math.cos(Radians(moon_longitude))*Math.cos(Radians(moon_latitude));
yh=r*Math.sin(Radians(moon_longitude))*Math.cos(Radians(moon_latitude));
zh=r*Math.sin(Radians(moon_latitude)); // rotate to rectangular equatorial
coordinates xequat=xh;
yequat=yh*Math.cos(Radians(sunangles[9]))-zh*Math.sin(Radians(sunangles[9]) );
zequat=yh*Math.sin(Radians(sunangles[9]))+zh*Math.cos(Radians(sunangles[9]) );
Moon_RA=Rev(Deg(Math.atan2(yh,xh))); // OK
Moon_Decl=Deg(Math.atan2(zh,Math.sqrt(xh*xh + yh*yh ) )); // trolig OK
Moon_RA=Rev(Deg(Math.atan2(yequat,xequat))); // OK
Moon_Decl=Deg(Math.atan2(zequat,Math.sqrt(xequat*xequat + yequat*yequat )
)); // trolig OK
//alert('moon_RA='+Moon_RA+'\nMoon_Decl='+Moon_Decl+'\nmoondistance='+r+'\n Obecl='+sunangles[9]);
GMST0=(Ls+180); //*********CALCULATE TIME *********************
UT=d-Math.floor(d); //alert("UT="+UT); SIDEREALTIME=GMST0+UT*360+SiteLon;
// ok HourAngle=SIDEREALTIME-Moon_RA; // trolig ok
x=Math.cos(HourAngle*pi/180) * Math.cos(Moon_Decl*pi/180);
y=Math.sin(HourAngle*pi/180) * Math.cos(Moon_Decl*pi/180);
z=Math.sin(Moon_Decl*pi/180); xhor=x*Math.sin(SiteLat*pi/180) -
z*Math.cos(SiteLat*pi/180);
//alert('sitelat='+SiteLat+'\nsitelon='+SiteLon); yhor=y;
zhor=x*Math.cos(SiteLat*pi/180) + z*Math.sin(SiteLat*pi/180);
MoonElevation=Deg( Math.asin(zhor)); // ok regner ikke måne elevation helt
riktig... MoonElevation=MoonElevation- Deg(Math.asin( 1/r *
Math.cos(Radians(MoonElevation)) )); GeometricElevation=MoonElevation;
MoonElevation=ElevationRefraction(MoonElevation); // atmospheric refraction
MoonAzimuth=Deg(Math.atan2(yhor,xhor)); angles[0]=MoonElevation; if
(SiteLat<0) angles[1]=MoonAzimuth+180 // added 180 deg else
angles[1]=MoonAzimuth+180; //alert("Moon Raw Az="+MoonAzimuth);
//alert('Moon Azimuth='+angles[1]+'\nMoon Elevation='+MoonElevation+'
Geometric elevation='+GeometricElevation); angles[2]=Moon_Decl;
angles[3]=moon_longitude; angles[4]=Moon_RA; angles[5]=Rev(GMST0);
angles[6]=Rev(M); angles[7]=Rev(w); angles[8]=Rev(e);
angles[9]=Rev(oblecl); angles[10]=GeometricElevation;
angles[11]=moon_latitude; angles[12]=MoonElevation; angles[13]=r;
return(angles); }
So it looks like this website has the code you want to calculate the
positions of the sun and the moon.
Tom
