Calculating azimuth from equatorial coordinates
I try to get the azimuth of an object from its equatorial coordinates using this formula:
$a = \arctan2(\sin(θ - α), \sin φ * \cos(θ - α) - \cos φ * \tan δ)$
Where
φ = geographic latitude of the observer (here: 0°)
θ = sidereal time (here: 0°)
δ = declination
α = right ascension
I made two JavaScript functions to implement this calculation:
obliq = deg2rad(23.44); // obliquity of ecliptic
lat2 = deg2rad(0); // observer's latitude
lmst = deg2rad(0); // siderial time
function equatorial(lat, lon) {
// returns equatorial from ecliptic coordinates
dec = Math.asin( Math.cos(obliq) * Math.sin(lat) + Math.sin(obliq) *
Math.cos(lat) * Math.sin(lon));
ra = Math.atan2(Math.cos(obliq) * Math.sin(lon) - Math.sin(obliq) * Math.tan(lat),
Math.cos(lon));
ra += 2 * Math.PI * (ra < 0);
return [dec, ra];
}
function horizontal(lat, lon) {
// returns horizontal from ecliptic coordinates
coords = equatorial(lat, lon);
dec = coords[0]; // δ
ra = coords[1]; // α
alt = Math.asin(Math.sin(lat2) * Math.sin(dec) + Math.cos(lat2) *
Math.cos(dec) * Math.cos(lmst - ra));
azm = Math.atan2(Math.sin(lmst - ra), Math.sin(lat2) * Math.cos(lmst - ra) -
Math.cos(lat2) * Math.tan(dec));
azm += 2 * Math.PI * (azm < 0);
return [alt, azm];
}
I cannot see any error, but I get strange results for azimuth (a) as can be seen in this table (the other values seem correct):
λ δ α h a
0 0.0000 0.0000 90.0000 0.0000
15 5.9094 13.8115 75.0000 246.5600
30 11.4723 27.9104 60.0000 246.5600
45 16.3366 42.5357 45.0000 246.5600
60 20.1510 57.8186 30.0000 246.5600
75 22.5962 73.7196 15.0000 246.5600
90 23.4400 90.0000 0.0000 246.5600
105 22.5962 106.2804 -15.0000 246.5600
120 20.1510 122.1814 -30.0000 246.5600
135 16.3366 137.4643 -45.0000 246.5600
150 11.4723 152.<PHONE_NUMBER>.0000 246.5600
165 5.9094 166.1885 -75.0000 246.5600
180 0.0000 180.0000 -90.0000 248.3079
195 -5.9094 193.8115 -75.0000 66.5600
210 -11.4723 207.9104 -60.0000 66.5600
225 -16.3366 222.5357 -45.0000 66.5600
240 -20.1510 237.8186 -30.0000 66.5600
255 -22.5962 253.7196 -15.0000 66.5600
270 -23.4400 270.0000 -0.0000 66.5600
285 -22.5962 286.2804 15.0000 66.5600
300 -20.1510 302.1814 30.0000 66.5600
315 -16.3366 317.4643 45.0000 66.5600
330 -11.4723 332.<PHONE_NUMBER>.0000 66.5600
345 -5.9094 346.1885 75.0000 66.5600
360 -0.0000 360.0000 90.0000 68.3079
Does anyone see the error? Thank you. 371