Astronomy: Transform coordinates from horizon to equatorial

Question

I'm using Mathematica 10. Giving a longitude & latitude on Earth, giving a local time, how can I transform Horizon Coordinte (az , alt) to Equatorial Coordinate (RA , DEC). Use function so I can change longitude, latitude & time when I call it.

Answer 1

Given the local sidereal time (LST) and local latitude you can convert (az,alt) to (ra,dec) with the following function (Input and Output are in degree (not radians!)):

AzElToRADec[{azimuth_, elevation_}, lattitude_, LST_] := 
 Module[{sinDec, cosLHA, sinLHA, Dec, RA, LHA}, 
  sinDec = Sin[elevation Degree] Sin[lattitude Degree] + 
  Cos[elevation Degree] Cos[lattitude Degree] Cos[azimuth Degree];
  Dec = ArcSin[sinDec]/Degree;
  sinLHA = -((Sin[azimuth Degree] Cos[elevation Degree])/Cos[Dec Degree]);
  cosLHA = (Sin[elevation Degree] - Sin[lattitude Degree] Sin[Dec Degree])/(Cos[Dec Degree] Cos[lattitude Degree]);
  LHA = ArcTan[cosLHA, sinLHA]/Degree;
  RA = Mod[LST - LHA, 360];
  {RA, Dec}]   

To get the LST, see this post. The conversion is explained here.

Example:

Plot[AzElToRADec[{0, 30}, 0, x*15], {x, 0, 48},  AxesLabel -> {"LST (hrs)", "angle"}]