AzEl_to_RaDec

Astronomy.AzEl_to_RaDec(azimuth, elevation, latitude, longitude, dateUTtime)

Convert azimuth and elevation to CIRS right ascension and declination

:param azimuth : east from north (clockwise) in degrees :type azimuth : float

:param elevation : above the horizon in degrees :type elevation :

:param latitude : above the equator, in degrees :type latitude : float

:param longitude : west from Greenwich :type longitude : float

:param dateUTtime : (year, DOY) tuple, with fractional day of year :type dateUTtime : (int, float)

Returns

(RA (hrs), dec (degs))

Notes

Horizon coordinates to celestial

HA and decl. define a point on the sky with respect to the local meridian, which corresponds to a RA equal to the local sidereal time. It doesn’t matter what the observer’s longitude is. The relationship between the RA of the sky point and the LST stays the same. So we can perform the calculation for longitude 0.

LST is the ST at Greenwich (long 0 deg) minus the west longitude of the local meridian:

LST = GST - long
                hr

HA is positive to the west, so is the LST minus the RA of the point in the sky:

HA = LST - RA

Consider a hypothetical observer on the Earth at longitude zero and the latitude of the actual observer. The sidereal time at the hypothetical observer’s location is the Greenwich sidereal time, which is the actual observer’s LST plus the west longitude. Then the HA at the actual observer’s position is the HA at the hypothetical observer’s position minus the actual observer’s longitude in hours:

HA    = HA    - long
  act     hyp       hr

Given the azimuth, elevation and time we compute the RA and dec of the sky position with respect to the hypothetical observer, and then the HA:

az, el, lat, time --> RA   ,dec
                        hyp

HA    = GST - RA
  hyp           hyp

The RA of the same az,el w.r.t. the actual observer is then:

RA    = RA    - long
  act     hyp       hr

HA    = GST - RA    - long
  act           hyp       hr
      = GST - RA
                act