# Transforming radio sources in a T-RECS catalogue from one field to another

I have sources that I extracted from The Tiered Radio Extragalactic Continuum Simulation (T-RECS) catalogue for a deep field. I use these sources to generate a sky model at different fields within a given field-of-view (fov). Imaging the sky model results in an 'elongated' fov, which suggests that I did not compute the RA correctly using the cosine declination rule to account for the angular separation.

For a field centre of (ra = 00h00m00s, dec = 00d00m00s) and a fov of 60 arcmin, below is the resulting image, and for a field centre of (ra = 15h04m00s, dec = -60d00m00s)--same fov as above, below is the resulting image. With my little understanding, I have correctly applied the cosine(declination) rule but it seems that during the transformation, the angular separation between the original sources to a new field was not preserved, hence the distortion seen on the second image.

Below is a code snippet of how I am calculating the ra and dec values for the new field given the longitudes and latitudes extracted from the catalogue. I seek help in understanding what I am doing wrong. Is the problem my logic or I am missing some fundamentals?

from astropy import units as u
from astropy.table import Table
from astropy.coordinates import SkyCoord, Angle

fov = Angle(60, unit=u.arcmin)

field_centre = SkyCoord('15 04 00 -60 00 00', unit=(u.hourangle, u.deg))

cat_centre = SkyCoord(0.0, 0.0, unit=u.deg)

cat_source_coords = SkyCoord(cat['longitudes'], cat['latitudes'], unit=u.deg)

separations = cat_centre.separation(cat_sources)

position_angles = cat_centre.position_angle(cat_sources)

source_offsets = field_centre.directional_offset_by(pos_angles, separations)

ra_deltas = source_offsets.ra - field_centre.ra

dec_deltas = source_offsets.dec - field_centre.dec

model_dec = field_centre.dec.deg + dec_deltas.deg

model_ra = (field_centre.ra.deg + ra_deltas.deg * np.cos(np.radians(model_dec))) % 360


Since the directional_offset_by() gives the new positions of the shifted sources of the catalogue based on the new field centre, there is no need to calculate the new change in both declination and right ascension. One just simple need to compute the correction for right ascension (RA) using the cosine of declination rule by simply dividing the new RA by the new DEC as follows;
model_dec = source_offsets.dec.deg