Visualizing difference in astropy's cylindrical representation

Question

I'm having trouble understanding why these two approaches have different results:

from astropy import units as u
from astropy.coordinates import SkyCoord

lon, lat, dist_pc = 123.7, -1.4, 1789

# Starting from galactic coordinates
c = SkyCoord(l=lon*u.degree, b=lat*u.degree, distance=dist_pc*u.pc, frame='galactic')
# To cylindrical
c.representation_type = 'cylindrical'
print(c)

# From galactic
c = SkyCoord(l=lon*u.degree, b=lat*u.degree, frame='galactic')
# To (ra, dec)
ra, dec = c.fk5.ra.deg, c.fk5.dec.deg
c = SkyCoord(ra=ra*u.degree, dec=dec*u.degree, distance=dist_pc*u.pc)
# To cylindrical
c.representation_type = 'cylindrical'
print(c)

where the results are:

<SkyCoord (Galactic): (rho, phi, z) in (pc, deg, pc)
    (1788.46596522, 123.7, -43.70916672)>

<SkyCoord (ICRS): (rho, phi, z) in (pc, deg, pc)
    (854.67518315, 14.46690657, 1571.63969513)>

I understand the Galactic results but I can't visualize what the ICRS results represent.

Answer 1

The two frames have different axes. In the galactic frame, the Z axis is perpendicular to the galactic equator. ICRS and its predecessor FK5 are equatorial, with Z axis perpendicular to Earth's equator as of 2000-01-01. The angle between the different Z axes is ~63°. The transformation from one frame to the other is a 3D rotation.

Here is a Stellarium screenshot showing the J2000 equatorial grid in blue and the galactic coordinate grid in brown.