# Why are the spherical and cartesian galactic coordinates in the ATNF Pulsar Catalogue different?

I am trying to relate Galactic Latitude (b) and Longitude (l) (spherical coordinates) to galactic cartesian x,y,z coordinates in the ATNF pulsar catalog.

This query shows some sample data with G_l, G_b, XX, YY, and ZZ; excerpt:

------------------------------------------------------------------
#     NAME                     Gl     Gb     ZZ     XX     YY
(deg)  (deg)  (kpc)  (kpc)  (kpc)
------------------------------------------------------------------
1     J0002+6216    cwp+17     117.33 -0.07  -0.00  0.00   8.50
2     J0006+1834    cnt96      108.17 -42.98 -0.59  0.60   8.70
3     J0007+7303    aaa+09c    119.66 10.46  0.25   1.20   9.18


The description of the variables from the ATNF documentation are as follows:

GL:          Galactic longitude (degrees)
GB:          Galactic latitude (degrees)
[...]
ZZ:          Distance from the Galactic plane, based on Dist
XX:          X-Distance in X-Y-Z Galactic coordinate system (kpc)
YY:          Y-Distance in X-Y-Z Galactic coordinate system (kpc)


My understanding is that these variables should be related by the following equations:

• tan(G_L) = YY/XX
• tan(G_b) = XX/ZZ

However, when I test this assumption my calculated values are very different:

I have tried exploring the possibility that the x,y,z coordinate system may be oriented differently than I expect, but I can find no orientation that yields similar results for G_l or G_b:

Where could I have gone wrong? I feel like I am losing my mind not being able to convert these with simple trig.

The ATNF Pulsar Catalogue's galactic longitude and latitude are heliocentric, but the origin of their rectangular coordinates is near the center of our galaxy.

The catalogue documentation, section 6. Distances, says:

The Galactocentric coordinate system (XX, YY, ZZ) is right-handed with the Sun at (0.0, 8.5 kpc, 0.0) and the ZZ axis directed toward the north Galactic pole.

From a heliocentric point of view (U, V, W) = (8.5 - YY, XX, ZZ). Then $\tan{l} = V / U$ and $\tan{b} = W / \sqrt{U^2 + V^2}$ as you'd expect.

• Aha, thank you! A few notes in case anyone runs into similar troubles: 1. my YY and XX column labels are swapped (oops). 2. This answer unconventionally maps yxz to uvw, more typically it is xyz to uvw 3. The last equation for G_b should be tan(b) = 90 - W/sqrt(u^2+v^2) Mar 30, 2018 at 14:52