Figure out the location of celestial objects relative to the Milky Way in x, y, z co-ordinates

Question

I am trying to place various celestial objects the correct distance from the Milky Way, using x, y, z co-ordinates.
So assuming the centre-of-mass of the Milky Way is at 0, 0, 0 - how can I figure out where to place a galaxy or star given it's celestial coordinates?
I'm just an amateur, and pushing 60 years old, so please excuse me if I have something wrong here...

Mike G · Answer

The spherical $(r, l, b)$ can be converted to
rectangular
$(U, V, W)$ as:
$$begin{align}
U &= r cos b cos l \
V &= r cos b sin l \
W &= r sin b
end{align}$$
Using $(r, l, b) = (770 pm 40 ~text{kpc}, 121.2^circ, -21.6^circ)$,
$$begin{align}
U &= -371 mp 19 ~text{kpc} \
V &= ~~~ 612 pm 32 ~text{kpc} \
W &= -283 mp 15 ~text{kpc}
end{align}$$
That's relative to the Sun.
For a position relative to the center of our galaxy,
subtract $8 pm 0.5 ~text{kpc}$ from $U$.

Figure out the location of celestial objects relative to the Milky Way in x, y, z co-ordinates

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