For S and S' in standard configuration, the Galilean transformations are:
x' = x - vt, y' = y, z' = z, t' = t
From the Lorentz transformations for v << c:
x' = x - vt, y' = y, z' = z, t' = t - vx/c^2
So it looks as if the Galilean transformations become increasingly accurate for:
vx -> 0, v << c
And exact for v = 0 for all x.
Yet, all text books I've come across state that the Galilean transformatons become more accurate for the condition v << c only.
So what are the conditions under which the Galilean transformations become more accurate and why?