  Accurate distances are key to obtaining intrinsic properties of astronomical
objects such as luminosity or size. Globular clusters (GCs) follow a
well-defined relation between their absolute magnitudes and internal stellar
velocity dispersions ($\sigma$), offering an independent way to measure
distances to their host galaxies via high-resolution spectroscopy. This is
reminiscent of the "Faber-Jackson" for elliptical galaxies. However, unlike
galaxies, GCs have a very narrow range of mass-to-light ratios and simple star
formation histories. Here we show that the GC $M_V - \text{log}_{10}(\sigma)$
relation is linear, whose slope is identical for the Milky Way and M31 GC
systems. Based on this, we use 94 Milky Way GCs which have distances from Gaia
parallaxes, or proper-motion dispersion profiles to derive a "GC velocity
dispersion" distance (GCVD) to M31, obtaining $(m-M)_0=24.51\pm0.08$
($d=798\pm28$ kpc), in excellent agreement with independent measurements.
Combining data for these two galaxies to create a fiducial relation using 296
GCs with high-quality measurements, we obtain a zeropoint uncertainty ($\pm
0.06$ mag) corresponding to a distance uncertainty of $\sim3\%$. We then use
GCVD to obtain a distance to the giant elliptical galaxy NGC\,5128 (Centaurus
A), finding $(m-M)_0= 27.95\pm0.09$ ($d=3.89\pm0.16$ Mpc). This is in excellent
agreement with, and in some cases more precise than, literature estimates from
the tip of the red giant branch or surface brightness fluctuations. We apply
GCVD to Local Group galaxies with appropriate data and find good agreement with
literature values even in cases with only one GC velocity dispersion
measurement.
