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The Faber-Jackson relation (FJR) is a relation between the luminosity of an elliptical galaxy and its central stellar velocity dispersion. It is something like a "Tully-Fisher relation for elliptical galaxies", serving as a method of estimating the distance to a galaxy: the velocity dispersion can be derived from spectrography, by observing the effects of redshift and blue shift on spectral lines of the stars, and given that, the relation yields a rough absolute magnitude of the galaxy. Having both the absolute and apparent magnitude of the galaxy, the distance can be estimated.
A more recently-observed, useful relation, the D-σ relation (aka Sigma-D relation) associates the diameter of an elliptical galaxy with its velocity dispersion. The fundamental plane is an even later development: a relation between radius, velocity dispersion, and surface brightness, which may yield an even better distance estimate through use of an additional observable.