  The shape of the angular power spectrum of galaxies in the linear regime is
defined by the horizon size at the matter-radiation equality. When calibrated
by cosmic microwave background measurements, the shape of the clustering
spectrum can be used as a standard ruler to estimate angular diameter distance
as a function of redshift at which galaxy clustering is measured. We apply the
proposed cosmological test of Cooray et al. (2001) to a recent set of luminous
red galaxy angular clustering spectra from the Sloan Digital Sky Survey between
redshifts of 0.2 and 0.6. Using the overall shape of the clustering power
spectrum in the linear regime, w e measure comoving angular diameter distances
to eight redshift bins by marginalizing over the bias factors that determine
the overall amplitude of the clustering spectrum in each of the bins. The
Hubble constant consistent with these distance estimates is 68.5^+6.7_-6.1 km
s^-1 Mpc-1 at the 68% confidence level. We comment on the expected improvements
with future surveys and the potential to measure dark energy parameters with
this method.
