  Peculiar motion of galaxies probes the structure growth in the Universe. In
this study we employ the galaxy stellar mass-binding energy (massE) relation
with only two nuisance parameters to build the largest peculiar-velocity (PV)
catalog to date, consisting of 229,890 ellipticals from the main galaxy sample
(MGS) of the Sloan Digital Sky Survey (SDSS). We quantify the distribution of
the massE-based distances in individual narrow redshift bins (dz=0.005), and
then estimate the PV of each galaxy based on its offset from the Gaussian mean
of the distribution. As demonstrated with the Uchuu-SDSS mock data, the derived
PV and momentum power spectra are insensitive to accurate calibration of the
massE relation itself, enabling measurements out to a redshift of 0.2, well
beyond the current limit of z=0.1 using other galaxy scaling laws. We then
measure the momentum power spectrum and demonstrate that it remains almost
unchanged if varying significantly the redshift bin size within which the
distance is measured, as well as the intercept and slope of the massE relation,
respectively. By fitting the spectra using the perturbation theory model with
four free parameters, f{\sigma}8 is constrained to f{\sigma}8
=0.459+0.068-0.069 over {\Delta}z=0.02-0.2, 0.416+0.074-0.076 over
{\Delta}z=0.02-0.1 and 0.526+0.133-0.143 over {\Delta}z=0.1-0.2. The error of
f{\sigma}8 is 2.1 times smaller than that by the redshift space distortion
(RSD) of the same sample. A Fisher-matrix forecast illustrates that the
constraint on f{\sigma}8 from the massE-based PV can potentially exceed that
from the stage-IV RSD in late universe (z<0.5).
