  Distance-redshift diagrams probe expansion history of the Universe. We show
that the stellar mass-binding energy (massE) relation of galaxies proposed in
our previous study offers a new distance ruler at cosmic scales. By using
elliptical galaxies in the main galaxy sample of the Sloan Digital Sky Survey
Data Release 7, we construct a distance-redshift diagram over the redshift
range from 0.05 to 0.2 with the massE ruler. The best-fit dark energy density
is 0.675+-0.079 for flat Lambda-CDM, consistent with those by other probes. At
the median redshift of 0.11, the median distance is estimated to have a
fractional error of 0.34%, much lower than those by supernova (SN) Ia and
baryonic acoustic oscillation (BAO) and even exceeding their future capability
at this redshift. The above low-z measurement is useful for probing dark energy
that dominates at the late Universe. For a flat dark energy equation of state
model (flat wCDM), the massE alone constrains w to an error that is only a
factor of 2.2, 1.7 and 1.3 times larger than those by BAO, SN Ia, and cosmic
microwave background (CMB), respectively.
