  We extend and apply a model-independent analysis method developed earlier by
Daly & Djorgovski to new samples of supernova standard candles, radio galaxy
and cluster standard rulers, and use it to constrain physical properties of the
dark energy as functions of redshift. Similar results are obtained for the
radio galaxy and supernova data sets. The first and second derivatives of the
distance are compared directly with predictions in a standard model based on
General Relativity. The good agreement indicates that General Relativity
provides an accurate description of the data on look-back time scales of about
ten billion years. The first and second derivatives are combined to obtain the
acceleration parameter, assuming only the validity of the Robertson-Walker
metric, independent of a theory of gravity and of the physical nature of the
dark energy. The acceleration of the universe at the current epoch is indicated
by the analysis. The effect of non-zero space curvature on q(z) is explored. We
solve for the pressure, energy density, equation of state, and potential and
kinetic energy of the dark energy as functions of redshift assuming that
General Relativity is the correct theory of gravity, and the results indicate
that a cosmological constant in a spatially flat universe provides a good
description of each of these quantities over the redshift range from zero to
about one. We define a new function, the dark energy indicator, in terms of the
first and second derivatives of the coordinate distance and show how this can
be used to measure deviations of w from -1 and to obtain a new and independent
measure of Omega.
