  Recent galaxy redshift surveys have brought in a large amount of accurate
cosmological data out to redshift 0.3, and future surveys are expected to
achieve a high degree of completeness out to a redshift exceeding 1.
Consequently, a numerical programme for determining the metric of the universe
from observational data will soon become practical; and thereby realise the
ultimate application of Einstein's equations. Apart from detailing the cosmic
geometry, this would allow us to verify and quantify homogeneity, rather than
assuming it, as has been necessary up to now, and to do that on a metric level,
and not merely at the mass distribution level. This paper is the beginning of a
project aimed at such a numerical implementation. The primary observational
data from our past light cone consists of galaxy redshifts, apparent
luminosities, angular diameters and number densities, together with source
evolution functions, absolute luminosities, true diameters and masses of
sources. Here we start with the simplest case, that of spherical symmetry and a
dust equation of state, and execute an algorithm that determines the unknown
metric functions from this data. We discuss the challenges of turning the
theoretical algorithm into a workable numerical procedure, particularly
addressing the origin and the maximum in the area distance. Our numerical
method is tested with several artificial data sets for homogeneous and
inhomogeneous models, successfully reproducing the original models. This
demonstrates the basic viability of such a scheme. Although current surveys
don't have sufficient completeness or accuracy, we expect this situation to
change in the near future, and in the meantime there are many refinements and
generalisations to be added.
