  We argue that the curvature generated by a gravitational field can be used to
calculate the corresponding metric which determines the trajectories of freely
falling test particles. To this end, we present a method to compute the metric
from a given curvature tensor. We use Petrov's classification to handle the
structure and properties of the curvature tensor, and Cartan's structure
equations in an orthonormal tetrad to investigate the differential equations
that relate the curvature with the metric. The second structure equation is
integrated to obtain the explicit expression for the connection $1-$form from
which the components of the orthonormal tetrad are obtained by using the first
structure equation. This opens the possibility of using the curvature of
astrophysical objects like the Earth to determine the position of freely
falling satellites that are used in modern navigation systems.
