  The basic elements of the relativistic positioning systems in a
two-dimensional space-time have been introduced in a previous work [Phys. Rev.
D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by
two geodesic emitters, have been considered in a flat space-time. Here, we want
to show in what precise senses positioning systems allow to make {\em
relativistic gravimetry}. For this purpose, we consider stationary positioning
systems, constituted by two uniformly accelerated emitters separated by a
constant distance, in two different situations: absence of gravitational field
(Minkowski plane) and presence of a gravitational mass (Schwarzschild plane).
The physical coordinate system constituted by the electromagnetic signals
broadcasting the proper time of the emitters are the so called {\em emission
coordinates}, and we show that, in such emission coordinates, the trajectories
of the emitters in both situations, absence and presence of a gravitational
field, are identical. The interesting point is that, in spite of this fact,
particular additional information on the system or on the user allows not only
to distinguish both space-times, but also to complete the dynamical description
of emitters and user and even to measure the mass of the gravitational field.
The precise information under which these dynamical and gravimetric results may
be obtained is carefully pointed out.
