The aim of modern astronomy is to uncover the properties of cosmic sources by measuring their key parameters and deducing their dynamics. Black holes are targets of particular interest for the role they have in understanding the cosmic puzzles and probing the correctness of current theories. Black holes can be considered simply as deep gravitational potential wells; therefore their existence can only be inferred by observing the behavior of the surrounding medium. The latter can be made of gas, dust, star fields, and obviously light, but all suffer tidal strains and deformations which herald, out of the observer's perspective, the black hole's existence and type. Essential tools for the acquisition of this knowledge are the equations of relative acceleration which stand as basic seeds for any physical measurement. We shall revisit them for specific applications, but will always neglect electric charge in our discussion.
Measurements in Schwarzschild space-time
Consider a collection of particles undergoing tidal deformations; we shall deduce how these would be measured by any particle of the collection, taken as a fiducial observer. Let us assume that the test particles of the collection move in spatially circular orbits in Schwarzschild space-time whose metric is given by (8.1). Indeed, the physical measurements which can be made in the rest frame of the fiducial observer in the collection are the most natural to be performed in satellite experiments.