  For metrology, geodesy and gravimetry in space, satellite based instruments
and measurement techniques are used and the orbits of the satellites as well as
possible deviations between nearby ones are of central interest. The
measurement of this deviation itself gives insight into the underlying
structure of the spacetime geometry, which is curved and therefore described by
the theory of general relativity (GR). In the context of GR, the deviation of
nearby geodesics can be described by the Jacobi equation that is a result of
linearizing the geodesic equation around a known reference geodesic with
respect to the deviation vector and the relative velocity. We review the
derivation of this Jacobi equation and restrict ourselves to the simple case of
the spacetime outside a spherically symmetric mass distribution and circular
reference geodesics to find solutions by projecting the Jacobi equation on a
parallel propagated tetrad as done by Fuchs. Using his results, we construct
solutions of the Jacobi equation for different physical initial scenarios
inspired by satellite gravimetry missions and give a set of parameter together
with their precise impact on satellite orbit deviation. We further consider the
Newtonian analog and construct the full solution, that exhibits a similar
structure, within this theory.
