  We discuss the linear gravitoelectromagnetic approach used to solve Einstein
equations in the weak-field and slow-motion approximation, which is a powerful
tool to explain, by analogy with electromagnetism, several gravitational
effects in the Solar System, where the approximation holds true. In particular,
we discuss the analogy according to which Einstein equations can be written as
Maxwell-like equations and focus on the definition of the
gravitoelectromagnetic fields in non stationary conditions. Furthermore, we
examine to what extent, starting from a given solution of Einstein equations,
gravitoelectromagnetic fields can be used to describe the motion of test
particles using a Lorentz-like force equation
