  The electrovacuum around a rotating massive body with electric charge density
is described by its multipole moments (mass moments, mass-current moments,
electric moments, and magnetic moments). A small uncharged test particle
orbiting around such a body moves on geodesics if gravitational radiation is
ignored. The waves emitted by the small body carry information about the
geometry of the central object, and hence, in principle, we can infer all its
multipole moments. Due to its axisymmetry the source is characterized now by
four families of scalar multipole moments: its mass moments $M_l$, its
mass-current moments $S_l$, its electrical moments $E_l$ and its magnetic
moments $H_l$, where $l=0,1,2,...$. Four measurable quantities, the energy
emitted by gravitational waves per logarithmic interval of frequency, the
precession of the periastron (assuming almost circular orbits), the precession
of the orbital plane (assuming almost equatorial orbits), and the number of
cycles emitted per logarithmic interval of frequency, are presented as power
series of the newtonian orbital velocity of the test body. The power series
coefficients are simple polynomials of the various moments.
