  Context. The orbits of the four small moons in the Pluto-Charon system, Styx,
Nix, Kerberos and Hydra, are circumbinary, as the former form a binary dwarf
planet. Consequently, the orbit of each one of them is characterized by a
number of frequencies, arising by the central binary and the mutual
gravitational interactions. Aims. In this work, we identify the most prominent
of these forced frequencies using Fast Fourier Transformations. Methods. Two
methods are implemented, a semi-analytic and a numerical one, and comparisons
are being made. Results. The results indicate that as a first approximation,
moon orbits may well be modelled as the superposition of a series of inevitable
oscillations, induced by Pluto and Charon, deviating from circular ones, even
if the eccentricity is set to zero. Moreover, the mutual gravitational effects
are significant in their long term evolution, especially for the lighter moons
Styx and Kerberos, activating modes that dominate the low-frequency region of
the power spectrum. This becomes evident through the comparison of simulations
where only one moon is included along with the binary dwarf planet and
simulations of the entire six-body system. These modes become noticeable over
long integration times and may affect the orbits of the lighter moons of the
system.
