The reconstruction of the orbital evolution of the propeller structure Blériot orbiting in Saturn ’ s A ring from recurrent observations in Cassini ISS images yielded a considerable offset motion from the expected Keplerian orbit ( 27 ) .
This offset motion can be composed by three sinusoidal harmonics with amplitudes and periods of 1845 , 152 , 58 km and 11.1 , 3.7 and 2.2 years , respectively ( 20 ) .
In this paper we present results from N-Body simulations , where we integrated the orbital evolution of a moonlet , which is placed at the radial position of Blériot under the gravitational action of the Saturnian satellites .
Our simulations yield , that especially the gravitational interactions with Prometheus , Pandora and Mimas is forcing the moonlet to librate with the right frequencies , but the libration-amplitudes are far too small to explain the observations .
Thus , further mechanisms are needed to explain the amplitudes of the forced librations – e.g .
moonlet-ring interactions .
Here , we develop a model , where the moonlet is allowed to be slightly displaced with respect to its created gaps , resulting in a breaking point-symmetry and in a repulsive force .
As a result , the evolution of the moonlet ’ s longitude can be described by a harmonic oscillator .
In the presence of external forcings by the outer moons , the libration amplitude gets the more amplified , the more the forcing frequency gets close to the eigenfrequency of the disturbed propeller oscillator .
Applying our model to Blériot , it is possible to reproduce a libration period of 13 years with an amplitude of about \SI 2000 \kilo \meter .