The secular approximation of the hierarchical three body systems has been proven to be very useful in addressing many astrophysical systems, from planets, stars to black holes. In such a system two objects are on a tight orbit, and the tertiary is on a much wider orbit. Here we study the dynamics of a system by taking the tertiary mass to zero and solve the hierarchical three body system up to the octupole level of approximation. We find a rich dynamics that the outer orbit undergoes due to gravitational perturbations from the inner binary. The nominal result of the precession of the nodes is mostly limited for the lowest order of approximation, however, when the octupole-level of approximation is introduced the system becomes chaotic, as expected, and the tertiary oscillates below and above 90 • , similarly to the non-test particle flip behavior (e.g., Naoz 2016). We provide the Hamiltonian of the system and investigate the dynamics of the system from the quadrupole to the octupole level of approximations. We also analyze the chaotic and quasi-periodic orbital evolution by studying the surfaces of sections. Furthermore, including general relativity, we show case the long term evolution of individual debris disk particles under the influence of a far away interior eccentric planet. We show that this dynamics can naturally result in retrograde objects and a puffy disk after a long timescale evolution (few Gyr) for initially aligned configuration.

Aims. We analyze the dynamics of small body reservoirs under the effects of an eccentric inner giant planet resulting from a planetary scattering event around a 0.5 M ⊙ star. Methods. First, we used a semi-analytical model to define the properties of the protoplanetary disk that lead to the formation of three Jupiter-mass planets. Then, we carried out N-body simulations assuming that the planets are close to their stability limit together with an outer planetesimal disk. In particular, the present work focused on the analysis of N-body simulations in which a single Jupiter-mass planet survives after the dynamical instability event.Results. Our simulations produce outer small body reservoirs with particles on prograde and retrograde orbits, and other ones whose orbital plane flips from prograde to retrograde and back again along their evolution ("Type-F particles"). We find strong correlations between the inclination i and the ascending node longitude Ω of Type-F particles. First, Ω librates around 90 • or/and 270 • . This property represents a necessary and sufficient condition for the flipping of an orbit. Moreover, the libration periods of i and Ω are equal and they are out to phase by a quarter period. We also remark that the larger the libration amplitude of i, the larger the libration amplitude of Ω. We analyze the orbital parameters of Type-F particles immediately after the instability event (post IE orbital parameters), when a single Jupiter-mass planet survives in the system. Our results suggest that the orbit of a particle can flip for any value of its post IE eccentricity, although we find only two Type-F particles with post IE inclinations i 17 • . Finally, our study indicates that the minimum value of the inclination of the Type-F particles in a given system decreases with an increase in the eccentricity of the giant planet.

The observations of the surfaces of the mid-sized Saturnian satellites made by Cassini-Huygens mission have shown a variety of features that allows study of the processes that took place and are taking place on those worlds. Research of the Saturnian satellite surfaces has clear implications not only for Saturn's history and Saturn's surroundings, but also for the Solar System. Crater counting from high definition images is very important and could serve for the determination of the age of the surfaces. In a recent paper, we have calculated the production of craters on the mid-sized Saturnian satellites by Centaur objects considering the current configuration of the Solar System. Also, we have compared our results with crater counts from Cassini images by other authors and we have noted that the number of observed small craters is less than our calculated theoretical number. In this paper we estimate the age of the surface for each observed terrain on each mid-sized satellite of Saturn. All the surfaces analyzed appear to be old with the exception of Enceladus. However, we have noticed that since there are less observed small craters than calculated (except on Iapetus), this results in younger ages than expected. This could be the result of efficient endogenous or exogenous process(es) for erasing small craters and/or crater saturation at those sizes. The size limit from which the observed number of smaller craters is less than the calculated is different for each satellite, possibly indicating processes that are unique to each, but other potential common explanations for this paucity of small craters would be crater saturation and/or deposition of Ering particles. These processes are also suggested by the findings that the smaller craters are being preferentially removed, and the erasure process is gradual.On Enceladus, only mid and high latitude plains have remnants of old terrains; the other regions could be young. In particular, the regions near the South Polar Terrain could be as young as 50 Myrs old. On the contrary for Iapetus, all the surface is old and it notably registers a primordial source of craters. As the crater size is decreased, it would be perceived to approach saturation until D 2 km-craters, where saturation is complete.