No abstract

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.

We study the Jupiter family comet (JFC) population assumed to come from the Scattered Disk and transferred to the Jupiter's zone through gravitational interactions with the Jovian planets. We shall define as JFCs those with orbital periods P < 20 yr and Tisserand parameters in the range 2 < T K 3:1, while those comets coming from the same source, but that do not fulfill the previous criteria (mainly because they have periods P > 20 yr) will be called 'non-JFCs'. We performed a series of numerical simulations of fictitious comets with a purely dynamical model and also with a more complete dynamical-physical model that includes besides nongravitational forces, sublimation and splitting mechanisms. With the dynamical model, we obtain a poor match between the computed distributions of orbital elements and the observed ones. However with the inclusion of physical effects in the complete model we are able to obtain good fits to observations. The best fits are attained with four splitting models with a relative weak dependence on q, and a mass loss in every splitting event that is less when the frequency is high and vice versa. The mean lifetime of JFCs with radii R > 1 km and q < 1:5 AU is found to be of about 150-200 revolutions ($10 3 yrÞ. The total population of JFCs with radii R > 1 km within Jupiter's zone is found to be of 450 AE 50. Yet, the population of non-JFCs with radii R > 1 km in Jupiter-crossing orbits may be $4 times greater, thus leading to a whole population of JFCs + non-JFCs of $2250 AE 250. Most of these comets have perihelia close to Jupiter's orbit. On the other hand, very few non-JFCs reach the Earth's vicinity (perihelion distances q K 2 AU) which gives additional support to the idea that JFCs and Halley-type comets have different dynamical origins. Our model allows us to define the zones of the orbital element space in which we would expect to find a large number of JFCs. This is the first time, to our knowledge, that a physicodynamical model is presented that includes sublimation and different splitting laws. Our work helps to understand the role played by these erosion effects in the distribution of the orbital elements and lifetimes of JFCs.

We present a series of numerical integrations of observed and fictitious Jupiter Trojan asteroids, under the gravitational effects of the four outer planets, for time-spans comparable with the age of the Solar System. From these results we calculate the escape rate from each Lagrange point, and construct dynamical maps of "permanence" time in different regions of the phase space.Fictitious asteroids in L 4 and L 5 show no significant difference, showing almost identical dynamical maps and escape rates. For real Trojans, however, we found that approximately 23% o f the members of the leading swarm escaped after 4.5 Gyrs, while this number increased to 28.3% for L 5 . This implies that the asymmetry between the two populations increases with time, indicating that it may have been smaller at the time of formation/capture of these asteroids. Nevertheless, the difference in chaotic diffusion cannot, in itself, account for the current observed asymmetry (∼ 40%), and must be primarily primordial and characteristic of the capture mechanism of the Trojans.Finally, we calculate new proper elements for all the numbered Trojans using the semi-analytical approach of Beaugé and Roig (2001), and compare the results with the numerical estimations by Brož and Rosehnal (2011). For asteroids that were already numbered in 2011, both methods yield very similar results, while significant differences were found for those bodies that