ALBERT

Description: Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disc between 1 and 3 au. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 au and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas drag, as has been proposed to explain the formation of close-in super-Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar system. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from discs of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Discs with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogues significantly more massive than the real planet. In contrast, a disc with a surface density gradient proportional to r –5.5 reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disc profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.

Description: The Erigone family is a C-type group in the inner main belt. Its age has been estimated by several researchers to be less then 300 Myr, so it is a relatively young cluster. Yarko-YORP Monte Carlo methods to study the chronology of the Erigone family confirm results obtained by other groups. The Erigone family, however, is also characterized by its interaction with the z 2 secular resonance. While less than 15 per cent of its members are currently in librating states of this resonance, the number of objects, members of the dynamical group, in resonant states is high enough to allow us to use the study of dynamics inside the z 2 resonance to set constraints on the family age. Like the 6 and z 1 secular resonances, the z 2 resonance is characterized by one stable equilibrium point at  = 180° in the z 2 resonance plane $(\sigma , \frac{{\rm d}\sigma }{{\rm d}t})$ , where is the resonant angle of the z 2 resonance. Diffusion in this plane occurs on time-scales of ~= 12 Myr, which sets a lower limit on the Erigone family age. Finally, the minimum time needed to reach a steady-state population of z 2 librators is about 90 Myr, which allows us to impose another, independent constraint on the group age.

Description: The rotational fission of asteroids has been studied previously with simplified models restricted to planar motion. However, the observed physical configuration of contact binaries leads one to conclude that most of them are not in a planar configuration and hence would not be restricted to planar motion once they undergo rotational fission. This motivated a study of the evolution of initially non-planar binaries created by fission. Using a two-ellipsoid model, we performed simulations taking only gravitational interactions between components into account. We simulate 91 different initial inclinations of the equator of the secondary body for 19 different mass ratios. After disruption, the binary system dynamics are chaotic, as predicted from theory. Starting the system in a non-planar configuration leads to a larger energy and enhanced coupling between the rotation state of the smaller fissioned body and the evolving orbital system, and enables re-impact to occur. This leads to differences with previous planar studies, with collisions and secondary spin fission occurring for all mass ratios with inclinations 0 ≥ 40 o , and mimics a Lidov–Kozai mechanism. Out of 1729 studied cases, we found that ~14 per cent result in secondary fission, ~25 per cent result in collisions and ~6 per cent have lifetimes longer than 200 yr. In Jacobson & Scheeres stable binaries only formed in cases with mass ratios q  〈 0.20. Our results indicate that it should be possible to obtain a stable binary with the same mechanisms for cases with mass ratios larger than this limit, but that the system should start in a non-planar configuration.

Description: The near-Earth Asteroid 2001 SN263 is a triple system of asteroids and it is the target of the ASTER mission – First Brazilian Deep Space Mission. The announcement of this mission has motivated a study aimed to characterize regions of stability of the system. Araujo et al., characterized the stable regions around the components of the triple system for the planar and prograde cases. Through numerical integrations they found that the stable regions are in two tiny internal zones, one of them placed very close to Alpha and another close to Beta, and in the external region. For a space mission aimed to place the probe in the internal region of the system those results do not seem to be very interesting. Therefore, knowing that the retrograde orbits are expected to be more stable, here we present a complementary study. We now considered particles orbiting the components of the system, in the internal and external regions, with relative inclinations between 90° 〈  I  ≤ 180°, i.e. particles with retrograde orbits. Our goal is to characterize the stable regions of the system for retrograde orbits, and then detach a preferred region to place the space probe. For a space mission, the most interesting regions would be those that are unstable for the prograde cases, but stable for the retrograde cases. Such configuration provide a stable region to place the mission probe with a relative retrograde orbit, and, at the same time, guarantees a region free of debris since they are expected to have prograde orbits. We found that in fact the internal and external stable regions significantly increase when compared to the prograde case. For particles with e  = 0 and I  = 180°, we found that nearly the whole region around Alpha and Beta remain stable. We then identified three internal regions and one external region that are very interesting to place the space probe. We present the stable regions found for the retrograde case and a discussion on those preferred regions. We also discuss the effects of resonances of the particles with Beta and Gamma, and the role of the Kozai mechanism in this scenario. These results help us understand and characterize the stability of the triple system 2001 SN263 when retrograde orbits are considered, and provide important parameters to the design of the ASTER mission.

Description: Recent data processing showed the existence of a difference that can reach 25 per cent for the dimensions of asteroid (216) Kleopatra between the radar observations and the light curves. We rebuild the shape of (216) Kleopatra from these new data applying a correction's factor of the size of 1.15 and estimate certain physical features by using the polyhedral model method. In our computations, we use a code that avoids singularities from the line integrals of a homogeneous arbitrary shaped polyhedral source. Then, we find the location of the equilibrium points through the pseudo-potential energy and zero-velocity curves. The behaviour of the zero-velocity curves differ substantially if we apply a scale size of 1.15 relative to the original shape of (216) Kleopatra. Taking the rotation of asteroid (216) Kleopatra into consideration, the aim of this work is to analyse the stability against impact and the dynamics of numerical simulations of 3D initially equatorial and polar orbits near the body. As results, we show that the minimum radii are more suited for the stability against impact. We find also that the minimum radius for direct, equatorial circular orbits that cannot impact with (216) Kleopatra surface is 300 km and the lower limit on radius for polar circular orbits is 240 km. Stable orbits occur at 280 km for equatorial circular orbits despite significant perturbations of its orbit. Moreover, as the orbits suffer less perturbations due to the irregular gravitational potential of (216) Kleopatra in the elliptic case, the most significant result of the analysis is that stable orbits exist at a periapsis radius of 250 km for initial eccentricities e i  = 0.2 in both cases. Finally, the polar orbits with eccentricities ranging between 0.1 and 0.2 appear to be more stable.

Description: Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disc between 1 and 3 au. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 au and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas drag, as has been proposed to explain the formation of close-in super-Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar system. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from discs of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Discs with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogues significantly more massive than the real planet. In contrast, a disc with a surface density gradient proportional to r –5.5 reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disc profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.

Description: One of the techniques used in the past decade to determine the shape with a good accuracy and estimate certain physical features (volume, mass, moments of inertia) of asteroids is the polyhedral model method. We rebuild the shape of the asteroid 433 Eros using data from 1998 December observations of the probe Near-Earth-Asteroid-Rendezvous-Shoemaker . In our computations, we use a code that avoids singularities from the line integrals of a homogeneous arbitrary shaped polyhedral source. This code evaluates the gravitational potential function and its first- and second-order derivatives. Taking the rotation of asteroid 433 Eros into consideration, the aim of this work is to analyse the dynamics of numerical simulations of 3D initially equatorial orbits near the body. We find that the minimum radius for direct, equatorial circular orbits that cannot impact with the Eros surface is 36 km and the minimum radius for stable orbits is 31 km despite significant perturbations of its orbit. Moreover, as the orbits suffer less perturbations due to the irregular gravitational potential of Eros in the elliptic case, the most significant result of the analysis is that stable orbits exist at a periapsis radius of 29 km for initial eccentricities e i ≤ 0.2.

Description: Giuliatti Winter et al. found several stable regions for a sample of test particles located between the orbits of Pluto and Charon. One peculiar stable region in the space of the initial orbital elements is located at a  = (0.5 d , 0.7 d ) and e  = (0.2, 0.9), where a and e are the initial semimajor axis and eccentricity of the particles, respectively, and d is the Pluto–Charon distance. This peculiar region (hereafter called the sailboat region) is associated with a family of periodic orbits derived from the planar, circular, restricted three-body problem (Pluto–Charon–particle). In this work, we study the origin of this stable region by analysing the evolution of such family of periodic orbits. We show that they are not in resonances with Charon. The period of the periodic orbit varies along the family, decreasing with the increase of the Jacobi constant. We also explore the extent of the sailboat region by adopting different initial values of the orbital inclination ( I ) and argument of the pericentre () of the particles. The sailboat region is present for I  = [0°, 90°] and for two intervals of ,  = [–10°, 10°] and (160°, 200°). A crude estimative of the size of the hypothetical bodies located at the sailboat region can be derived by computing the tidal damping in their eccentricities. If we neglect the orbital evolution of Pluto and Charon, the time-scale for circularization of their orbits is longer than the age of the Solar system for bodies smaller than 500 m in radius.

Description: In a previous work, Giuliatti Winter et al. found several stable regions for test particles in orbit around Pluto associated with families of periodic orbits obtained in the circular, restricted three-body problem. They have shown that a possible eccentricity of the Pluto–Charon binary slightly reduces but does not destroy any of these stable regions. In this work, we extended their results by analysing the cases with the orbital inclination ( I ) equal to zero and considering the argument of pericentre () equal to 90°, 180° and 270°. We explore the influence of the orbital inclination of the particles in these stable regions. In this case, the initial inclination varies from 10° to 170° in steps of 10°. We also present a sample of results for the longitude of the ascending node  = 90°, considering the cases I  = 20°, 50°, 130° and 180°. Our results show that stable regions are present in all of the inclined cases, except when the initial inclination of the particles is equal to 110°. A sample of 3D trajectories of quasi-periodic orbits were found related to the periodic orbits obtained in the planar case by Giuliatti Winter et al.