Gravitational Capture of Asteroids by Gas Drag

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamical erosion of asteroid groups in the region of the Phocaea family

In a previous paper, the current state of knowledge of the region containing the Phocaea dynamical family was revised. Here, the dynamical evolution and possible origin of the Phocaea dynamical family and asteroid groups in the region are investigated. First, I study the case of asteroids at high eccentricity (e > 0.31). I find that these objects are unstable because of encounters with Mars on time-scales of up to 270 Myr. The minimum time needed by members of the Phocaea classical family to reach the orbital locations of these objects, 370 Myr, can be used to set a lower limit on the age of the Phocaea family.Next, attention is focused on the chaotic layer previously identified near the nu(6) secular resonance border. Using analytical and numerical tools, I find that the presence of the nu(6) secular resonance forces asteroids with vertical bar g-g(6)vertical bar < 2.55 arcsec yr(-1) to reach eccentricities high enough to allow them to experience deep, close encounters with Mars. Results of the analytical model of Yoshikawa and of my numerical simulations fully explain the low-inclination chaotic region found by Carruba.Finally, I investigate the long-term stability of the minor families and clumps identified in the previous paper, with particular emphasis on a clump only identifiable in the domain of proper frequencies (n, g, g - s) around (6246) Komurotoru. I find that while the clumps identified in the space of proper elements quickly disperse when the Yarkovsky effect is considered, the family around (19536) is still observable for time-scales of more than 50 Myr. The (6246) clump, characterized by its interaction with the nu(5) + nu(16) and 2 nu(6) - nu(16) secular resonances, is robust on time-scales of 50 Myr. I confirm that this group may be the first clump ever detected in the frequency domain that can be associated with a real collisional event.

Dynamical erosion of asteroid groups in the region of the Pallas family

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Irregular satellites of Jupiter: capture configurations of binary-asteroids

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Emmenthal distribution of highly inclined asteroids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An analysis of the region of the Phocaea dynamical family

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nebular gas drag and co-orbital system dynamics

Aims. We study trajectories of planetesimals whose orbits decay due to gas drag in a primordial solar nebula and are perturbed by the gravity of the secondary body on an eccentric orbit whose mass ratio takes values from mu(2) = 10(-7) to mu(2) = 10(-3) increasing ten times at each step. Each planetesimal ultimately suffers one of the three possible fates: (1) trapping in a mean motion resonance with the secondary body; (2) collision with the secondary body and consequent increase of its mass; or (3) diffusion after crossing the orbit of the secondary body.Methods. We take the Burlirsh-Stoer numerical algorithm in order to integrate the Newtonian equations of the planar, elliptical restricted three-body problem with the secondary body and the planetesimal orbiting the primary. It is assumed that there is no interaction among planetesimals, and also that the gas does not affect the orbit of the secondary body.Results. The results show that the optimal value of the gas drag constant k for the 1: 1 resonance is between 0.9 and 1.25, representing a meter size planetesimal for each AU of orbital radius. In this study, the conditions of the gas drag are such that in theory, L4 no longer exists in the circular case for a critical value of k that defines a limit size of the planetesimal, but for a secondary body with an eccentricity larger than 0.05 when mu(2) = 10(-6), it reappears. The decrease of the cutoff collision radius increase the difusions but does not affect the distribution of trapping. The contribution to the mass accretion of the secondary body is over 40% with a collision radius 0.05R(Hill) and less than 15% with 0.005R(Hill) for mu(2) = 10(-7). The trappings no longer occur when the drag constant k reachs 30. That means that the size limit of planetesimal trapping is 0.2 m per AU of orbital radius. In most cases, this accretion occurs for a weak gas drag and small secondary eccentricity. The diffusions represent most of the simulations showing that gas drag is an efficient process in scattering planetesimals and that the trapping of planetesimals in the 1: 1 resonance is a less probable fate. These results depend on the specific drag force chosen.

Co-orbital satellites of Saturn: congenital formation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the dynamics of some resonances of Phobos in the future

A probable capture of Phobos into an interesting resonance was presented in our previous work. With a simple model, considering Mars in a Keplerian and circular orbit, it was shown that once captured in the resonance, the inclination of the satellite reaches very high values. Here, the integrations are extended to much longer times and escape situations are analyzed. These escapes are due to the interaction of new additional resonances, which appear as the inclination starts to increase reaching some specific values. Compared to classical capture in mean motion resonances, we see some interesting differences in this problem. We also include the effect of Mars' eccentricity in the process of the capture. The role played by this eccentricity becomes important, particularly when Phobos encounters a double resonance at a approximate to 2.619R(M). Planetary perturbations acting on Mars and variation of its equator are also included. In general, some possible scenarios of the future of Phobos are presented.

Effect of Jupiter's mass growth on satellite capture

We study the effects of Jupiter mass growth in order to permanently capture prograde satellites. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time while considering the decrease in Jupiter's mass. We considered the particle's initial conditions to be prograde, at pericenter, in the region 100R(4) <= a <= 400R(4) and 0 <= e <= 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values give an indication of the conditions that are necessary for capture. An analysis of these results shows that prograde satellite capture is more complex than a retrograde one. It occurs in a two-step process. First, when the particles get inside about 0.85R(Hill) (Hills' radius), they become weakly bound to Jupiter. Then, they keep migrating toward the planet with a strong decrease in eccentricity, while the planet is growing. The radial oscillation of the particles reduces significantly when they reach a radial distance that is less than about 0.45R(Hill) from the planet. Three-dimensional simulations for the known prograde satellites of Jupiter were performed. The results indicate that Leda, Himalia, Lysithea, and Elara could have been permanently captured when Jupiter had between 50% and 60% of its present mass.

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.

On the V-type asteroids outside the Vesta family - II. Is (21238) 1995 WV7 a fragment of the long-lost basaltic crust of (15) Eunomia?

Context. The V-type asteroids are associated with basaltic composition. Apart from ( 1459) Magnya, an asteroid that is clearly dynamically and mineralogically unconnected to the Vesta family, all currently known V-type asteroids are either members of the Vesta family, or are hypothesized to be former members of the dynamical family that migrated to their current orbital positions. The recent identification of ( 21238) 1995 WV7 as a V-type asteroid introduces the possibility that a second basaltic asteroid not connected with the Vesta family exists. This asteroid is on the opposite side of the 3: 1 mean motion resonance with respect to Vesta, and it would be very unlikely that a member of the Vesta family of its size (D > 5km) migrating via either the Yarkovsky effect or repeated close encounters with Vesta survived the passage through such a resonance.Aims. In this work we investigate the possibility that ( 21238) 1995 WV7 originated as a fragment of the parent body of the Eunomia family and then migrated via the interplay of the Yarkovsky effect and some powerful nonlinear secular resonances, such as the (s - s(6)) - ( g(5) - g(6)). If (15) Eunomia is, as claimed, a differentiated object whose originally pyroxene-enriched crust layer was lost in a collision that either created the Eunomia family or preceded its formation, can (21238) be a fragment of its long-lost basaltic crust that migrated to the current position?Methods. We mapped the phase space around (21238) and determined which of the nonlinear secular resonances that we identified are stronger and more capable of having caused the current difference in proper i between (21238) and members of the Eunomia family. We simulated the Yarkovsky effect by using the SWIFT-RMVSY integrator.Results. Our results suggest that it is possible to migrate from the Eunomia dynamical family to the current orbital location of ( 21238) via the interplay of the Yarkovsky effect and the (s - s6) - (g5 - g6) nonlinear secular resonance, on time-scales of at least 2.6 Gyr.Conclusions. (15) Eunomia might be the third currently known parent body for V-type asteroids.

On the orbits of the outer satellites of Jupiter

In this work we study the basic aspects concerning the stability of the outer satellites of Jupiter. Including the effects of the four giant planets and the Sun we study a large grid of initial conditions. Some important regions where satellites cannot survive are found. Basically these regions are due to Kozai and other resonances. We give an analytical explanation for the libration of the pericenters (ω) over bar - (ω) over bar (J). Another different center is also found. The period and amplitude of these librations are quite sensitive to initial conditions, so that precise observational data are needed for Pasiphae and Sinope. The effect of Jupiter's mass variation is briefly presented. This effect can be responsible for satellite capture and also for locking (ω) over bar - (ω) over bar (J) in temporary libration.

The effect of Jupiter's mass growth on satellite capture - Retrograde case

Gravitational capture can be used to explain the existence of the irregular satellites of giants planets. However, it is only the first step since the gravitational capture is temporary. Therefore, some kind of non-conservative effect is necessary to to turn the temporary capture into a permanent one. In the present work we study the effects of Jupiter mass growth for the permanent capture of retrograde satellites. An analysis of the zero velocity curves at the Lagrangian point L-1 indicates that mass accretion provides an increase of the confinement region ( delimited by the zero velocity curve, where particles cannot escape from the planet) favoring permanent captures. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time considering the decrease of M-4. We considered initial conditions of the particles to be retrograde, at pericenter, in the region 100 R-4 less than or equal to a less than or equal to 400 R-4 and 0 less than or equal to e < 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values are an indication of the necessary conditions that could provide capture. An analysis of these results shows that retrograde satellites would be captured as soon as they get inside the Hills' radius and after that they keep migrating toward the planet while it is growing. For the region where the orbits of the four old retrograde satellites of Jupiter ( Ananke, Carme, Pasiphae and Sinope) are located we found that such satellites could have been permanently captured when Jupiter had between 62% and 93% of its present mass.