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Register a new userCapture Probability in the 3:1 Mean Motion Resonance with Jupiter
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We study the capture and crossing probabilities into the 3:1 mean motion resonance with Jupiter for a small asteroid that migrates from the inner to the middle Main Belt under the action of the Yarkovsky effect. We use an algebraic mapping of the averaged planar restricted three-body problem based on the symplectic mapping of Hadjidemetriou (1993), adding the secular variations of the orbit of Jupiter and non-symplectic terms to simulate the migration. We found that, for fast migration rates, the captures occur at discrete windows of initial eccentricities whose specific locations depend on the initial resonant angles, indicating that the capture phenomenon is not probabilistic. For slow migration rates, these windows become narrower and start to accumulate at low eccentricities, generating a region of mutual overlap where the capture probability tends to 100%, in agreement with the theoretical predictions for the adiabatic regime. Our simulations allow to predict the capture probabilities in both the adiabatic and non-adiabatic cases, in good agreement with results of Gomes (1995) and Quillen (2006). We apply our model to the case of the Vesta asteroid family in the same context as Roig et al. (2008), and found results indicating that the high capture probability of Vesta family members into the 3:1 mean motion resonance is basically governed by the eccentricity of Jupiter and its secular variations.
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We study the dynamical evolution of Jupiter and Saturn embedded in a gaseous, solar-nebula-type disc by means of hydrodynamics simulations with the FARGO2D1D code. We study the evolution for different initial separations of the planets orbits, Delta a_SJ , to investigate whether they become captured in mean motion resonance (MMR) and the direction of the subsequent migration of the planet (inward or outward). We also provide an assessment of the planets orbital dynamics at different epochs of Saturns growth. We find that the evolution of initially compact orbital configurations is dependent on the value of Delta a_SJ . This implies that an evolution as that proposed in the Grand Tack model depends on the precise initial orbits of Jupiter and Saturn and on the timescales for their formation. Capture in the 1:2 MMR and inward or (nearly) stalled migration are highly favoured. Within its limits, our work suggests that the reversed migration, associated with the resonance capture of Jupiter and Saturn, may be a low probability evolutionary scenario, so that other planetary systems with giant planets are not expected to have experienced a Grand Tack-like evolutionary path.
Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this paper, we investigate the phase-space structure of the retrograde 1:1 resonance in detail within the framework of the circular restricted three-body problem. We construct a simple integrable approximation for the planar retrograde resonance using canonical contact transformation and numerically employ the averaging procedure in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We thoroughly analyze all possible librations in the co-orbital region and uncover a new apocentric libration for the retrograde 1:1 resonance inside the planets orbit. We also observe the significant jumps in orbital elements for outer and inner apocentric librations, which are caused by close encounters with the perturber.
The paper analyses possible transfers of bodies from the main asteroid belt (MBA) to the Centaur region. The orbits of asteroids in the 2:1 mean motion resonance (MMR) with Jupiter are analysed. We selected the asteroids that are in resonant orbits with e > 0.3 whose absolute magnitudes H do not exceed 16m. The total number of the orbits amounts to 152. Numerical calculations were performed to evaluate the evolution of the orbits over 100,000-year time interval with projects for the future. Six bodies are found to have moved from the 2:1 commensurability zone to the Centaur population. The transfer time of these bodies to the Centaur zone ranges from 4,600 to 70,000 yr. Such transfers occur after orbits leave the resonance and the bodies approach Jupiter. Where after reaching sufficient orbital eccentricities bodies approach a terrestrial planet, their orbits go out of the MMR. Accuracy estimations are carried out to confirm the possible asteroid transfers to the Centaur region.
We study the formation of the 9:7 mean motion resonance in a system of two low-mass planets ($m_{1}=m_{2}=3M_{oplus}$) embedded in a gaseous protoplanetary disk employing a full 2D hydrodynamic treatment of the disk-planet interactions. Our aim is to determine the disk properties that favor a capture of two equal-mass super-Earths into this second-order resonance. For this purpose, we have performed a series of numerical hydrodynamic simulations of the system of two super-Earths migrating in disks with a variety of different initial parameters and found conditions for the permanent or temporary locking in the 9:7 resonance. We observe that capture occurs during the convergent migration of planets if their resonance angle at the moment of arrival at the resonance assumes values in a certain range (inside a window of capture). The width of such a window depends on the relative migration and circularization rates that are determined by the disk parameters. The window is wide if the relative migration rate is slow, and it becomes narrower as the relative migration rate increases. The window will be closed if the migration rate is sufficiently high, and the capture will not take place. We illustrate also how the 9:7 resonance window of capture is affected by the initial eccentricities and the initial orbits of the planets.
The K2 mission has recently begun to discover new and diverse planetary systems. In December 2014 Campaign 1 data from the mission was released, providing high-precision photometry for ~22000 objects over an 80 day timespan. We searched these data with the aim of detecting further important new objects. Our search through two separate pipelines led to the independent discovery of K2-19b & c, a two-planet system of Neptune sized objects (4.2 and 7.2 $R_oplus$), orbiting a K dwarf extremely close to the 3:2 mean motion resonance. The two planets each show transits, sometimes simultaneously due to their proximity to resonance and alignment of conjunctions. We obtain further ground based photometry of the larger planet with the NITES telescope, demonstrating the presence of large transit timing variations (TTVs), and use the observed TTVs to place mass constraints on the transiting objects under the hypothesis that the objects are near but not in resonance. We then statistically validate the planets through the texttt{PASTIS} tool, independently of the TTV analysis.
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