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The terrestrial planets formed by accretion of asteroid-like objects within the inner solar system's protoplanetary disk. Previous works have found that forming a small-mass Mars requires the disk to contain little mass beyond ~ 1.5 au (i.e., the disk mass was concentrated within this boundary). The asteroid belt also holds crucial information about the origin of such a narrow disk. Several scenarios may produce a narrow disk. However, simultaneously replicating the four terrestrial planets and the inner solar system properties remains elusive. Here, we found that chaotic excitation of disk objects generated by a near-resonant configuration of Jupiter–Saturn can create a narrow disk, allowing the formation of the terrestrial planets and the asteroid belt. Our simulations showed that this mechanism could typically deplete a massive disk beyond ~ 1.5 au on a 5–10 Myr timescale. The resulting terrestrial systems reproduced the current orbits and masses of Venus, Earth and Mars. Adding an inner region disk component within ~ 0.8–0.9 au allowed several terrestrial systems to simultaneously form analogues of the four terrestrial planets. Our terrestrial systems also frequently satisfied additional constraints: Moon-forming giant impacts occurring after a median ~ 30–55 Myr, late impactors represented by disk objects formed within 2 au, and effective water delivery during the first 10–20 Myr of Earth's formation. Finally, our model asteroid belt explained the asteroid belt's orbital structure, small mass and taxonomy (S-, C- and D/P-types). [ABSTRACT FROM AUTHOR]

The Jupiter–Saturn chaotic excitation (JSCE) scenario proposes that the protoplanetary disk was dynamically excited and depleted beyond ∼1–1.5 au in a few Myr, offering a new and plausible explanation for several observed properties of the inner solar system. Here, we expanded our previous work by conducting a comprehensive analysis of 37 optimal terrestrial planet systems obtained in the context of the JSCE scenario. Each optimal system harbored exactly four terrestrial planets analogs to Mercury, Venus, Earth, and Mars. We further investigated water delivery, feeding zones, and accretion history for the planet analogs, which allowed us to better constrain the water distribution in the disk. The main findings of this work are as follows: 1) the formation of four terrestrial planets with orbits and masses similar to those observed in our solar system in most of our sample, as evidenced by the dynamically colder and hotter orbits of Venus–Earth and Mercury–Mars analogs, and the high success rates of similar mutual orbital separations (∼40–85%) and mass ratios of the planets (∼70–90%) among the 37 systems; and 2) water was delivered to all terrestrial planets during their formation through the accretion of water-bearing disk objects from beyond ∼1–1.5 au. The achievement of Earth's estimated bulk water content required the disk to contain sufficient water mass distributed within those objects initially. This requirement implies that Mercury, Venus, and Mars acquired water similar to the amount on Earth during their formation. Several of our planet analogs also matched additional constraints, such as the timing of Moon formation by a giant impact, Earth's late accretion mass and composition, and Mars's formation timescale. • Our scenario yielded four terrestrial planets with similar orbits and masses to ours. • All terrestrial planets acquired comparable water abundances during their formation. • Terrestrial planets accreted their bulk water from objects beyond 1 au within ∼40 Myr. • Earth accreted most of its CC material from within 2 au during protracted accretion. • Mars analogs matched Mars' mass, eccentricity, inclination, and distance from Earth. [ABSTRACT FROM AUTHOR]

A successful Solar system model must reproduce the four terrestrial planets. Here, we focus on (1) the likelihood of forming Mercury and the four terrestrial planets in the same system (a 4-P system); (2) the orbital properties and masses of each terrestrial planet; and (3) the timing of Earth's last giant impact and the mass accreted by our planet thereafter. Addressing these constraints, we performed 450 N -body simulations of terrestrial planet formation based on narrow protoplanetary discs with mass confined to 0.7–1.0 au. We identified 164 analogue systems, but only 24 systems contained Mercury analogues, and eight systems were 4-P ones. We found that narrow discs containing a small number of embryos with individual masses comparable to that of Mars and the giant planets on their current orbits yielded the best prospects for satisfying those constraints. However, serious shortcomings remain. The formation of Mercury analogues and 4-P systems was too inefficient (5 per cent and 2 per cent, respectively), and most Venus-to-Earth analogue mass ratios were incorrect. Mercury and Venus analogues also formed too close to each other (∼0.15–0.21 au) compared to reality (0.34 au). Similarly, the mutual distances between the Venus and Earth analogues were greater than those observed (0.34 versus 0.28 au). Furthermore, the Venus–Earth pair was not reproduced in orbital-mass space statistically. Overall, our results suggest serious problems with using narrow discs to explain the inner Solar system. In particular, the formation of Mercury remains an outstanding problem for terrestrial planet formation models. [ABSTRACT FROM AUTHOR]

The newly formed giant planets may have migrated and crossed a number of mutual mean motion resonances (MMRs) when smaller objects (embryos) were accreting to form the terrestrial planets in the planetesimal disk. We investigated the effects of the planetesimal-driven migration of Jupiter and Saturn, and the influence of their mutual 1:2 MMR crossing on terrestrial planet formation for the first time, by performing N-body simulations. These simulations considered distinct timescales ofMMRcrossing and planet migration. In total, 68 high-resolution simulation runs using 2000 disk planetesimals were performed, which was a significant improvement on previously published results. Even when the effects of the 1:2MMRcrossing and planet migration were included in the system, Venus and Earth analogs (considering both orbits and masses) successfully formed in several runs. In addition, we found that the orbits of planetesimals beyond a ~ 1.5-2 AU were dynamically depleted by the strengthened sweeping secular resonances associated with Jupiter's and Saturn'smore eccentric orbits (relative to the present day) during planet migration. However, this depletion did not prevent the formation of massive Mars analogs (planets with more than 1.5 times Mars's mass). Although late MMR crossings (at t > 30 Myr) could remove such planets, Mars-like small mass planets survived on overly excited orbits (high e and/or i), or were completely lost in these systems. We conclude that the orbital migration and crossing of the mutual 1:2 MMR of Jupiter and Saturn are unlikely to provide suitable orbital conditions for the formation of solar system terrestrial planets. This suggests that to explain Mars's small mass and the absence of other planets between Mars and Jupiter, the outer asteroid belt must have suffered a severe depletion due to interactions with Jupiter/Saturn, or by an alternative mechanism (e.g., rogue super-Earths). [ABSTRACT FROM AUTHOR]

Abstract: We investigate the dynamical evolution of trans-neptunian objects (TNOs) in typical scattered disk orbits (scattered TNOs) by performing simulations using several thousand particles lying initially on Neptune-encountering orbits. We explore the role of resonance sticking in the scattered disk, a phenomenon characterized by multiple temporary resonance captures (‘resonances’ refers to external mean motion resonances with Neptune, which can be described in the form , where the arguments r and s are integers). First, all scattered TNOs evolve through intermittent temporary resonance capture events and gravitational scattering by Neptune. Each scattered TNO experiences tens to hundreds of resonance captures over a period of 4 Gyr, which represents about 38% of the object''s lifetime (mean value). Second, resonance sticking plays an important role at semimajor axes , where the great majority of such captures occurred. It is noteworthy that the stickiest (i.e., dominant) resonances in the scattered disk are located within this distance range and are those possessing the lowest argument s. This was evinced by , and resonances, which played the greatest role during resonance sticking evolution, often leading to captures in several of their neighboring resonances. Finally, the timescales and likelihood of temporary resonance captures are roughly proportional to resonance strength. The dominance of low s resonances is also related to the latter. In sum, resonance sticking has an important impact on the evolution of scattered TNOs, contributing significantly to the longevity of these objects. [Copyright &y& Elsevier]

Abstract: Resonance occupation of trans-neptunian objects (TNOs) in the scattered disk () was investigated by integrating the orbits of 85 observed members for 4 Gyr. Twenty seven TNOs were locked in the 9:4, 16:7, 7:3, 12:5, 5:2, 8:3, 3:1, 4:1, 11:2, and 27:4 resonances. We then explored mechanisms for the origin of the resonant structure in the scattered disk, in particular the long-term 9:4, 5:2, and 8:3 resonant TNOs (median 4 Gyr), by performing large scale simulations involving Neptune scattering and planetary migration over an initially excited planetesimals disk (wide range of eccentricities and inclinations). To explain the formation of Gyr-resident populations in such distant resonances, our results suggest the existence of a primordial planetesimal disk of at least 45–50 AU radius that suffered a dynamical perturbation leading to 0.1–0.3 or greater eccentricities and a range of inclinations up to ∼20° during early stages of the Solar System history, before planetary migration. [Copyright &y& Elsevier]

Abstract: In our preliminary study, we have investigated basic properties and dynamical evolution of classical TNOs around the 7:4 mean motion resonance with Neptune (a∼43.7AU), motivated by observational evidences that apparently present irregular features near this resonance (see [Lykawka and Mukai, 2005a. Exploring the 7:4 mean motion resonance—I. Dynamical evolution of classical trans-Neptunian objects (TNOs). Space Planet. Sci. 53, 1175–1187]; hereafter “Paper I”). In this paper, we aim to explore the dynamical long-term evolution in the scattered disk (but not its early formation) based on the computer simulations performed in Paper I together with extra computations. Specifically, we integrated the orbital motion of test particles (totalizing a bit more than 10,000) placed around the 7:4 mean motion resonance under the effect of the four giant planets for the age of the Solar System. In order to investigate chaotic diffusion, we also conducted a special simulation with on-line computation of proper elements following tracks in phase space over 4–5Gyr. We found that: (1) A few percent (1–2%) of the test particles survived in the scattered disk with direct influence of other Neptunian mean motion resonances, indicating that resonance sticking is an extremely common phenomenon and that it helps to enhance scattered objects longevity. (2) In the same region, the so-called extended scattered TNOs are able to form via very long resonance trapping under certain conditions. Namely, if the body spends more than about 80% of its dynamical lifetime trapped in mean motion resonance(s) and there is the action of a k+1 or (k+2)/2 mean motion resonance (e.g., external mean motion resonances with Neptune described as with and , respectively). According to this hypothetical mechanism, 5–15% of current scattered TNOs would possess thus probably constituting a significant part of the extended scattered disk. (3) Moreover, considering hot orbital initial conditions, it is likely that the trans-Neptunian belt (or Edgeworth–Kuiper belt) has been providing members to the scattered disk, so that scattered TNOs observed today would consist of primordial scattered bodies mixed with TNOs that came from unstable regions of the trans-Neptunian belt in the past. Considering the three points together, our results demonstrated that the scattered disk has been evolving continuously since early times until present. [Copyright &y& Elsevier]

Abstract: Transneptunian objects (TNOs) orbit beyond Neptune and do offer important clues about the formation of our solar system. Although observations have been increasing the number of discovered TNOs and improving their orbital elements, very little is known about elementary physical properties such as sizes, albedos and compositions. Due to TNOs large distances (>40AU) and observational limitations, reliable physical information can be obtained only from brighter objects (supposedly larger bodies). According to size and albedo measurements available, it is evident the traditionally assumed albedo cannot hold for all TNOs, especially those with approximately absolute magnitudes . That is, the largest TNOs possess higher albedos (generally >0.04) that strongly appear to increase as a function of size. Using a compilation of published data, we derived empirical relations which can provide estimations of diameters and albedos as a function of absolute magnitude. Calculations result in more accurate size/albedo estimations for TNOs with than just assuming . Nevertheless, considering low statistics, the value sounds still convenient for non-binary TNOs as a group. We also discuss about physical processes (e.g., collisions, intrinsic activity and the presence of tenuous atmospheres) responsible for the increase of albedo among large bodies. Currently, all big TNOs (>700km) would be capable to sustain thin atmospheres or icy frosts composed of CH4, CO or N2 even for body bulk densities as low as 0.5gcm−3. A size-dependent albedo has important consequences for the TNOs size distribution, cumulative luminosity function and total mass estimations. According to our analysis, the latter can be reduced up to 50% if higher albedos are common among large bodies. Lastly, by analyzing orbital properties of classical TNOs (), we confirm that cold and hot classical TNOs have different concentration of large bodies. For both populations, distinct absolute magnitude distributions are maximized for an inclination threshold equal to 4.5° at >99.63% confidence level. Furthermore, more massive classical bodies are anomalously present at , a result statistically significant and apparently not caused by observational biases. This feature would provide a new constraint for transneptunian belt formation models. [Copyright &y& Elsevier]

Classical trans-Neptunian objects (TNOs) are believed to represent the most dynamically pristine population in the trans-Neptunian belt (TNB) offering unprecedented clues about the formation of our Solar System. The long term dynamical evolution of classical TNOs was investigated using extensive simulations. We followed the evolution of more than 17000 particles with a wide range of initial conditions taking into account the perturbations from the four giant planets for 4 Gyr. The evolution of objects in the classical region is dependent on both their inclination and semimajor axes, with the inner (a<45 AU) and outer regions (a>45 AU) evolving differently. The reason is the influence of overlapping secular resonances with Uranus and Neptune (40–42 AU) and the 5:3 (a∼ ∼42.3 AU), 7:4 (a∼ ∼43.7 AU), 9:5 (a∼ ∼44.5 AU) and 11:6 (a∼ ∼ 45.0 AU) mean motion resonances strongly sculpting the inner region, while in the outer region only the 2:1 mean motion resonance (a∼ ∼47.7 AU) causes important perturbations. In particular, we found: (a) A substantial erosion of low-i bodies (i<10°) in the inner region caused by the secular resonances, except those objects that remained protected inside mean motion resonances which survived for billion of years; (b) An optimal stable region located at 45 AU40 AU and i>5° free of major perturbations; (c) Better defined boundaries for the classical region: 42–47.5 AU (q>38 AU) for cold classical TNOs and 40–47.5 AU (q>35 AU) for hot ones, with i=4.5° as the best threshold to distinguish between both populations; (d) The high inclination TNOs seen in the 40–42 AU region reflect their initial conditions. Therefore they should be classified as hot classical TNOs. Lastly, we report a good match between our results and observations, indicating that the former can provide explanations and predictions for the orbital structure in the classical region. [ABSTRACT FROM AUTHOR]

Abstract: In the transneptunian classical region (), an unexpected orbital excitation in eccentricity and inclination, dynamically distinct populations and the presence of chaotic regions are observed. For instance, the 7:4 mean motion resonance () appears to have been causing unique dynamical excitation according to observational evidences, namely, an apparent shallow gap in number density and anomalies in the colour distribution, both features enhanced near the 7:4 mean motion resonance location. In order to investigate the resonance dynamics, we present extensive computer simulation results totalizing almost 10,000 test particles under the effect of the four giant planets for the age of the solar system. A chaotic diffusion experiment was also performed to follow tracks in phase space over 4–5Gyr. The 7:4 mean motion resonance is weakly chaotic causing irregular eccentricity and inclination evolution for billions of years. Most 7:4 resonant particles suffered significant eccentricities and/or inclinations excitation, an outcome shared even by those located in the vicinity of the resonance. Particles in stable resonance locking are rare and usually had . For other regions, 7:4 resonants had quite large mobility in phase space typically leaving the resonance (and being scattered) after reaching a critical . The escape happened in 108–109 yr time scales. Concerning the inclination dependence for 7:4 resonants, we found strong instability islands for approximately . Taking into account those particles still locked in the resonance at the end of the simulations, we determined a retainability of 12–15% for real 7:4 resonant transneptunian objects (TNOs). Lastly, our results demonstrate that classical TNOs associated with the 7:4 mean motion resonance have been evolving continuously until present with non-negligible mixing of populations. [Copyright &y& Elsevier]

Abstract Since 2002, we have obtained size frequency distributions (SFDs) of main belt asteroids (MBAs), Hildas, and Jupiter Trojans (JTs) by using the 8.2-m Subaru Telescope equipped with the wide-field CCD cameras: Suprime-Cam (SC) or Hyper Suprime-Cam (HSC). After combining these SFDs with SFDs obtained from other surveys, we performed a comparative study of SFDs for each group of small bodies in an attempt to obtain clues about planet migration that affected those populations. The large aperture of the Subaru Telescope and the wide field of view of SC or HSC allowed us to detect small moving objects up to apparent magnitudes 24.4–24.5 mag (R c -band), which corresponds to sub–km in diameter (D) for MBAs and about 1 km for Hildas and JTs. We combined the SFDs obtained from our surveys with those derived from published data to obtain the individual representative SFD for MBAs, Hildas and JTs in the size range of sub–km to 1000 km. We found that the SFDs of JTs and Hildas are roughly flat in the R -plot while that of MBAs has a wavy structure. We also investigated the SFDs of MBAs in the inner, middle, and outer regions of the main belt. We found that the shape of the SFDs changes gradually with increasing heliocentric distance across these regions. This trend continues beyond the outer region, where the SFD becomes flatter as shown by the SFDs of JTs and Hildas. Recent planet migration models suggest that the current JTs originated in the trans-Neptunian region and were captured as Trojans during planet migration. The finding of a gradual change of the SFDs from the inner MBAs to JTs is in line with the idea that trans-Neptunian objects (TNOs) were implanted not only into the JT region, but also into the main belt outer region (including the Hildas) at the early solar system. In order to investigate this implantation hypothesis, we considered a synthetic population of TNOs assuming with a SFD represented by a power-law distribution of N > D ∝ D - 3 , (estimated from crater record on Pluto and Charon). We then added this synthetic population to the MBA populations in various proportions. We found that the higher the proportion, the flatter the wavy SFD of MBAs becomes. This simple model yields a rough explanation for the gradual change of SFDs found from the inner main belt to the JT region. However, the shape of the modelled SFDs does not match observations for all sizes. In particular, because important discrepancies are seen in the small size range, we need to consider the removal of small objects by collisional evolution and/or Yarkovsky effect in the future. Highlights • We investigated the size frequency distributions (SFDs) of main belt asteroids (MBAs), Hildas, and Jupiter Trojans (JTs). • We found that the SFDs of JTs and Hildas are roughly flat in the R -plot, while that of MBAs has a wavy structure. • We also found that the shape of the SFDs changes gradually with increasing heliocentric distance from the main belt to Jupiter Trojan region. • We proposed that the SFD shape of each solar system population can be used as a probe for the radial mixing of small body populations caused by planet migration. [ABSTRACT FROM AUTHOR]

The authors regret that we found several typographic errors and inconsistencies in figures in the above article. Specifically, we would like make corrections in Abstract, Figs. 3, 5, 6, and References. All of the corrections are minor, and none of them gives any serious impacts on the discussions or conclusions of the article. The authors would like to apologize for any inconvenience caused. [ABSTRACT FROM AUTHOR]