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The debiased absolute-magnitude and orbit distributions as well as source regions for near-Earth objects (NEOs) provide a fundamental frame of reference for studies of individual NEOs and more complex population-level questions. We present a new four-dimensional model of the NEO population that describes debiased steady-state distributions of semimajor axis, eccentricity, inclination, and absolute magnitude H in the range 17 <  H  < 25. The modeling approach improves upon the methodology originally developed by Bottke et al. (2000, Science 288, 2190–2194) in that it is, for example, based on more realistic orbit distributions and uses source-specific absolute-magnitude distributions that allow for a power-law slope that varies with H . We divide the main asteroid belt into six different entrance routes or regions (ER) to the NEO region: the ν 6 , 3:1J, 5:2J and 2:1J resonance complexes as well as Hungarias and Phocaeas. In addition we include the Jupiter-family comets as the primary cometary source of NEOs. We calibrate the model against NEO detections by Catalina Sky Surveys’ stations 703 and G96 during 2005–2012, and utilize the complementary nature of these two systems to quantify the systematic uncertainties associated to the resulting model. We find that the (fitted) H distributions have significant differences, although most of them show a minimum power-law slope at H  ∼ 20. As a consequence of the differences between the ER-specific H distributions we find significant variations in, for example, the NEO orbit distribution, average lifetime, and the relative contribution of different ERs as a function of H . The most important ERs are the ν 6 and 3:1J resonance complexes with JFCs contributing a few percent of NEOs on average. A significant contribution from the Hungaria group leads to notable changes compared to the predictions by Bottke et al. in, for example, the orbit distribution and average lifetime of NEOs. We predict that there are 962 − 56 + 52 ( 802 − 42 + 48 × 10 3 ) NEOs with H  < 17.75 ( H  < 25) and these numbers are in agreement with the most recent estimates found in the literature (the uncertainty estimates only account for the random component). Based on our model we find that relative shares between different NEO groups (Amor, Apollo, Aten, Atira, Vatira) are (39.4,54.4,3.5,1.2,0.3)%, respectively, for the considered H range and that these ratios have a negligible dependence on H . Finally, we find an agreement between our estimate for the rate of Earth impacts by NEOs and recent estimates in the literature, but there remains a potentially significant discrepancy in the frequency of Tunguska-sized and Chelyabinsk-sized impacts. [ABSTRACT FROM AUTHOR]

The Dwarf Planet Ceres revealed the presence of ammonia and other unique properties compared to other asteroids in the main belt which suggests that it was not formed in situ. We model the early dynamical evolution of the outer Solar System to study possible dynamical mechanisms to implant a Ceres-sized planetesimal in the asteroid belt from the trans-Saturnian region. We calculate that the fraction of the population of Ceres-sized planetesimals that are captured in the asteroid belt is in the range of 2. 8 × 1 0 − 5 to 1. 2 × 1 0 − 3 depending on the initial location in the outer planetesimal disk. The captured bodies have a 70% probability to have a semimajor axis between 2.5 and 3 au, a 33% probability to have an eccentricity smaller than 0.2 and a 45% probability to have an orbital inclination smaller than 10°. Assuming the existence of 3,600 Ceres-size planetesimals in the inner part of the trans-Saturnian disk, consistent with the estimate of Nesvorný and Vokrouhlický (2016) for the trans-Neptunian disk, our estimated capture probability and a final 80% depletion of the asteroid belt during the subsequent giant planet instability, lead to capture ∼ 1 Ceres in the asteroid belt, with a probability of 15%, 34%, and 51% to be located in the inner, middle and outer belt respectively. • We model the early evolution of Solar System to investigate the origin of Ceres. • Our model can lead to capture of one Ceres in the Asteroid Belt. • The probability of Ceres is in the inner belt is 15%. • The probability of Ceres is in the middle belt is 34%. • The probability of Ceres is in the outer belt is 51%. [ABSTRACT FROM AUTHOR]

Abstract: How big were the first planetesimals? We attempt to answer this question by conducting coagulation simulations in which the planetesimals grow by mutual collisions and form larger bodies and planetary embryos. The size frequency distribution (SFD) of the initial planetesimals is considered a free parameter in these simulations, and we search for the one that produces at the end objects with a SFD that is consistent with Asteroid belt constraints. We find that, if the initial planetesimals were small (e.g. km-sized), the final SFD fails to fulfill these constraints. In particular, reproducing the bump observed at diameter in the current SFD of the asteroids requires that the minimal size of the initial planetesimals was also ∼100km. This supports the idea that planetesimals formed big, namely that the size of solids in the proto-planetary disk “jumped” from sub-meter scale to multi-kilometer scale, without passing through intermediate values. Moreover, we find evidence that the initial planetesimals had to have sizes ranging from 100 to several 100km, probably even 1000km, and that their SFD had to have a slope over this interval that was similar to the one characterizing the current asteroids in the same size range. This result sets a new constraint on planetesimal formation models and opens new perspectives for the investigation of the collisional evolution in the Asteroid and Kuiper belts as well as of the accretion of the cores of the giant planets. [Copyright &y& Elsevier]

Abstract: By examining the absolute magnitude (H) distributions (hereafter HD) of the cold and hot populations in the Kuiper belt and of the Trojans of Jupiter, we find evidence that the Trojans have been captured from the outer part of the primordial trans-neptunian planetesimal disk. We develop a sketch model of the HDs in the inner and outer parts of the disk that is consistent with the observed distributions and with the dynamical evolution scenario known as the ‘Nice model’. This leads us to predict that the HD of the hot population should have the same slope of the HD of the cold population for , both as steep as the slope of the Trojans'' HD. Current data partially support this prediction, but future observations are needed to clarify this issue. Because the HD of the Trojans rolls over at to a collisional equilibrium slope that should have been acquired when the Trojans were still embedded in the primordial trans-neptunian disk, our model implies that the same roll-over should characterize the HDs of the Kuiper belt populations, in agreement with the results of Bernstein et al. [Bernstein, G.M., and 5 colleagues, 2004. Astron. J. 128, 1364–1390] and Fuentes and Holman [Fuentes, C.I., Holman, M.J., 2008. Astron. J. 136, 83–97]. Finally, we show that the constraint on the total mass of the primordial trans-neptunian disk imposed by the Nice model implies that it is unlikely that the cold population formed beyond 35 AU. [Copyright &y& Elsevier]

Abstract: The origin of Saturn''s massive ring system is still unknown. Two popular scenarios—the tidal splitting of passing comets and the collisional destruction of a satellite—rely on a high cometary flux in the past. In the present paper we attempt to quantify the cometary flux during the Late Heavy Bombardment (LHB) to assess the likelihood of both scenarios. Our analysis relies on the so-called “Nice model” of the origin of the LHB [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461; Morbidelli, A., Levison, H.H., Tsiganis, K., Gomes, R., 2005. Nature 435, 462–465; Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466–469] and on the size distribution of the primordial trans-neptunian planetesimals constrained in [Charnoz, S., Morbidelli, A., 2007. Icarus 188, 468–480]. We find that the cometary flux on Saturn during the LHB was so high that both scenarios for the formation of Saturn rings are viable in principle. However, a more detailed study shows that the comet tidal disruption scenario implies that all four giant planets should have comparable ring systems whereas the destroyed satellite scenario would work only for Saturn, and perhaps Jupiter. This is because in Saturn''s system, the synchronous orbit is interior to the Roche Limit, which is a necessary condition for maintaining a satellite in the Roche Zone up to the time of the LHB. We also discuss the apparent elimination of silicates from the ring parent body implied by the purity of the ice in Saturn''s rings. The LHB has also strong implications for the survival of the saturnian satellites: all satellites smaller than Mimas would have been destroyed during the LHB, whereas Enceladus would have had from 40% to 70% chance of survival depending on the disruption model. In conclusion, these results suggest that the LHB is the “sweet moment” for the formation of a massive ring system around Saturn. [Copyright &y& Elsevier]

Abstract: We explore the origin and orbital evolution of the Kuiper belt in the framework of a recent model of the dynamical evolution of the giant planets, sometimes known as the Nice model. This model is characterized by a short, but violent, instability phase, during which the planets were on large eccentricity orbits. It successfully explains, for the first time, the current orbital architecture of the giant planets [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461], the existence of the Trojans populations of Jupiter and Neptune [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462–465], and the origin of the late heavy bombardment of the terrestrial planets [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466–469]. One characteristic of this model is that the proto-planetary disk must have been truncated at roughly 30 to so that Neptune would stop migrating at its currently observed location. As a result, the Kuiper belt would have initially been empty. In this paper we present a new dynamical mechanism which can deliver objects from the region interior to to the Kuiper belt without excessive inclination excitation. In particular, we show that during the phase when Neptune''s eccentricity is large, the region interior to its 1:2 mean motion resonance becomes unstable and disk particles can diffuse into this area. In addition, we perform numerical simulations where the planets are forced to evolve using fictitious analytic forces, in a way consistent with the direct N-body simulations of the Nice model. Assuming that the last encounter with Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of and an eccentricity of ∼0.3, and that subsequently Neptune''s eccentricity damped in ∼1 My, our simulations reproduce the main observed properties of the Kuiper belt at an unprecedented level. In particular, our results explain, at least qualitatively: (1) the co-existence of resonant and non-resonant populations, (2) the eccentricity–inclination distribution of the Plutinos, (3) the peculiar semi-major axis—eccentricity distribution in the classical belt, (4) the outer edge at the 1:2 mean motion resonance with Neptune, (5) the bi-modal inclination distribution of the classical population, (6) the correlations between inclination and physical properties in the classical Kuiper belt, and (7) the existence of the so-called extended scattered disk. Nevertheless, we observe in the simulations a deficit of nearly-circular objects in the classical Kuiper belt. [Copyright &y& Elsevier]

Abstract: We have performed new simulations of two different scenarios for the excitation and depletion of the primordial asteroid belt, assuming Jupiter and Saturn on initially circular orbits as predicted by the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466–469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462–465]. First, we study the effects of sweeping secular resonances driven by the depletion of the solar nebula. We find that these sweeping secular resonances are incapable of giving sufficient dynamical excitation to the asteroids for nebula depletion timescales consistent with estimates for solar-type stars, and in addition cannot cause significant mass depletion in the asteroid belt or produce the observed radial mixing of different asteroid taxonomic types. Second, we study the effects of planetary embryos embedded in the primordial asteroid belt. These embedded planetary embryos, combined with the action of jovian and saturnian resonances, can lead to dynamical excitation and radial mixing comparable to the current asteroid belt. The mass depletion driven by embedded planetary embryos alone, even in the case of an eccentric Jupiter and Saturn, is roughly 10–20× less than necessary to explain the current mass of the main belt, and thus a secondary depletion event, such as that which occurs naturally in the Nice Model, is required. We discuss the implications of our new simulations for the dynamical and collisional evolution of the main belt. [Copyright &y& Elsevier]

Abstract: We study the possibility that the mutual interactions between Jupiter and Saturn prevented Type II migration from driving these planets much closer to the Sun. Our work extends previous results by Masset and Snellgrove [Masset, F., Snellgrove, M., 2001. Mon. Not. R. Astron. Soc. 320, L55–L59], by exploring a wider set of initial conditions and disk parameters, and by using a new hydrodynamical code that properly describes for the global viscous evolution of the disk. Initially both planets migrate towards the Sun, and Saturn''s migration tends to be faster. As a consequence, they eventually end up locked in a mean motion resonance. If this happens in the 2:3 resonance, the resonant motion is particularly stable, and the gaps opened by the planets in the disk may overlap. This causes a drastic change in the torque balance for the two planets, which substantially slows down the planets'' inward migration. If the gap overlap is substantial, planet migration may even be stopped or reversed. As the widths of the gaps depend on disk viscosity and scale height, this mechanism is particularly efficient in low viscosity, cool disks. The initial locking of the planets in the 2:3 resonance is a likely outcome if Saturn formed at the edge of Jupiter''s gap, but also if Saturn initially migrated rapidly from further away. We also explore the possibility of trapping in other resonances, and the subsequent evolutions. We discuss the compatibility of our results with the initial conditions adopted in Tsiganis et al. [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461] and Gomes et al. [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466–469] to explain the current orbital architecture of the giant planets and the origin of the Late Heavy Bombardment of the Moon. [Copyright &y& Elsevier]

Abstract: Chiang et al. [Chiang, E., Lithwick, Y., Murray-Clay, R., Buie, M., Grundy, W., Holman, M., 2007. In: Protostars and Planets V, pp. 895–911] have recently proposed that the observed structure of the Kuiper belt could be the result of a dynamical instability of a system of ∼5 primordial ice-giant planets in the outer Solar System. According to this scenario, before the instability occurred, these giants were growing in a highly collisionally damped environment according to the arguments in Goldreich et al. [Goldreich, P., Lithwick, Y., Sari, R., 2004. Astrophys. J. 614, 497–507; Annu. Rev. Astron. Astrophys. 42, 549–601]. Here we test this hypothesis with a series of numerical simulations using a new code designed to incorporate the dynamical effects of collisions. We find that we cannot reproduce the observed Solar System. In particular, Goldreich et al. [Goldreich, P., Lithwick, Y., Sari, R., 2004. Astrophys. J. 614, 497–507; Annu. Rev. Astron. Astrophys. 42, 549–601] and Chiang et al. [Chiang, E., Lithwick, Y., Murray-Clay, R., Buie, M., Grundy, W., Holman, M., 2007. In: Protostars and Planets V, pp. 895–911] argue that during the instability, all but two of the ice giants would be ejected from the Solar System by Jupiter and Saturn, leaving Uranus and Neptune behind. We find that ejections are actually rare and that instead the systems spread outward. This always leads to a configuration with too many planets that are too far from the Sun. Thus, we conclude that both Goldreich et al.''s scheme for the formation of Uranus and Neptune and Chiang et al.''s Kuiper belt formation scenario are not viable in their current forms. [Copyright &y& Elsevier]

Abstract: The Oort Cloud, the Kuiper belt and the Scattered Disk are dynamically distinct populations of small bodies evolving in the outer regions of the Solar System. Whereas their collisional activity is now quiet, gravitational interactions with giant planets may have shaped these populations both dynamically and collisionally during their formation. Using a hybrid approach [Charnoz, S., Morbidelli, A., 2003. Icarus 166, 141–166], the present paper tries to couple the primordial collisional and dynamical evolution of these three populations in a self-consistent way. A critical parameter is the primordial size-distribution. We show that the initial planetesimal size distribution that allows an effective mass depletion of the Kuiper belt by collisional grinding, would decimate also the population of comet-size bodies that end in the Oort Cloud and, in particular, in the Scattered Disk. As a consequence, the Oort Cloud and the Scattered Disk would be too anemic, by a factor 20 to 100, relative to the estimates achieved from the observation of the fluxes of long period and Jupiter family comets, respectively. For these two reservoirs to have a sufficient number of comets, the initial size distribution in the planetesimal disk had to be such that the mass depletion by collisional erosion of the Kuiper belt was negligible. Consequently the current mass deficit of the Kuiper belt needs to be explained by dynamical mechanisms. [Copyright &y& Elsevier]

Abstract: We study the population of faint Jupiter family comets (JFCs) that approach the Earth (perihelion distances ) by applying a debiasing technique to the observed sample. We found for the debiased cumulative luminosity function (CLF) of absolute total magnitudes a bimodal distribution in which brighter comets () follow a linear relation with a steep slope , while fainter comets follow a much shallower slope down to . The slope can be pushed up to if a second break in the distribution to a much shallower slope is introduced at . We estimate a population of about 103 faint JFCs with and (radii ). The shallowness of the CLF for faint near-Earth JFCs may be explained either as: (i) the source population (the scattered disk) has an equally very shallow distribution in the considered size range, or (ii) the distribution is flattened by the disintegration of small objects before that they have a chance of being observed. The fact that the slope of the magnitude distribution of the faint active JFCs is very similar to that found for a sample of dormant JFCs candidates suggests that for a surviving (i.e., not disintegrated) object, the probability of becoming dormant versus keeping some activity is roughly size independent. [Copyright &y& Elsevier]

Abstract: We have performed 8 numerical simulations of the final stages of accretion of the terrestrial planets, each starting with over 5× more gravitationally interacting bodies than in any previous simulations. We use a bimodal initial population spanning the region from 0.3 to 4 AU with 25 roughly Mars-mass embryos and an equal mass of material in a population of ∼1000 smaller planetesimals, consistent with models of the oligarchic growth of protoplanetary embryos. Given the large number of small planetesimals in our simulations, we are able to more accurately treat the effects of dynamical friction during the accretion process. We find that dynamical friction can significantly lower the timescales for accretion of the terrestrial planets and leads to systems of terrestrial planets that are much less dynamically excited than in previous simulations with fewer initial bodies. In addition, we study the effects of the orbits of Jupiter and Saturn on the final planetary systems by running 4 of our simulations with the present, eccentric orbits of Jupiter and Saturn (the EJS simulations) and the other 4 using a nearly circular and co-planar Jupiter and Saturn as predicted in the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466–469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462–465] (the CJS simulations). Our EJS simulations provide a better match to our Solar System in terms of the number and average mass of the final planets and the mass-weighted mean semi-major axis of the final planetary systems, although increased dynamical friction can potentially improve the fit of the CJS simulations as well. However, we find that in our EJS simulations, essentially no water-bearing material from the outer asteroid belt ends up in the final terrestrial planets, while a large amount is delivered in the CJS simulations. In addition, the terrestrial planets in the EJS simulations receive a late veneer of material after the last giant impact event that is likely too massive to reconcile with the siderophile abundances in the Earth''s mantle, while the late veneer in the CJS simulations is much more consistent with geochemical evidence. [Copyright &y& Elsevier]

Abstract: We estimate the total number and the slope of the size–frequency distribution (SFD) of dormant Jupiter family comets (JFCs) by fitting a one-parameter model to the known population. We first select 61 near-Earth objects (NEOs) that are likely to be dormant JFCs because their orbits are dynamically coupled to Jupiter [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J., Levison, H.F., Michel, P., Metcalfe, T.S., 2002a. Icarus 156, 399–433]. Then, from the numerical simulations of Levison and Duncan [1997. Icarus 127, 13–32], we construct an orbit distribution model for JFCs in the NEO orbital element space. We assume an orbit-independent SFD for all JFCs, the slope of which is our unique free parameter. Finally, we compute observational biases for dormant JFCs using a calibrated NEO survey simulator [Jedicke, R., Morbidelli, A., Spahr, T., Petit, J., Bottke, W.F., 2003. Icarus 161, 17–33]. By fitting the biased model to the data, we estimate that there are ∼75 dormant JFCs with in the NEO region and that the slope of their cumulative SFD is . Our slope for the SFD of dormant JFCs is very close to that of active JFCs as determined by Weissman and Lowry [2003. Lunar Planet. Sci. 34. Abstract 2003]. Thus, we argue that when JFCs fade they are likely to become dormant rather than to disrupt and that the fate of faded comets is size-independent. Our results imply that the size distribution of the JFC progenitors—the scattered disk trans-neptunian population—either (i) has a similar and shallow SFD or () is slightly steeper and physical processes acting on the comets in a size-dependent manner creates the shallower active comet SFD. Our measured slope, typical of collisionally evolved populations with a size-dependent impact strength [Benz, W., Asphaug, E., 1999. Icarus 142, 5–20], suggests that scattered disk bodies reached collisional equilibrium inside the protoplanetary disk prior to their removal from the planetary region. [Copyright &y& Elsevier]

We study planetary migration in a gas-free disk of planetesimals. In the case of our Solar System we show that Neptune could have had either a damped migration, limited to a few AUs, or a forced migration up to the disk''s edge, depending on the disk''s mass density. We also study the possibility of runaway migration of isolated planets in very massive disk, which might be relevant for extra-solar systems. We investigate the problem of the mass depletion of the Kuiper belt in the light of planetary migration and conclude that the belt lost its pristine mass well before that Neptune reached its current position. Therefore, Neptune effectively hit the outer edge of the proto-planetary disk. We also investigate the dynamics of massive planetary embryos embedded in the planetesimal disk. We conclude that the elimination of Earth-mass or Mars-mass embryos originally placed outside the initial location of Neptune also requires the existence of a disk edge near 30 AU. [Copyright &y& Elsevier]

We present a new algorithm designed to compute the collisional erosion of a population of small bodies undergoing a complex and rapid dynamical evolution induced by strong gravitational perturbations. Usual particle-in-a-box models have been extensively and successfully used to study the evolution of asteroids or KBOs. However, they cannot track the evolution of small bodies in rapid dynamical evolution, due to their oversimplified description of the dynamics. Our code is based on both (1) a direct simulation of the dynamical evolution which is used to compute local encounter rates and (2) a classical fragmentation model. Such a code may be used to track the erosional evolution of the planetesimal disk under the action of newly formed giant-planets, a passing star or a population of massive planetary-embryos. We present here an application to a problem related to the formation of the Oort cloud. The usually accepted formation scenario is that planetesimals, originally formed in the giant planet region, have been transported to the Oort cloud by gravitational scattering. However, it has been suggested that, during the initial transport phase, the mutual large encounter velocities might have induced a rapid and intense collisional evolution of the planetesimal population, potentially causing a significant reduction of the Oort cloud formation process. This mechanism is explored with our new algorithm. Because the advantages of our new approach are better highlighted for a population undergoing a violent dynamical evolution, we concentrate in this paper on the planetesimals originally in the Jupiter–Saturn region, although it is known that they are only minor contributors to the final Oort cloud population. A wide range of parameters is explored (mass of the particle disk, initial size-distribution, material strength): depending upon the assumed parameter values, we find that from 15 to 90% of the mass contained in bodies larger than 1 km survives the collisional process; for our preferred choice of the parameters this fraction is ∼70%. It is also found that the majority of planetesimals larger than 1–10 km are pristine, and not fragments. We show also that collisional damping may not prevent planetesimals from being ejected to the outer Solar System. Thus, although the collisional activity is high during the scattering by Jupiter and Saturn, collisional grinding does not lower by orders of magnitude the mass contained in bodies larger than 1 km, originally in the Jupiter–Saturn region. These conclusions seem to support the classical collisionless scenario of Oort cloud formation, at least for the Jupiter–Saturn region. [Copyright &y& Elsevier]

The orbital and absolute magnitude distribution of the near-Earth objects (NEOs) is difficult to compute, partly because only a modest fraction of the entire NEO population has been discovered so far, but also because the known NEOs are biased by complicated observational selection effects. To circumvent these problems, we created a model NEO population which was fit to known NEOs discovered or accidentally rediscovered by Spacewatch. Our method was to numerically integrate thousands of test particles from five source regions that we believe provide most NEOs to the inner Solar System. Four of these source regions are in or adjacent to the main asteroid belt, while the fifth one is associated with the transneptunian disk. The nearly isotropic comets, which include the Halley-type comets and the long-period comets, were not included in our model. Test bodies from our source regions that passed into the NEO region (perihelia q<1.3 AU and aphelia Q≥0.983 AU) were tracked until they were eliminated by striking the Sun or a planet or were ejected out of the inner Solar System. These integrations were used to create five residence time probability distributions in semimajor axis, eccentricity, and inclination space (one for each source). These distributions show where NEOs from a given source are statistically most likely to be located. Combining these five residence time probability distributions with an NEO absolute magnitude distribution computed from previous work and a probability function representing the observational biases associated with the Spacewatch NEO survey, we produced an NEO model population that could be fit to 138 NEOs discovered or accidentally rediscovered by Spacewatch. By testing a range of possible source combinations, a best-fit NEO model was computed which (i) provided the debiased orbital and absolute magnitude distributions for the NEO population and (ii) indicated the relative importance of each NEO source region.Our best-fit model is consistent with 960±120 NEOs having H<18 and a<7.4 AU. Approximately 44% (as of December 2000) have been found so far. The limits on this estimate are conditional, since our model does not include nearly isotropic comets. Nearly isotropic comets are generally restricted to a Tisserand parameter (with respect to Jupiter) of T<2, such that few are believed to have a<7.4 AU. Our computed NEO orbital distribution, which is valid for bodies as faint as H<22, indicates that the Amor, Apollo, and Aten populations contain 32±1%, 62±1%, and 6±1% of the NEO population, respectively. We estimate that the population of objects completely inside Earth''s orbit (IEOs) arising from our source regions is 2% the size of the NEO population. This value does not include the putative Vulcanoid population located inside Mercury''s orbit. Overall, our model predicts that ∼61% of the NEO population comes from the inner main belt (a<2.5 AU), ∼24% comes from the central main belt (2.52.8 AU), and ∼6% comes from the Jupiter-family comet region (2

The dynamical structure of the Solar System can be explained by a period of orbital instability experienced by the giant planets. While a late instability was originally proposed to explain the Late Heavy Bombardment, recent work favors an early instability. Here we model the early dynamical evolution of the outer Solar System to self-consistently constrain the most likely timing of the instability. We first simulate the dynamical sculpting of the primordial outer planetesimal disk during the accretion of Uranus and Neptune from migrating planetary embryos during the gas disk phase, and determine the separation between Neptune and the inner edge of the planetesimal disk. We performed simulations with a range of (inward and outward) migration histories for Jupiter. We find that, unless Jupiter migrated inwards by 10 AU or more, the instability almost certainly happened within 100 Myr of the start of Solar System formation. There are two distinct possible instability triggers. The first is an instability that is triggered by the planets themselves, with no appreciable influence from the planetesimal disk. About half of the planetary systems that we consider have a self-triggered instability. Of those, the median instability time is ∼ 4Myr. Among self-stable systems – where the planets are locked in a resonant chain that remains stable in the absence of a planetesimal's disk– our self-consistently sculpted planetesimal disks nonetheless trigger a giant planet instability with a median instability time of 37–62 Myr for a reasonable range of migration histories of Jupiter. The simulations that give the latest instability times are those that invoked long-range inward migration of Jupiter from 15 AU or beyond; however these simulations over-excited the inclinations of Kuiper belt objects and are inconsistent with the present-day Solar System. We conclude on dynamical grounds that the giant planet instability is likely to have occurred early in Solar System history. • The dynamical structure of Solar System can be explained by giant planet instability. • The early evolution of giant planets is used to get the timing of the instability. • The giant planet instability is likely to have occurred early in Solar System. [ABSTRACT FROM AUTHOR]

• Simulations with an excited Neptune overexcite the KB cold population. • A self graviting planetesimal disk helps objects to return to an unexcited mode. • The self-gravity is effective just for a cold population with Pluto-sized objects. • Without self gravity, we need very specific secular configurations for Neptune. The link between the dynamical evolution of the giant planets and the Kuiper Belt orbital structure can provide clues and insight about the dynamical history of the Solar System. The classical region of the Kuiper Belt has two populations (the cold and hot populations) with completely different physical and dynamical properties. These properties have been explained in the framework of a sub-set of the simulations of the Nice Model , in which Neptune remained on a low-eccentricity orbit (Neptune's eccentricity is never larger than 0.1) throughout the giant planet instability (Nesvorný 2015a,b). However, recent simulations (Gomes et al., 2018) have showed that the remaining Nice model simulations, in which Neptune temporarily acquires a large-eccentricity orbit (larger than 0.1), are also consistent with the preservation of the cold population (inclination smaller than 4°), if the latter formed in situ. However, the resulting a cold population showed in many of the simulations eccentricities larger than those observed for the real population. The purpose of this work is to discuss the dynamical effects on the Kuiper belt region due to an excited Neptune phase. We focus on a short period of time, of about six hundred thousand years, which is characterized by Neptune's large eccentricity and smooth migration with a slow precession of Neptune's perihelion. This phase was observed during a full simulation of the Nice Model (Gomes et al., 2018) just after the last jump of Neptune's orbit due to an encounter with another planet. We show that if self-gravity is considered in the disk, the precession rate of the particles longitude of perihelion ϖ is slowed down, which in turn speeds up the cycle of ϖ N − ϖ (the subscript N referring to Neptune), associated to the particles eccentricity evolution. This, combined with the effect of mutual scattering among the bodies, which spreads all orbital elements, allows some objects to return to low eccentricities. However, we show that if the cold population originally had a small total mass, this effect is negligible. Thus, we conclude that the only possibilities to keep at low eccentricity some cold-population objects during a high-eccentricity phase of Neptune are that (i) either Neptune's precession was rapid, as suggested by Batygin et al. (2011) or (ii) Neptune's slow precession phase was long enough to allow some particles to experience a full secular cycle of ϖ − ϖ N. [ABSTRACT FROM AUTHOR]

The origin of the orbital structure of the cold component of the Kuiper belt is still a hot subject of investigation. Several features of the solar system suggest that the giant planets underwent a phase of global dynamical instability, but the actual dynamical evolution of the planets during the instability is still debated. To explain the structure of the cold Kuiper belt, Nesvorny (2015, AJ 150,68) argued for a ”soft” instability, during which Neptune never achieved a very eccentric orbit. Here we investigate the possibility of a more violent instability, from an initially more compact fully resonant configuration of 5 giant planets. We show that the orbital structure of the cold Kuiper belt can be reproduced quite well provided that the cold population formed in situ, with an outer edge between 44 − 45 au and never had a large mass. [ABSTRACT FROM AUTHOR]

There are only a few known main belt (MB) asteroid families with ages greater than 2 Gyr (Brož et al., 2013; Spoto et al., 2015). Estimates based on the family producing collision rate suggest that the lack of > 2 Gyr-old families may be due to a selection bias in current techniques used to identify families. Family fragments disperse in their orbital elements, semi-major axis, a , eccentricity, e , and inclination, i , due to secular resonances, close encounters with massive asteroids and the non-gravitational Yarkovsky force. This causes the family fragments to be indistinguishable from the background of the main belt making them more difficult to identify with the hierarchical clustering method (HCM) with increasing family age. The discovery of the Eulalia and new Polana families in the inner belt relied on new techniques because Yarkovsky spreading made them too disperse to be identified using the classical HCM. The techniques used to discover the new Polana and Eulalia families are modified here to identify asteroid families by searching for correlations between a and asteroid diameter, D , or absolute magnitude, H . A group of asteroids is identified as a collisional family if its boundary in the a vs. 1 D or a vs. H planes has a characteristic V-shape which is due to the size dependent Yarkovsky spreading. The V-shape boundary is identified with two separate techniques. The first technique identifies a border by measuring a steep drop between the number of objects inside and outside of the border. The second technique identifies the V-shape border by measuring a peak in the number density of objects in a vs. 1 D , H space. Families are identified with just one or both V-shape identifying techniques. The V-shape techniques are demonstrated on the known families of Erigone, Vesta, Koronis, and families difficult to identify by HCM such as Flora, Baptistina, new Polana, Eulalia and Karin. Future applications of the technique, such as in a large scale search for > 2 Gyr-old families throughout the MB, are discussed. [ABSTRACT FROM AUTHOR]

Uncovering the formation process that reproduces the distinct properties of compact super-Earth exoplanet systems is a major goal of planet formation theory. The most successful model argues that non-resonant systems begin as resonant chains of planets that later experience a dynamical instability. However, both the boundary of stability in resonant chains and the mechanism of the instability itself are poorly understood. Previous work postulated that a secondary resonance between the fastest libration frequency and a difference in synodic frequencies destabilizes the system. Here, we use that hypothesis to produce a simple and general criterion for resonant chain stability that depends only on planet orbital periods and masses. We show that the criterion accurately predicts the maximum mass of planets in synthetic resonant chains up to six planets. More complicated resonant chains produced in population synthesis simulations are found to be less stable than expected, although our criterion remains useful and superior to machine learning models. • Resonant chain stability is set by interaction of synodic and libration frequencies • A simple criterion for stability accurately predicts emergence of chaotic behavior • Resonant chains formed in population synthesis models are less stable than expected [ABSTRACT FROM AUTHOR]

A new model for terrestrial planet formation (Hansen [2009]. Astrophys. J., 703, 1131-1140; Walsh, K.J., et al. [2011]. Nature, 2011, 206-209) has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. (Walsh, K.J., et al. [2011]. Nature, 2011, 206-209) tested a possible mechanism to truncate the disk--a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies--the inner belt is filled by bodies originating inside of 3AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as 'primitive' bodies). One implication of the truncation mechanism proposed in Walsh et al. (Walsh, K.J., et al. [2011]. Nature, 2011, 206-209) is the scattering of primitive planetesimals onto planet-crossing orbits during the formation of the planets. We find here that the planets will accrete on order 1-2% of their total mass from these bodies. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. The radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system. However, we find that a truncated disk leads to formation timescales more rapid than suggested by radiometric chronometers. In particular, the last giant impact is typically earlier than 20Myr, and a substantial amount of mass is accreted after that event. This is at odds with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with those constraints. [ABSTRACT FROM AUTHOR]

Abstract: To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets – Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N =1000–2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the “Nice model”. We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars’ mass is too large by a factor of 5–10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e =0.07–0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. Our simulations leave us with a problem: we can reasonably satisfy the observed constraints (except for Earth’s water) with a configuration of Jupiter and Saturn that is at best marginally consistent with models of the outer Solar System, as it does not allow for any outer planet migration after a few Myr. Alternately, giant planet configurations which are consistent with the Nice model fail to reproduce Mars’ small size. [Copyright &y& Elsevier]

Abstract: Establishing connections between meteorites and their parent asteroids is an important goal of planetary science. Several links have been proposed in the past, including a spectroscopic match between basaltic meteorites and (4) Vesta, that are helping scientists understand the formation and evolution of the Solar System bodies. Here we show that the shocked L chondrite meteorites, which represent about two thirds of all L chondrite falls, may be fragments of a disrupted asteroid with orbital semimajor axis . This breakup left behind thousands of identified 1–15 km asteroid fragments known as the Gefion family. Fossil L chondrite meteorites and iridium enrichment found in an ≈467 Ma old marine limestone quarry in southern Sweden, and perhaps also ∼5 large terrestrial craters with corresponding radiometric ages, may be tracing the immediate aftermath of the family-forming collision when numerous Gefion fragments evolved into the Earth-crossing orbits by the 5:2 resonance with Jupiter. This work has major implications for our understanding of the source regions of ordinary chondrite meteorites because it implies that they can sample more distant asteroid material than was previously thought possible. [Copyright &y& Elsevier]

Abstract: We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. [Laughlin, G., Steinacker, A., Adams, F.C., 2004. Astrophys. J. 608, 489–496]. The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas is also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar System. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼10−4 times MMSN). However, in this case, on average, too many (≳6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4–5 at 0.5–2 AU, which is more consistent with Solar System, for relatively wide range of disk gas surface density ( times MMSN). [Copyright &y& Elsevier]

This paper considers the origin of water on Mars, in the context of a dynamical model that accounts for most of the Earth''s water as a product of collisions between the growing Earth and planet-sized “embryos” from the asteroid belt. Mars'' history is found to be different; to explain the present mass of Mars requires that it suffer essentially no giant collisions and the bulk of its growth is through addition of smaller bodies. Asteroids and comets from beyond 2.5 AU provide the source of Mars'' water, which totals 6–27% of the Earth''s present ocean (1 Earth ocean≡1.5×1021 kg), equivalent to 600–2700-m depth on the martian surface. The D/H ratio of this material is 1.2–1.6 times Standard Mean Ocean Water, the smaller value obtaining for the larger amount of water accreted. The upper half of the range of total water accreted, while many times less than that acquired by the Earth, is consistent with geological data on Mars, and the D/H value is that derived for martian magmatic water from SNC meteorites. Both together are consistent with published interpretations of the high D/H in present-day martian atmospheric water in terms of water loss through atmospheric escape. [Copyright &y& Elsevier]

The lunar crater record features ∼ 50 basins. The radiometric dating of Apollo samples indicates that the Imbrium basin formed relatively late — from the planet formation perspective — some ≃ 3. 9 Ga. Here we develop a dynamical model for impactors in the inner solar system to provide context for the interpretation of the lunar crater record. The contribution of cometary impactors is found to be insignificant. Asteroids produced most large impacts on the terrestrial worlds in the last ≃ 3 Gyr. The great majority of early impactors were rocky planetesimals left behind at ∼ 0. 5 –1.5 au after the terrestrial planet accretion. The population of terrestrial planetesimals was reduced by disruptive collisions in the first t ∼ 20 Myr after the gas disk dispersal. We estimate that there were ∼ 4 × 1 0 5 diameter d > 10 km bodies when the Moon formed (total planetesimal mass ∼ 0. 015 M Earth at t ∼ 50 Myr). The early bombardment of the Moon was intense. To accommodate ∼ 50 known basins, the lunar basins that formed before ≃ 4. 35 –4.41 Ga must have been erased. The late formation of Imbrium occurs with a ∼ 15 –35% probability in our model. About 20 d > 10 -km bodies were expected to hit the Earth between 2.5 and 3.5 Ga, which is comparable to the number of known spherule beds in the late Archean. We discuss implications of our model for the lunar/Martian crater chronologies, Late Veneer, and noble gases in the Earth atmosphere. • The leftover planetesimals produced most lunar impacts in the first 1 Gyr. • The early lunar crater record in the first 200 Myr must have been erased. • The Imbrium basin formation happens with a 15%–35% probability in our model. • Applying the lunar chronology to Mars can lead to incorrect age estimates. • The model explains the terrestrial spherule beds found in the late Archean. [ABSTRACT FROM AUTHOR]

The Asteroid Belt is characterized by the radial mixing of bodies with different physical properties, a very low mass compared to Minimum Mass Solar Nebula expectations and has an excited orbital distribution, with eccentricities and inclinations covering the entire range of values allowed by the constraints of dynamical stability. Models of the evolution of the Asteroid Belt show that the origin of its structure is strongly linked to the process of terrestrial planet formation. The Grand Tack model presents a possible solution to the conundrum of reconciling the small mass of Mars with the properties of the Asteroid Belt, including the mass depletion, radial mixing and orbital excitation. However, while the inclination distribution produced in the Grand Tack model is in good agreement with the one observed, the eccentricity distribution is skewed towards values larger than those found today. Here, we evaluate the evolution of the orbital properties of the Asteroid Belt from the end of the Grand Tack model (at the end of the gas nebula phase when planets emerge from the dispersing gas disk), throughout the subsequent evolution of the Solar System including an instability of the Giant Planets approximately 400 Myr later. Before the instability, the terrestrial planets were modeled on dynamically cold orbits with Jupiter and Saturn locked in a 3:2 mean motion resonance. The model continues for an additional 4.1 Gyr after the giant planet instability. Our results show that the eccentricity distribution obtained in the Grand Tack model evolves towards one very similar to that currently observed, and the semimajor axis distribution does the same. The inclination distribution remains nearly unchanged with a slight preference for depletion at low inclination; this leads to the conclusion that the inclination distribution at the end of the Grand Tack is a bit over-excited. Also, we constrain the primordial eccentricities of Jupiter and Saturn, which have a major influence on the dynamical evolution of the Asteroid Belt and its final orbital structure. [ABSTRACT FROM AUTHOR]

Abstract: The main belt is believed to have originally contained an Earth mass or more of material, enough to allow the asteroids to accrete on relatively short timescales. The present-day main belt, however, only contains Earth masses. Numerical simulations suggest that this mass loss can be explained by the dynamical depletion of main belt material via gravitational perturbations from planetary embryos and a newly-formed Jupiter. To explore this scenario, we combined dynamical results from Petit et al. [Petit, J. Morbidelli, A., Chambers, J., 2001. The primordial excitation and clearing of the asteroid belt. Icarus 153, 338–347] with a collisional evolution code capable of tracking how the main belt undergoes comminution and dynamical depletion over 4.6 Gyr [Bottke, W.F., Durda, D., Nesvorny, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H., 2005. The fossilized size distribution of the main asteroid belt. Icarus 175, 111–140]. Our results were constrained by the main belt''s size–frequency distribution, the number of asteroid families produced by disruption events from diameter parent bodies over the last 3–4 Gyr, the presence of a single large impact crater on Vesta''s intact basaltic crust, and the relatively constant lunar and terrestrial impactor flux over the last 3 Gyr. We used our model to set limits on the initial size of the main belt as well as Jupiter''s formation time. We find the most likely formation time for Jupiter was after the onset of fragmentation in the main belt. These results are consistent with the estimated mean disk lifetime of 3 Myr predicted by Haisch et al. [Haisch, K.E., Lada, E.A., Lada, C.J., 2001. Disk frequencies and lifetimes in young clusters. Astrophys. J. 553, L153–L156]. The post-accretion main belt population, in the form of diameter planetesimals, was likely to have been times the current main belt''s mass. This corresponds to Earth masses, only a small fraction of the total mass thought to have existed in the main belt zone during planet formation. The remaining mass was most likely taken up by planetary embryos formed in the same region. Our results suggest that numerous planetesimals disrupted early in Solar System history, but only a small fraction of their fragments survived the dynamical depletion event described above. We believe this may explain the limited presence of iron-rich M-type, olivine-rich A-type, and non-Vesta V-type asteroids in the main belt today. The collisional lifetimes determined for main belt asteroids agree with the cosmic ray exposure ages of stony meteorites and are consistent with the limited collisional evolution detected among large Koronis family members. Using the same model, we investigated the near-Earth object (NEO) population. We show the shape of the NEO size distribution is a reflection of the main belt population, with main belt asteroids driven to resonances by Yarkovsky thermal forces. We used our model of the NEO population over the last 3 Gyr, which is consistent with the current population determined by telescopic and satellite data, to explore whether the majority of small craters () formed on Mercury, the Moon, and Mars were produced by primary impacts or by secondary impacts generated by ejecta from large craters. Our results suggest that most small craters formed on these worlds were a by-product of secondary rather than primary impacts. [Copyright &y& Elsevier]

Abstract: Planet formation models suggest the primordial main belt experienced a short but intense period of collisional evolution shortly after the formation of planetary embryos. This period is believed to have lasted until Jupiter reached its full size, when dynamical processes (e.g., sweeping resonances, excitation via planetary embryos) ejected most planetesimals from the main belt zone. The few planetesimals left behind continued to undergo comminution at a reduced rate until the present day. We investigated how this scenario affects the main belt size distribution over Solar System history using a collisional evolution model (CoEM) that accounts for these events. CoEM does not explicitly include results from dynamical models, but instead treats the unknown size of the primordial main belt and the nature/timing of its dynamical depletion using innovative but approximate methods. Model constraints were provided by the observed size frequency distribution of the asteroid belt, the observed population of asteroid families, the cratered surface of differentiated Asteroid (4) Vesta, and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr. Using CoEM, we solved for both the shape of the initial main belt size distribution after accretion and the asteroid disruption scaling law . In contrast to previous efforts, we find our derived function is very similar to results produced by numerical hydrocode simulations of asteroid impacts. Our best fit results suggest the asteroid belt experienced as much comminution over its early history as it has since it reached its low-mass state approximately 3.9–4.5 Ga. These results suggest the main belt''s wavy-shaped size-frequency distribution is a “fossil” from this violent early epoch. We find that most diameter asteroids are primordial, with their physical properties likely determined during the accretion epoch. Conversely, most smaller asteroids are byproducts of fragmentation events. The observed changes in the asteroid spin rate and lightcurve distributions near are likely to be a byproduct of this difference. Estimates based on our results imply the primordial main belt population (in the form of bodies) was 150–250 times larger than it is today, in agreement with recent dynamical simulations. [Copyright &y& Elsevier]