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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2007.11.035 Byline: Harold F. Levison (a), Alessandro Morbidelli (b), Christa VanLaerhoven (c), Rodney Gomes (d), Kleomenis Tsiganis (e) Keywords: Origin; Solar System; Kuiper belt; Trans-neptunian objects; Planets; migration; Celestial mechanics 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 35AU 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 [approximately equal to]35AU 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 [approximately equal to]27AU and an eccentricity of [approximately equal to]0.3, and that subsequently Neptune's eccentricity damped in [approximately equal to]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. Author Affiliation: (a) Southwest Research Institute, Department of Space Studies, 1050 Walnut Street, Suite 400, Boulder, CO 80302, USA (b) Observatoire de la CA[acute accent]te d' Azur, BP 4229, 06304 Nice Cedex 4, France (c) Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver BC, V6T 1Z1, Canada (d) Observatorio Nacional/MCT, Rua General Jose Cristino 77, 20921-400 Rio de Janeiro, RJ, Brazil (e) Section of Astrophysics, Astronomy & Mechanics, Department of Phyiscs, Aristotle University of Thessaloniki, GR 54 124 Thessaloniki, Greece Article History: Received 30 December 2006; Revised 13 November 2007

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2006.05.026 Byline: Rodney S. Gomes (a), John J. Matese (b), Jack J. Lissauer (c) Keywords: Trans-neptunian belt; Comets; dynamics Abstract: Most known trans-neptunian objects (TNO's) are either on low eccentricity orbits or could have been perturbed to their current trajectories via gravitational interactions with known bodies. However, one or two recently-discovered TNO's are distant detached objects (DDO's) (perihelion, q40AU and semimajor axis, a50AU) whose origins are not as easily understood. We investigate the parameter space of a hypothetical distant planetary-mass solar companion which could detach the perihelion of a Neptune-dominated TNO into a DDO orbit. Perturbations of the giant planets are also included. The problem is analyzed using two models. In the first model, we start with a distribution of undetached, low-inclination TNO's having a wide range of semimajor axes. The planetary perturbations and the companion perturbation are treated in the adiabatic, secularly averaged tidal approximation. This provides a starting point for a more detailed analysis by providing insights as to the companion parameter space likely to create DDO's. The second model includes the companion and the planets and numerically integrates perturbations on a sampling that is based on the real population of scattered disk objects (SDO's). A single calculation is performed including the mutual interactions and migration of the planets. By comparing these models, we distinguish the distant detached population that can be attributable to the secular interaction from those that require additional planetary perturbations. We find that a DDO can be produced by a hypothetical Neptune-mass companion having semiminor axis, b.sub.ca[c]1/22000AU or a Jupiter-mass companion with b.sub.ca[c]1/25000AU. DDO's produced by such a companion are likely to have small inclinations to the ecliptic only if the companion's orbit is significantly inclined. We also discuss the possibility that the tilt of the planets' invariable plane relative to the solar equatorial plane has been produced by such a hypothetical distant planetary-mass companion. Perturbations of a companion on Oort cloud comets are also considered. Author Affiliation: (a) Observatorio Nacional, Rua General Jose Cristino, 77, 20921-400 Rio de Janeiro, RJ, Brazil (b) Department of Physics, University of Louisiana at Lafayette, Lafayette, LA 70504-4210, USA (c) Space Science and Astrobiology Division, MS 245-3, NASA Ames Research Center, Moffett Field, CA 94035, USA Article History: Received 16 December 2005; Revised 18 May 2006

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. Keywords: Kuiper belt Resonance; Solar System formation

Abstract: Numerical integrations of the equations of motion of the giant planets and scattering particles show that there is a possible orbital itinerary that a particle may follow from a scattering mode up to a stable position near the orbit of 2004 XR190. This orbital evolution requires that the particle gets trapped in a mean motion resonance with Neptune coupled with the Kozai resonance. Imposing migration on Neptune while a particle is experiencing both resonances can entail an escape from resonance at a low particle’s eccentricity. This eccentricity and the associated inclination are always similar to those of 2004 XR190. I conclude that 2004 XR190 was most likely a scattered object that went through those resonance processes and was eventually deposited at its current position. By the same argument, it is expected that there must exist several other objects with similar semimajor axis, eccentricity and inclination as those of 2004 XR190. [Copyright &y& Elsevier]

We review two main scenarios that may have implanted Sedna, 2004 VN112 and 2000 CR105 on their current peculiar orbits. These scenarios are based on perihelion lifting mechanisms that acted upon primordial scattered icy bodies. Supposing that the Sun was formed in a dense star cluster and that the gas giants were also forming while the cluster was still dense, an inner Oort cloud that includes Sedna at its inner edge could have been formed by the circularization of icy leftovers orbits scattered by the gas giants. A putative planetary mass solar companion can also produce a similar population of icy bodies through a perihelion lifting mechanism induced by secular resonances from the companion. A third scenario also dependent on a primordial dense cluster may contribute to adding a significant number of extrasolar icy bodies to the main solar component of the population created by the cluster model. These extrasolar objects are transferred to Sun orbits from the scattered disk of passing stars that were numerous in the dense primordial environment. We compare the scenarios as to the orbital distribution of the induced populations as well as their total mass. We conclude that both the cluster model and the solar companion model can produce icy body populations consistent with Sedna's orbit. It is also quite possible that this inner Oort cloud may be composed of roughly one tenth of extrasolar objects. [ABSTRACT FROM PUBLISHER]

Before the discovery of the first member of the Kuiper belt in 1992, the trans-Neptunian population was supposed to lie on a flat disk and each member would follow a barely eccentric orbit. While less conventional orbits for the trans-Neptunian objects were being discovered, our understanding of its orbital structure and origin was continually changed. A basic classification of the trans-Neptunian population as to their orbits identifies a classical low inclination Kuiper belt population, a resonant population, a high inclination Kuiper belt population, a scattered population and an extended population. Several mechanisms have been proposed to explain the orbital architecture of the Kuiper belt population. Presently, the most plausible scenarios are unequivocally related with the primordial planetary migration induced by a planetesimal disk. Low inclination orbits in the Kuiper belt may have been moderately pushed out from a dynamically cold primordial disk by the resonance sweeping mechanism. The origin of high inclination objects in the classical Kuiper belt is however to be found in a primordial Neptune scattered population, through a perihelion increasing mechanism based on secular resonances. Another push-out mechanism based on the sweeping of the 1:2 resonance with Neptune has also been invoked to explain the low inclination orbits in the classical Kuiper belt. Assuming these last two mechanisms, Kuiper belt objects do not need to have been formed in situ. This kind of formation process would demand a quite large original mass in the Kuiper belt region, which would have brought Neptune beyond its present position at 30 AU. Thus with the exception of the low inclination classical Kuiper belt objects and a few resonant ones, all other trans-Neptunian objects are present or past scattered objects. This notion also includes the case for Sedna, so far the only certain member of the extended population. In its most plausible formation scenario, it was a primordial scattered object by Neptune whose perihelion was increased by the close passage of a star. [ABSTRACT FROM PUBLISHER]

In this paper, the theory of Sagnier was applied to the major planets, in order to have a first evaluation of this theory which was built, primarily, to study the galilean satellites of Jupiter. In this application we included the first order of the intermediary solution and the solution of the linear variational equations. Results from other theories, mainly those of Simon and Bretagnon, have been used as basis for comparisons. The results and their comparisons are shown by means of tables of coefficients and proper frequencies and graphs of variations of the orbital elements. [ABSTRACT FROM AUTHOR]