Chaotic motions of prometheus and pandora

Recent HST images of the saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20°. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 days at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.3 year⁻¹ for satellite masses based on a nominal density of 0.63 g cm⁻³. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 years when their apses are antialigned. In this context, we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occurred around the time their apsidal lines were antialigned.     

The evidence of an early stellar encounter in Edgeworth-Kuiper belt

We investigate the influence of a stellar fly-by encounter on the Edgeworth-Kuiper belt objects through numerical orbital calculations, in order to explain both mass depletion and high orbital inclinations of the classical Edgeworth-Kuiper belt (CEKB) objects, which have semimajor axis of 42-48 AU and perihelia beyond 35 AU. The observationally inferred total mass of the CEKB is ∼1/10 Earth masses, which is only ∼0.02 of that extrapolated from the minimum-mass solar nebula model. The CEKB consists of bimodal population: “hot population” with inclinations i?0.2-0.6 radians and “cold population” with i?0.1. The observationally suggested difference in size and color of objects between the two populations may imply different origins of the two populations. We find that both the depletion of solid materials in the CEKB and the formation of the hot population are accounted for by a single close stellar encounter with pericenter distance of 80-100 AU and inclination relative to the initial protoplanetary disk ?50°-70°. Such a stellar encounter highly pumps up eccentricities of most objects in the CEKB and then their perihelia migrate within 35 AU. These objects would be removed by Neptune's perturbations after Neptune is formed at or migrates to the current position (30 AU). Less than 10% of the original objects remain in stable orbits with small eccentricities and perihelion distances larger than 35 AU, in the CEKB, which is consistent with the observation. We find that i of the remaining objects are as large as that of the observed hot population. The only problem is how to stop Neptune's migration at ∼30 AU, which is addressed in a separate paper. The depletion by the stellar encounter extends deeply into ∼30-35 AU, which provides the basis of the formation model for the cold population through Neptune's outward migration by Levison and Morbidelli (2003, Nature, 426, 419-421). The combination of our model with Levison and Morbidelli's model could consistently explain the mass depletion, truncation at 50 AU, bimodal distribution in i, and differences in size and color between the hot and the cold populations in the CEKB.     

The dynamics of two massive planets on inclined orbits

The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on inclined orbits through both analytical techniques and extensive numerical scattering experiments. We derive a criterion for two equal mass planets on circular inclined orbits to achieve Hill stability, and conclude that significant radial migration and eccentricity pumping of both planets occurs predominantly by 2:1 and 5:3 mean motion resonant interactions. Using Laplace-Lagrange secular theory, we obtain analytical secular solutions for the orbital inclinations and longitudes of ascending nodes, and use those solutions to distinguish between the secular and resonant dynamics which arise in numerical simulations. We also illustrate how encounter maps, typically used to trace the motion of massless particles, may be modified to reproduce the gross instability seen by the numerical integrations. Such a correlation suggests promising future use of such maps to model the dynamics of more coplanar massive planet systems.     

On separation of major meteoroid streams from the sporadic background

The paper deals with a search for chosen photographic meteoroid streams compiled from the IAU Meteor Data Center Lund catalogue from which less than 2% of the orbits had to be removed due to internal inconsistency among the orbit parameters. Additional 35 orbits were removed due to extremely high hyperbolic velocities. The final set consists of 3411 orbits. Members of the Quadrantids, Lyrids, Perseids and Geminids were searched for, firstly, by a stream-search procedure utilizing the Southworth-HawkinsD-criterion. This choice, as a rule, represents the most abundant filament of the stream. Secondly, rate distribution histograms ofD were divided into region of shower meteors and region of sporadic background meteors. The searched database with a relatively low abundance of sporadic meteors in the analyzed periods simplified this choice, and followingly, fitting the obtained values by means of power and exponential functions, the limitingD _s for particular showers were derived. The derivedD _s appears as the optimum value, as for higherD, the number of sporadic meteors included in the stream sample increases more rapidly than the number of additional shower meteors, and for smallerD, the number of shower meteors decreases quicker than the number of omitted sporadic meteors. The following counts of shower meteorsN and limitingD _s were found: Quadrantids (39, 0.22), Lyrids (11, 0.15), Perseids (595, 0.53) and Geminids (224, 0.32). Efficiency of the procedure was tested comparing the number of sporadic meteors in the region of radiant area and the neighbouring regions of the same size.     

Embedded star clusters and the formation of the Oort Cloud

Observations suggest most stars originate in clusters embedded in giant molecular clouds [Lada, C.J., Lada, E.A., 2003. Annu. Rev. Astron. Astrophys. 41, 57-115]. Our Solar System likely spent 1-5 Myrs in such regions just after it formed. Thus the Oort Cloud (OC) possibly retains evidence of the Sun's early dynamical history and of the stellar and tidal influence of the cluster. Indeed, the newly found objects (90377) Sedna and 2000 CR₁₀₅ may have been put on their present orbits by such processes [Morbidelli, A., Levison, H.F., 2004. Astron. J. 128, 2564-2576]. Results are presented here of numerical simulations of the orbital evolution of comets subject to the influence of the Sun, Jupiter and Saturn (with their current masses on orbits appropriate to the period before the Late Heavy Bombardment (LHB) [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461]), passing stars and tidal force associated with the gas and stars of an embedded star cluster. The cluster was taken to be a Plummer model with 200-400 stars, with a range of initial central densities. The Sun's orbit was integrated in the cluster potential together with Jupiter and Saturn and the test particles. Stellar encounters were incorporated by directly integrating the effects of stars passing within a sphere centred on the Sun of radius equal to the Plummer radius for low-density clusters and half a Plummer radius for high-density clusters. The gravitational influence of the gas was modeled using the tidal force of the cluster potential. For a given solar orbit, the mean density, 〈ρ〉, was computed by orbit-averaging the density of material encountered. This parameter proved to be a good measure for predicting the properties of the OC. On average 2-18% of our initial sample of comets end up in the OC after 1-3 Myr. A comet is defined to be part of the OC if it is bound and has q>35 AU. Our models show that the median distance of an object in the OC scales approximately as 〈ρ〉^−1/2 when . Our models easily produce objects on orbits like that of (90377) Sedna [Brown, M.E., Trujillo, C., Rabinowitz, D., 2004. Astrophys. J. 617, 645-649] within ∼1 Myr in cases where the mean density is or higher; one needs mean densities of order to create objects like 2000 CR₁₀₅ by this mechanism, which are reasonable (see, e.g., Guthermuth, R.A., Megeath, S.T., Pipher, J.L., Williams, J.P., Allen, L.E., Myers, P.C., Raines, S.N., 2005. Astrophys. J. 632, 397-420). Thus the latter object may also be part of the OC. Close stellar passages can stir the primordial Kuiper Belt to sufficiently high eccentricities (e?0.05; Kenyon, S.J., Bromley, B.C., 2002. Astron. J. 123, 1757-1775) that collisions become destructive. From the simulations performed it is determined that there is a 50% or better chance to stir the primordial Kuiper Belt to eccentricities e?0.05 at 50 AU when . The orbit of the new object 2003 UB₃₁₃ [Brown, M.E., Trujillo, C.A., Rabinowitz, D.L., 2005. Astrophys. J. 635, L97-L100] is only reproduced for mean cluster densities of the order of , but in the simulations it could not come to be on its current orbit by this mechanism without disrupting the formation of bodies in the primordial Kuiper Belt down to 20 AU. It is therefore improbable that the latter object is created by this mechanism.