Andrea Carusi

Planetary close encounters: geometry of approach and post-encounter orbital parameters

AbstractÖpiks assumptions on the geometry of particle trajectories leading to and through planetary close encounters are used to compute the distribution of changes in heliocentric orbital elements that result from such encounters for a range of initial heliocentric orbits. Behaviour at encounter is assumed to follow two-body (particle—planet) gravitational scattering, while before and after encounter particle motion is only governed by the force of the Sun. Derivation of these distributions allows precise analysis of the probability of various outcomes in terms of the physical characteristics of the bodies involved. For example, they allow an explanation and prediction of the asymmetry of the extreme energy perturbations for different initial orbits. The formulae derived here may be applied to problems including the original accumulation of planets and satellites, and the continuing evolution of populations of small bodies, such as asteroids and comets.

Planetary accretion rates: Analytical derivation

Abstract Analytic formulae for estimating planetary accretion rates have long been available for conditions where random motion of planetesimals controls velocities relative to a growing planet. Recent Monte Carlo studies have explored a wider range of conditions, but gave impact rates only for the specific conditions under which those numerical experiments were performed. Now analytical formulae, which are valid even when keplerian shear controls the approach velocity, and which accurately reproduce the Monte Carlo results, give accretion rates over a wide range of conditions relevant to the problem of planet formation.

Outcomes of planetary close encounters: A systematic comparison of methodologies

Abstract Motion during a planetary close encounter can be described reasonably well by a two-body approximation, in which the effect of the Sun is temporarily neglected. The approximation is suspect for very slow encounters, such as occur in the quiescent swarm of planetesimals that encountered early planetary embryos. Opiks formulation of the two-body approximation fails under those conditions, predicting motion different from the correct three-body behavior. The differences are generally due to small distant perturbations of heliocentric orbits during approach toward encounter, rather than due to failure of the two-body model at close encounter. This conclusion comes from intercomparison of several ways of computing and estimating the outcomes of encounters. Comparison and physical interpretation is facilitated by a strategy of studying suites of trajectories in a revealing graphical display. Reinterpretation of past Monte Carlo studies also shows that the two-body approximation can be valid even where the Opik method is not. The approximation may apply to the quiescent planetesimal swarm if the physical effects that cause failure of the Opik method are accounted for. The prevalent effects of distant perturbations often yield horseshoe orbits, which may substantially reduce accretion from a wide band within the feeding zone of a planetary embryo. Use of the two-body approximation in swarms will require that encounters offset by distant perturbations be statistically replaced and compensated by other perturbed trajectories. In some cases the two-body model will need to account for partial rotation of relative velocity vectors, rather than full asymptote-to-asymptote rotation. Further studies are needed to find the real limits of the two-body model. Special attention will need to be focused on close encounters of tangential and not-quite-crossing orbits, which are moderately probable and potentially deviate from two-body behavior.

High-order librations of Halley-type comets

Halley-type comets, usually referred to as those with revolution periods of 20 to 200 yr, can be dynamically defined by the values of their Tisserand invariants with respect to Jupiter, which account for the processes that brought these comets into the present orbits. Long-term integrations of their motion show oscillations of their heliocentric elements when the comets are far from the Sun and the centre of their motion is the barycentre of the solar system. The shift from barycentric to heliocentric motion is also responsible for the major changes of orbital elements within a single revolution which, in the case of direct orbits, may follow regular libration patterns with typical periods of 350–400 yr. This is the reason for the concentration of periods around 70 yr. Some examples of this behaviour and a short discussion of its importance for the dynamical history of Halley-type comets are presented.

Atens: Importance among Near-Earth Asteroids and search strategies

Abstract The class of Near-Earth Asteroids known as Atens are very important search targets for two reasons: first, recent studies have shown that they have the highest intrinsic frequency of close encounters with the Earth, and second, they are probably undersampled in the known NEA population, as searches have always concentrated toward the opposition region. In order to remove this bias, we outline a few search strategies to increase their discovery rate with the available equipment, before an all-sky survey up to magnitude 22 is implemented (the Spaceguard Survey). Searches should concentrate on two regions located between 50° and 120° of elongation from the Sun. The Campo Imperatore Near-Earth Object Survey (CINEOS) will be the first specific search program to implement such a strategy.

Planetary close encounters: Importance of nearly tangent orbits

It is shown that close encounters between Jupiter and minor bodies are generally more efficient if the initial orbit of the small body is nearly tangent to that of the planet. Starting from the analysis of the results of previous numerical simulations, some indications on the mobility of the small bodies in the semiaxis-eccentricity diagram are given.

The effect of orbital eccentricities on the shape of the hill-type analytical stability surfaces in the general three-body problem

Hill-type stability surfaces are computed for the general hierarchical three-body problem for non-zero eccentricities of the initial osculating orbits. Significant differences are found between them and the one obtained for initial zero eccentricities. Application is made to the triple subgroups of the Solar System; in particular it is found that no analytical guarantee of Hill-type stability can be given to any of the satellites against solar perturbations.

Spaceguard-1: a space-based observatory for NEO physical characterization and discovery

We investigate a broad system design for a space-based observatory operating at mid-infrared and visible wavelengths to perform physical characterization and discovery of near-Earth objects (NEOs) in the inner solar system. Our goals require measurements that are much more efficiently done from space. The mission objectives are to obtain accurate diameters, albedos and multiband reflectance properties for the known NEOs, and to conduct a search for objects spending most or all their orbital period inside Earths orbit. The purpose is to observe a large fraction of the existing population during a mission operational lifetime of two years. A rather modest sized telescope (70 cm primary mirror and Ritchey-Chretien optical configuration) is found to be adequate to meet the objectives.

Effects of a close encounter with Jupiter on different populations of planet-crossing objects

The evolutions of different planet-crossing populations due to a close encounter with Jupiter are examined and the implications on materials displacement throughout the solar system are discussed. The effects of the encounter are shown to be very important for those planet-crossers that could be responsible of planets surface cratering.

On the Past Orbital History of Comet P/Halley

In recent papers (Carusi et al.; 1986, 1987) the authors reported the discovery of temporary librating behaviours about high order mean motion resonances with Jupiter of a number of short-period comets of Halley type, taking place in the period 1585 – 2406 AD. These comets are: P/Brorsen-Metcalf, P/Pons-Brooks and P/O1bers, all librating about the 6∶1 resonance, P/Dubiago, about the 5∶1, and P/Vaisala 2, about the 7∶1.