Dynamics Of Small Bodies Research Articles

GTasb3D: A Novel 3D Framework for Modeling Thermal Evolution and Rarefied Flows in Porous Active Small Bodies with Various Shapes

Volatiles in small bodies provide important clues to solar system evolution and are of in-situ-resource-utilization interest. Explicit modeling of small bodies’ global thermophysical process is essential to assess volatiles’ evolution and abundance. Previous numerical studies commonly use a finite difference/volume method, which has limited capability in simulating the interior thermal dynamics of small bodies with realistic shapes. Here we developed a novel 3D framework using the generalized finite difference method for modeling thermal evolution of active small bodies (GTasb3D). By fully solving the energy and mass conservation equations using a mesh-free, Cartesian-coordinate-based method, this framework can evaluate the heat and mass transport in a porous cometary body of various shapes. Several tests and comparisons with previous studies have been carried out to verify this framework's accuracy and efficiency. We show that the timescale to achieve thermal equilibrium and the global temperature distribution are in good agreement with previous theoretical and numerical estimates. The GTasb3D simulations show that ice sublimation mainly occurs near the ice front, and parts of the resulting vapor recondense beneath the ice front. The surface gas density dramatically decreases as the ice retreats. For a 1 km radius object located at 3 au with initially homogeneous dust-ice distribution, the depth to ice at the equator is >∼2 cm after ∼10 yr, assuming that a dust mantle is left behind after ice depletion. At this stage, the global gas production rate is below the gas emission detection capability but is capable of lifting submillimeter-sized dust from the nucleus’s near-subsurface.

Space history of the High Possil and Strathmore meteorites from Ne and Ar isotopes

The High Possil and Strathmore L6 chondrites fell in Scotland in 1804 and 1917 respectively. Unravelling their cosmic-ray exposure (CRE) ages provides crucial information about when they were ejected from the parent body, how they were delivered to Earth and is ultimately important for understanding the dynamics of small bodies in the solar system. Here we use new measurements of the Ne and Ar isotopic composition to determine CRE ages of both meteorites. Duplicated cosmogenic 21 Ne and 38 Ar concentrations yield CRE ages of 44.6 ± 4.6 Ma for High Possil and 15.4 ± 1.3 Ma for Strathmore. These coincide with well-established peaks in the ejection record for the L6 chondrites. They yield 40 Ar gas retention ages in excess of 3.15 Ga, which is consistent with both meteorites originating at depth within the parent body at the time of asteroidal break-up. Thematic collection: This article is part of the Early Career Research collection available at: https://www.lyellcollection.org/cc/SJG-early-career-research

Closed-form perturbation theory in the restricted three-body problem without relegation

We propose a closed-form normalization method suitable for the study of the secular dynamics of small bodies in heliocentric orbits perturbed by the tidal potential of a planet with orbit external to the orbit of the small body. The method makes no use of relegation, thus circumventing all convergence issues related to that technique. The method is based on a convenient use of a book-keeping parameter keeping simultaneously track of all the small quantities in the problem. The book-keeping affects both the Lie series and the Poisson structure employed in successive perturbative steps. In particular, it affects the definition of the normal form remainder at every normalization step. We show the results obtained by assuming Jupiter as perturbing planet, and we discuss the validity and limits of the method.

High-fidelity landing simulation of small body landers: Modeling and mass distribution effects on bouncing motion

The surface dynamics of small bodies is a key problem for landing and sample return missions. It is also very meaningful for the research of morphologic evolution of small bodies. However, such surface dynamics problem is so difficult that the high-fidelity simulation of a lander on and above the surface of a small body is still a big challenge. This paper proposes a method to simulate six degrees of freedom motion of arbitrary-shaped landers in the neighborhood of a small body with multi-contact. In detail, the contacts between the lander and the small body are processed by utilizing the Polygonal Contact Model (PCM). Considering the orbital and attitude dynamics, the dynamical model of a lander in six degrees of freedom is constructed over a small body. Some specific issues in the numerical integration are addressed and figured out. Furthermore, two methods are proposed to reduce the computational cost significantly, which make the Monte Carlo simulations feasible. Finally, the effect of the lander mass distribution on its bouncing motion is investigated parametrically to illustrate the effectiveness of the above method.

Dynamics of small bodies in orbits between Jupiter and Saturn

We examine the dynamics of small bodies in orbits similar to that of comet 29P/Schwassmann-Wachmann 1, i.e. near-circular orbits between Jupiter and Saturn. As of late 2019, there are 14 other known bodies in this region that lie in similar orbits. Previous research has shown that this region of the solar system, which in this work we call the “near Centaur region” (NCR), is not stable, suggesting that any bodies found in it would have very short lifetimes. We performed 20 Myr high-precision numerical simulations of the evolution of massless particles, initially located in the Kuiper belt but close to Neptune, with perihelia slightly below 33 au (“Neptune crossers”). Some of these particles quickly migrate inward, passing through the NCR before becoming Jupiter Family Comets. We find that objects in the NCR do indeed generally travel through it very quickly. However, our simulations reveal that resonant behavior in this region is somewhat common and can trap objects for up to 100 Kyr. We summarize the dynamics of 29P and other observed bodies in the region—two of which seem to be clearly exhibiting resonant behavior—and use our simulations to put limits on the reservoir size of the Neptune crossers, which at its time determines the reservoir size of the Kuiper belt. Finally, we put some constraints on the current population of Centaurs and particularly of the NCR population, based on the injection rates required to keep the observed population of Jupiter family comets in steady-state.

The use of particle distributions in Solar system small body dynamics

ABSTRACT The extraterrestrial material, called meteoroids, that constantly enters the Earth’s atmosphere gives us a unique opportunity to examine the motion and population of small bodies in the Solar system. This exploration requires simulating the motion of these particles. Currently, only the timing of meteoroids encountering the Earth is well predicted by such simulations, while other parameters are uncertain. This can be remedied by proper stochastic representation and estimation using a sufficient number of samples. We propose methods to both represent simulations in a stochastic manner and to improve sampling using Importance Sampling. We also demonstrate these methods practically with a test model. Using the test model resulted in an error reduction by a factor of 3 without increase in computation time. Thus, we validated that these techniques can be implemented on and are compatible with Solar system small body dynamics models. Based on these results we predict that when properly implemented on a larger and more complex model, Importance Sampling can improve sampling numbers by several orders of magnitude without increasing computation time, depending on the simulation in question. The methods presented here bring advantages such as; greatly reduced estimation errors, fitting models without re-running simulations, model comparisons without sample variations, circumventing unknown properties using invariant measures, representing large particle numbers without additional errors. This methodology has wide application possibility and will enable larger, more reliable and reusable simulations of dynamical astronomy.

Closed-form perturbation theory in the Sun-Jupiter restricted three body problem without relegation

AbstractWe present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the Lie series organization but also in the Poisson bracket structure employed in all perturbative steps. In particular, we show how the above scheme leads to a redefinition of the remainder of the normal form at every step of the formal solution of the homological equation. An application is given for the semi-analytical representation of the orbits of main belt asteroids.

Chaos in the inert Oort cloud

Context. Distant trans-Neptunian objects are subject to planetary perturbations and galactic tides. The former decrease with the distance, while the latter increase. In the intermediate regime where they have the same order of magnitude (the “inert Oort cloud”), both are weak, resulting in very long evolution timescales. To date, three observed objects can be considered to belong to this category. Aims. We aim to provide a clear understanding of where this transition occurs, and to characterise the long-term dynamics of small bodies in the intermediate regime: relevant resonances, chaotic zones (if any), and timescales at play. Methods. The different regimes are explored analytically and numerically. We also monitored the behaviour of swarms of particles during 4.5 Gyrs in order to identify which of the dynamical features are discernible in a realistic amount of time. Results. There exists a tilted equilibrium plane (Laplace plane) about which orbits precess. The dynamics is integrable in the low and high semi-major axis regimes, but mostly chaotic in between. From about 800 to 1100 astronomical units (au), the chaos covers almost all the eccentricity range. The diffusion timescales are large, but not to the point of being indiscernible in a 4.5 Gyrs duration: the perihelion distance can actually vary from tens to hundreds of au. Orbital variations are damped near the ecliptic (where previous studies focussed), but favoured in specific ranges of inclination corresponding to well-defined resonances. Moreover, starting from uniform distributions, the orbital angles cluster after 4.5 Gyrs for semi-major axes larger than 500 au, because of a very slow differential precession. Conclusions. Even if it is characterised by very long timescales, the inert Oort cloud mostly features chaotic regions; it is therefore much less inert than it appears. Orbits can be considered inert over 4.5 Gyrs only in small portions of the space of orbital elements, which include (90377) Sedna and 2012VP113. Effects of the galactic tides are discernible down to semi-major axes of about 500 au. We advocate including the galactic tides in simulations of distant trans-Neptunian objects, especially when studying the formation of detached bodies or the clustering of orbital elements.

A Monte Carlo-type simulation toolbox for Solar System small body dynamics: Application to the October Draconids

We present the current status and first results from a Monte Carlo-type simulation toolbox for Solar System small body dynamics. We also present fundamental methods for evaluating the results of this type of simulations using convergence criteria. The calculations consider a body in the Solar System with a mass loss mechanism that generates smaller particles. In our application the body, or parent body, is a comet and the mass loss mechanism is a sublimation process. In order to study mass propagation from parent bodies to Earth, we use the toolbox to sample the uncertainty distributions of relevant comet parameters and to find the resulting Earth influx distributions. The initial distributions considered represent orbital elements, sublimation distance, cometary and meteoroid densities, comet and meteoroid sizes and cometary surface activity. Simulations include perturbations from all major planets, radiation pressure and the Poynting-Robertson effect. In this paper we present the results of an initial software validation performed by producing synthetic versions of the 1933, 1946, 2011 and 2012 October Draconids meteor outbursts and comparing them with observational data and previous models. The synthetic meteor showers were generated by ejecting and propagating material from the recognized parent body of the October Draconids; the comet 21P/Giacobini-Zinner. Material was ejected during 17 perihelion passages between 1866 and 1972. Each perihelion passage was sampled with 50 clones of the parent body, all producing meteoroid streams. The clones were drawn from a multidimensional Gaussian distribution on the orbital elements, with distribution variances proportional to observational uncertainties. In the simulations, each clone ejected 8000 particles. Each particle was assigned an individual weight proportional to the mass loss it represented. This generated a total of 6.7 million test particles, out of which 43 thousand entered the Earth's Hill sphere during 1900–2020 and were considered encounters. The simulation reproduces the predictions and observations of the 1933, 1946, 2011 and 2012 October Draconids, including the unexpected but measured deviation of the meteoroid mass index from a power law in 2012 as compared to 2011. We show that when convergence is sufficient in the simulation, the fraction between two encountered mass distributions is independent of the assumed input mass distribution. Finally, we predict an outburst for the 2018 October Draconids with a peak on October 8–9 that could be up to twice as large as the 2011 and 2012 outbursts.

A Study of the Lunisolar Secular Resonance 2ω˙+Ω˙=0

The dynamics of small bodies around the Earth has gained a renewed interest, since the awareness of the problems that space debris can cause in the nearby future. A relevant role in space debris is played by lunisolar secular resonances, which might contribute to an increase of the orbital elements, typically of the eccentricity. We concentrate our attention on the lunisolar secular resonance described by the relation $2\dot{\omega}+\dot{\Omega}=0$, where $\omega$ and $\Omega$ denote the argument of perigee and the longitude of the ascending node of the space debris. We introduce three different models with increasing complexity. We show that the growth in eccentricity, as observed in space debris located in the MEO region at the inclination about equal to $56^\circ$, can be explained as a natural effect of the secular resonance $2\dot{\omega}+\dot{\Omega}=0$, while the chaotic variations of the orbital parameters are the result of interaction and overlapping of nearby resonances.

Automated stable region generation, detection, and representation for applications to mission design

This paper presents an automated algorithm to extract dynamical features, such as stability constraints, from phase space maps. The functional representation of these constraints allows their inclusion in optimization problems and thus expands the use of dynamical tools in space mission design. The challenge to autonomously detect the regions of interest in stability maps is discussed through utilizing image processing algorithms to cluster map data. Additionally, to use the detected regions, both discrete and smooth functional representations are studied. Based on similar clustering techniques that have been considered in extracting and representing features of phase space maps, we proposed an adaptively map generation algorithm. It creates a nonuniform grid of points on a map which is denser near the boundaries of the regions of interest. Both representation and map generation algorithms provide significant performance enhancements in phase space analysis. All these techniques are illustrated on examples of stability maps in small body dynamics.

ASTEROID SECULAR DYNAMICS: CERES’ FINGERPRINT IDENTIFIED

Here we report on the significant role of a so far overlooked dynamical aspect, namely, a secular resonance between the dwarf planet Ceres and other asteroids. We demonstrate that this type of secular resonance can be the dominant dynamical factor in certain regions of the main asteroid belt. Specifically, we performed a dynamical analysis of the asteroids belonging to the (1726) Hoffmeister family. To identify which dynamical mechanisms are actually at work in this part of the main asteroid belt, i.e., to isolate the main perturber(s), we study the evolution of this family in time. The study is accomplished using numerical integrations of test particles performed within different dynamical models. The obtained results reveal that the post-impact evolution of the Hoffmeister asteroid family is a direct consequence of the nodal secular resonance with Ceres. This leads us to the conclusion that similar effects must exist in other parts of the asteroid belt. In this respect, the obtained results shed light on an important and entirely new aspect of the long-term dynamics of small bodies. Ceres' fingerprint in asteroid dynamics, expressed through the discovered secular resonance effect, completely changes our understanding of the way in which perturbations by Ceres-like objects affect the orbits of nearby bodies.

Yarkovsky-driven spreading of the Eureka family of Mars Trojans

Out of nine known stable Mars Trojans, seven appear to be members of an orbital grouping including the largest Trojan, Eureka. In order to test if this could be a genetic family, we simulated the long term evolution of a tight orbital cluster centered on Eureka. We explored two cases: cluster dispersal through planetary gravity alone over 1Gyr, and a 1Gyr evolution due to both gravity and the Yarkovsky effect. We find that the dispersal of the cluster in eccentricity is primarily due to dynamical chaos, while the inclinations and libration amplitudes are primarily changed by the Yarkovsky effect. Current distribution of the cluster members orbits is indicative of an initially tight orbital grouping that was affected by a negative acceleration (i.e. one against the orbital motion) consistent with the thermal Yarkovsky effect. We conclude that the cluster is a genetic family formed either in a collision or through multiple rotational fissions. The cluster’s age is on the order of 1Gyr, and its long-term orbital evolution is likely dominated by the seasonal, rather than diurnal, Yarkovsky effect. If confirmed, Gyr-scale dominance of the seasonal Yarkovsky effect may indicate suppression of the diurnal Yarkovsky drift by the related YORP effect. Further study of Mars Trojans is essential for understanding the long-term orbital and rotational dynamics of small bodies in the absence of frequent collisions.

PURSUING THE PLANET–DEBRIS DISK CONNECTION: ANALYSIS OF UPPER LIMITS FROM THE ANGLO-AUSTRALIAN PLANET SEARCH

Solid material in protoplanetary discs will suffer one of two fates after the epoch of planet formation; either being bound up into planetary bodies, or remaining in smaller planetesimals to be ground into dust. These end states are identified through detection of sub-stellar companions by periodic radial velocity (or transit) variations of the star, and excess emission at mid- and far-infrared wavelengths, respectively. Since the material that goes into producing the observable outcomes of planet formation is the same, we might expect these components to be related both to each other and their host star. Heretofore, our knowledge of planetary systems around other stars has been strongly limited by instrumental sensitivity. In this work, we combine observations at far-infrared wavelengths by IRAS, Spitzer, and Herschel with limits on planetary companions derived from non-detections in the 16-year Anglo-Australian Planet Search to clarify the architectures of these (potential) planetary systems and search for evidence of correlations between their constituent parts. We find no convincing evidence of such correlations, possibly owing to the dynamical history of the disk systems, or the greater distance of the planet-search targets. Our results place robust limits on the presence of Jupiter analogs which, in concert with the debris disk observations, provides insights on the small-body dynamics of these nearby systems.

Adaptive Reachability Analysis to Achieve Mission Objectives in Strongly Non-Keplerian Systems

Adaptive numerical reachability analysis is studied as a tool for coping with sensitive, strongly non-Keplerian dynamics when planning impulsive spacecraft maneuvers in pursuit of mission objectives at small-body systems. The concept of an objective reachability map is developed beginning from analytical results for the Kepler problem and is shown to become intricately structured for the environments of asteroid Itokawa and Martian satellite Phobos. An existing method for efficient map computation via heuristic refinement, originally applied to chart safety outcomes on a planar maneuver domain, is extended for application to spherical domains and two types of non-Boolean science objectives defined for target locations on the body surface: cumulative observation time and surface payload deployment accuracy. In addition to its potential as a tool for preliminary mission design and the general study of small-body dynamics, this reachability analysis method is also examined and discussed as a resource for receding-horizon planning onboard an autonomous spacecraft.

Secular dynamics of planetesimals in tight binary systems: application toγ-Cephei

The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbital parameters of the secondary star. We construct a second-order theory (with respect to the masses) for the planar secular motion of small planetasimals and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for Gamma-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for Gamma-Cephei may affect the dynamics of small bodies in circunmstellar motion. For Gamma-Cephei, we find that the classical first-order expressions for the secular frequency and forced eccentricity lead to large inaccuracies around 50 % for semimajor axes larger than one tenth the orbital separation between the stellar components. Low eccentricities and/or masses reduce the importance of the second-order terms. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components, and the same result is found including the effects of a nonlinear gas drag. Thus, the possibility of planetary formation in this binary system largely appears insensitive to the orbital fits adopted for the stellar components, and any future alterations in the system parameters (due to new observations) should not change this picture. Finally, we show that planetesimals migrating because of gas drag may be trapped in mean-motion resonances with the binary, even though the migration is divergent.

Dynamics of small bodies in the solar system

In this chapter we review key results on the dynamics of small solar-system bodies, such as asteroids and comets. We begin by presenting the main populations of small bodies in the solar system, in terms of their orbital characteristics. We define the different types of resonant interactions for small bodies, relating them to the orbital structure of the main belts. In the next section, we present the basic theoretical background on the dynamics of small bodies, referring to applications in selected problems. First, we introduce the reader to the basics of the three-body and N(>3)-body problem with a central mass, using a Hamiltonian framework. We then analyze the expansion of the disturbing function and discuss the classification of terms. Elements of canonical perturbation theory, with the use of Lie series, are also given. The analytical solution of the linearized secular problem (Lagrange-Laplace theory) and the definition of proper elements is then presented. The extension to higher-order/degree secular theories is discussed. Subsequently, we present a derivation of low-order resonant normal forms, suitable for studying motion in mean motion resonances (MMRs, averaged Hamiltonians). The single-resonance model and MMR multiplets (in two-body and three-body MMRs) are then analyzed. We show that the application of the resonance-overlap criterion explains the origin of chaos and chaotic diffusion in resonances; an analytical description of the different diffusion regimes is also given. This section ends with a discussion on extended chaos in the outer asteroid belt and on the origin of the Kirkwood gaps. In the last part of this chapter, we discuss the evolution of small-body reservoirs during the early phases of solar system evolution, namely the epoch of planet migration. We present different models of planet migration (i.e. “smooth vs. chaotic”) and discuss resonant capture, which can explain the origin of different small-body resonant populations. These results show how the observed orbital distribution of small bodies, combined with suitable dynamical modeling, can be used as a proxy to unveil the evolutionary history of the Solar System. A short discussion devoted to open problems concludes this chapter.

Structure Preserving Approximations of Conservative Forces for Application to Small-Body Dynamics

Approximation-based methods, such as the cubetree algorithm, have proven to be significantly faster than traditional methods for complex force evaluations near small irregular bodies. Such methods also hold the promise of simplifying the inclusion of experimental data to update the force model. However, the cubetree algorithm does not preserve intrinsic properties of the gravitational force such as continuity, divergence freedom, or exactness. These properties may be needed for trajectory optimization, for the use of geometric (e.g., symplectic) integrators for long-term propagation, and for other trajectory design problems. This paper presents several adaptive schemes preserving global continuity, exactness, or divergence freedom, and discusses the difficulties involved in preserving all of these properties globally.

George West Wetherill

George West Wetherill

Meteoroid orbital characteristics by radar surveilence

H.F. radars are a powerful diagnostic for examining the orbits and spatial characteristics of the dust-meteoroid complex. Data on those properties are essential in realistic studies of the dynamics of small bodies in the solar system. An outline is here presented of the various programmes and their techniques employed in radar operations over the last 40 years. The particular value and contribution of radar facilities and comparisons with other methods is emphasised. Some of the features of the only current routine survey are discussed and, to illustrate to power of the system, examples of the types of data presentation are given.