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Title: Long-term influence of asteroids on planet longitudes and chaotic dynamics of the solar system
Author: Freddy Bouchet (1), E Woillez (2) ((1) CNRS (2) Phys-ENS)

The aim of this paper is to compare different sources of stochasticity in the solar system. More precisely we study the importance of the long term influence of asteroids on the chaotic dynamics of the solar system. We show that the effects of asteroids on planets is similar to a white noise process, when those effects are considered on a time scale much larger than the correlation time tau_phi} \simeq 10^4 yr of asteroid trajectories. We compute the time scale tau_4 after which the effects of the stochastic evolution of the asteroids lead to a loss of information for the initial conditions of the perturbed Laplace\textendash Lagrange secular dynamics. The order of magnitude of this time scale is precisely determined by theoretical argument. This time scale should be compared with the Lyapunov time tau_i of the solar system without asteroids (intrinsic chaos). We conclude that tau_i \simeq 10 Myr \ll tau_e \simeq 10^4 Myr, showing that the external sources of chaoticity arise as a small perturbation in the stochastic secular behaviour of the solar system, rather due to intrinsic chaos.

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Title: Shape models and physical properties of asteroids
Author: T. Santana-Ros, G. Dudziski, P. Bartczak

Despite the large amount of high quality data generated in recent space encounters with asteroids, the majority of our knowledge about these objects comes from ground based observations. Asteroids travelling in orbits that are potentially hazardous for the Earth form an especially interesting group to be studied. In order to predict their orbital evolution, it is necessary to investigate their physical properties. This paper briefly describes the data requirements and different techniques used to solve the lightcurve inversion problem. Although photometry is the most abundant type of observational data, models of asteroids can be obtained using various data types and techniques. We describe the potential of radar imaging and stellar occultation timings to be combined with disk-integrated photometry in order to reveal information about physical properties of asteroids.

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Title: Asteroid Surface Geophysics
Author: Naomi Murdoch, Paul Sanchez, Stephen R. Schwartz, Hideaki Miyamoto

The regolith-covered surfaces of asteroids preserve records of geophysical processes that have occurred both at their surfaces and sometimes also in their interiors. As a result of the unique micro-gravity environment that these bodies posses, a complex and varied geophysics has given birth to fascinating features that we are just now beginning to understand. The processes that formed such features were first hypothesised through detailed spacecraft observations and have been further studied using theoretical, numerical and experimental methods that often combine several scientific disciplines. These multiple approaches are now merging towards a further understanding of the geophysical states of the surfaces of asteroids. In this chapter we provide a concise summary of what the scientific community has learned so far about the surfaces of these small planetary bodies and the processes that have shaped them. We also discuss the state of the art in terms of experimental techniques and numerical simulations that are currently being used to investigate regolith processes occurring on small-body surfaces and that are contributing to the interpretation of observations and the design of future space missions.

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Title: Micro-meteoroid seismic uplift and regolith concentration on kilometric scale asteroids
Author: Raphael F. Garcia, Naomi Murdoch, David Mimoun

Seismic shaking is an attractive mechanism to explain the destabilisation of regolith slopes and the regolith migration found on the surfaces of asteroids (Richardson et al. 2004; Miyamoto et al. 2007). Here, we use a continuum mechanics method to simulate the seismic wave propagation in an asteroid. Assuming that asteroids can be described by a cohesive core surrounded by a thin non-cohesive regolith layer, our numerical simulations of vibrations induced by micro-meteoroids suggest that the surface peak ground accelerations induced by micro-meteoroid impacts may have been previously under-estimated. Our lower bound estimate of vertical accelerations induced by seismic waves is about 50 times larger than previous estimates. It suggests that impact events triggering seismic activity are more frequent than previously assumed for asteroids in the kilometric and sub-kilometric size range. The regolith lofting is also estimated by a first order ballistic approximation. Vertical displacements are small, but lofting times are long compared to the duration of the seismic signals. The regolith movement has a non-linear dependence on the distance to the impact source which is induced by the type of seismic wave generating the first movement. The implications of regolith concentration in lows of surface acceleration potential are also discussed. We suggest that the resulting surface thermal inertia variations of small fast rotators may induce an increased sensitivity of these objects to the Yarkovsky effect.

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Title: Asteroid Models from Multiple Data Sources
Author: J. Durech, B. Carry, M. Delbo, M. Kaasalainen, M. Viikinkoski

In the past decade, hundreds of asteroid shape models have been derived using the lightcurve inversion method. At the same time, a new framework of 3-D shape modeling based on the combined analysis of widely different data sources such as optical lightcurves, disk-resolved images, stellar occultation timings, mid-infrared thermal radiometry, optical interferometry, and radar delay-Doppler data, has been developed. This multi-data approach allows the determination of most of the physical and surface properties of asteroids in a single, coherent inversion, with spectacular results. We review the main results of asteroid lightcurve inversion and also recent advances in multi-data modelling. We show that models based on remote sensing data were confirmed by spacecraft encounters with asteroids, and we discuss how the multiplication of highly detailed 3-D models will help to refine our general knowledge of the asteroid population. The physical and surface properties of asteroids, i.e., their spin, 3-D shape, density, thermal inertia, surface roughness, are among the least known of all asteroid properties. Apart for the albedo and diameter, we have access to the whole picture for only a few hundreds of asteroids. These quantities are nevertheless very important to understand as they affect the non-gravitational Yarkovsky effect responsible for meteorite delivery to Earth, or the bulk composition and internal structure of asteroids.

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Asteroid Belt
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Title: The Dynamical Evolution of the Asteroid Belt
Author: Alessandro Morbidelli, Kevin J. Walsh, David P. O'Brien, David A. Minton, William F. Bottke

The asteroid belt is the leftover of the original planetesimal population in the inner solar system. However, currently the asteroids have orbits with all possible values of eccentricities and inclinations compatible with long-term dynamical stability, whereas the initial planetesimal orbits should have been quasi-circular and almost co-planar. The total mass in the asteroid population is a small fraction of that existing primordially. Also, asteroids with different chemical/mineralogical properties are not ranked in an orderly manner with mean heliocentric distance as one could expect from the existence of a radial gradient of the temperature in the proto-planetary disk, but they are partially mixed. These properties show that the asteroid belt has been severely sculpted by one or a series of processes during its lifetime. This paper reviews the processes that have been proposed so far, discussing the properties that they explain and the problems that they are confronted with. Emphasis is paid to the interplay between the dynamical and the collisional evolution of the asteroid population, which allows the use of the size distribution to constrain the dynamical models. We divide the asteroid belt evolution into three phases. The first phase started during the lifetime of the gaseous proto-planetary disk, when the giant planets formed and presumably experienced large-scale migrations, and continued after the removal of the gas, during the build-up of the terrestrial planets. The second phase occurred after the removal of the gaseous proto-planetary disk and it became particularly lively for the asteroid belt when the giant planets suddenly changed their orbits, as a result of a mutual dynamical instability and the interaction with the trans-Neptunian planetesimal disk. The third phase covers the aftermath of the giant planet instability, until today.

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Title: Asteroids' physical models from combined dense and sparse photometry and scaling of the YORP effect by the observed obliquity distribution
Authors: J. Hanu, J. Durech, M. Bro, A. Marciniak, B. D. Warner, F. Pilcher, R. Stephens, R. Behrend, B. Carry, D. Capek, P. Antonini, M. Audejean, K. Augustesen, E. Barbotin, P. Baudouin, A. Bayol, L. Bernasconi, W. Borczyk, J.-G. Bosch, E. Brochard, L. Brunetto, S. Casulli, A. Cazenave, S. Charbonnel, B. Christophe, F. Colas, J. Coloma, M. Conjat, W. Cooney, H. Correira, V. Cotrez, A. Coupier, R. Crippa, M. Cristofanelli, Ch. Dalmas, C. Danavaro, C. Demeautis, T. Droege, R. Durkee, N. Esseiva, M. Esteban, M. Fagas, G. Farroni, M. Fauvaud, S. Fauvaud, F. Del Freo, L. Garcia, S. Geier, C. Godon, K. Grangeon, H. Hamanowa, H. Hamanowa, N. Heck, S. Hellmich, D. Higgins, R. Hirsch, M. Husarik, T. Itkonen, O. Jade, K. Kaminski, P. Kankiewicz, A. Klotz, R. A. Koff, A. Kryszczynska, et al. (56 additional authors not shown)

The larger number of models of asteroid shapes and their rotational states derived by the lightcurve inversion give us better insight into both the nature of individual objects and the whole asteroid population. With a larger statistical sample we can study the physical properties of asteroid populations, such as main-belt asteroids or individual asteroid families, in more detail. Shape models can also be used in combination with other types of observational data (IR, adaptive optics images, stellar occultations), e.g., to determine sizes and thermal properties. We use all available photometric data of asteroids to derive their physical models by the lightcurve inversion method and compare the observed pole latitude distributions of all asteroids with known convex shape models with the simulated pole latitude distributions. We used classical dense photometric lightcurves from several sources and sparse-in-time photometry from the U.S. Naval Observatory in Flagstaff, Catalina Sky Survey, and La Palma surveys (IAU codes 689, 703, 950) in the lightcurve inversion method to determine asteroid convex models and their rotational states. We also extended a simple dynamical model for the spin evolution of asteroids used in our previous paper. We present 119 new asteroid models derived from combined dense and sparse-in-time photometry. We discuss the reliability of asteroid shape models derived only from Catalina Sky Survey data (IAU code 703) and present 20 such models. By using different values for a scaling parameter cYORP (corresponds to the magnitude of the YORP momentum) in the dynamical model for the spin evolution and by comparing synthetics and observed pole-latitude distributions, we were able to constrain the typical values of the cYORP parameter as between 0.05 and 0.6.

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Title: Space weathering of asteroids
Authors: D. I. Shestopalov, L. F. Golubeva, E. A. Cloutis

Analysis of laboratory experiments simulating space weathering optical effects on atmosphereless planetary bodies reveals that the time needed to alter the spectrum of an ordinary chondrite meteorite to resemble the overall spectral shape and slope of an S-type asteroid is about ~ 0.1 Myr. The time required to reduce the visible albedo of samples to ~ 0.05 is ~ 1 Myr. Since both these timescales are much less than the average collisional lifetime of asteroids larger than several kilometres in size, numerous low-albedo asteroids having reddish spectra with subdued absorption bands should be observed instead of an S-type dominated population. It is not the case because asteroid surfaces cannot be considered as undisturbed, unlike laboratory samples. We have estimated the number of collisions occurring in the time of 105 yr between asteroids and projectiles of various sizes and show that impact-activated motions of regolith particles counteract the progress of optical maturation of asteroid surfaces. Continual rejuvenation of asteroid surfaces by impacts does not allow bodies with the ordinary chondrite composition to be masked among S asteroids. Spectroscopic analysis, using relatively invariant spectral parameters, such as band centers and band area ratios, can determine whether the surface of an S asteroid has chondritic composition or not. Differences in the environment of the main asteroid belt versus that at 1 AU, and the physical difference between the Moon and main belt asteroids (i.e., size) can account for the lack of lunar-type weathering on main belt asteroids.

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Asteroid Belts
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Asteroid Belts at Just the Right Place are Friendly to Life

Solar systems with life-bearing planets may be rare if they are dependent on the presence of asteroid belts of just the right mass, according to a study by Rebecca Martin, a NASA Sagan Fellow from the University of Colorado in Boulder, and astronomer Mario Livio of the Space Telescope Science Institute in Baltimore, Md.
They suggest that the size and location of an asteroid belt, shaped by the evolution of the sun's planet-forming disk and by the gravitational influence of a nearby giant Jupiter-like planet, may determine whether complex life will evolve on an Earth-like planet.
This might sound surprising because asteroids are considered a nuisance due to their potential to impact Earth and trigger mass extinctions. But an emerging view proposes that asteroid collisions with planets may provide a boost to the birth and evolution of complex life.

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Title: Asteroids dimensions and the Truncated Pareto distribution
Authors: L. Zaninetti, M. Ferraro

In this chapter first the statistics of the standard and truncated Pareto distributions are derived and used to fit empirical values of asteroids diameters from different families, namely, Koronis, Eos and Themis, and from the Astorb database. A theoretical analysis is then carried out and two possible physical mechanisms are suggested that account for Pareto tails in distributions of asteroids diameter.

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