Environment Of Asteroid Research Articles

Position-attitude coupling guidance and control for asteroid landing with a flexible lander

Landing on an asteroid is a highly valuable endeavor accompanied by significant challenges, making it a promising area for further research. This paper aims to present a flexible lander specifically designed for asteroid landing missions while also studying the guidance and control techniques involved in its descent phase. Firstly, the paper briefly introduces the mission simulation model and asteroid environment from previous work. It then provides a detailed exposition on the guidance model which facilitates trajectory planning and the attitude control model used for managing the lander's attitude. The parametric trajectory is subsequently applied to obtain the position-attitude coupling trajectory that allows for the flexible lander's trajectory planning. The generating set search method is used to optimize the parametric trajectory under the appropriate constraints, ensuring high efficiency. In tracking the proposed trajectory, an open-loop control is applied for position tracking, while a closed-loop attitude controller is proposed for attitude control. An attitude control technique involving a combination of the nonsingular sliding mode control method with RBF to capture perturbations and unmodeled dynamics is adopted, and its global stability is proven using a Lyapunov-based approach. Monte Carlo simulation is conducted to test the performance of the proposed trajectory planning technique with results showing that real-time trajectory generation and refreshing are achieved. The feasibility and accuracy of the proposed guidance and control technique are further verified with another set of Monte Carlo simulation. Finally, the paper highlights one successful scenario including the descent and touching phases of asteroid landing with the flexible lander, illustrating its feasibility further.

Finding regions of bounded motion in binary asteroid environment using Lagrangian descriptors

Trajectory design in highly-perturbed environments like binary asteroids is challenging. It typically requires using realistic, non-autonomous dynamical models in which periodic solutions derived in autonomous systems vanish. In this work, Lagrangian descriptors are employed in the perturbed planar bi-elliptic restricted four-body problem to find regions of bounded motion over a finite horizon about Dimorphos, the secondary body of the (65803) Didymos binary system. Results show that Lagrangian descriptors successfully reveal phase space organizing structures both in the unperturbed and perturbed planar bi-elliptic restricted four-body problem. With no solar radiation pressure, regions of bounded motion are visually identified, so granting access to a vast selection of bounded orbits about Dimorphos. Conversely, the presence of solar radiation pressure breaks down the majority of structures, leading to a large region of unstable motion with rare exceptions. Lagrangian descriptors are computationally inexpensive dynamical indicators that could be conveniently applied to astrodynamics.

Experimental and analytical methods for thermal infrared spectroscopy of complex dust coatings in a simulated asteroid environment

Abstract Airless bodies in the Solar system are commonly dominated by complex regolith mixtures consisting of coarse and fine particulates. These materials often manifest as coatings with the potential to modify or obscure the spectral signatures of underlying substrates. This can make accurate spectral analysis of surface materials challenging, especially for thermal infrared (TIR) techniques of which the spectral properties concurrently depend on grain size and albedo. Further complexity is presented when these coatings occur as discontinuous patterns in which some substrate is exposed and some is masked. Discontinuous patterns are distinguished by scale as having macroscopic or microscopic discontinuity, with the former being patches of homogeneous dust covering portions of the substrate and the latter being randomly distributed individual particles on the substrate. Investigations of asteroid (101955) Bennu’s surface by NASA’s Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer have revealed contradictions between spectral and thermophysical results that are hypothesized to indicate the presence of thin and/or laterally discontinuous dust coatings. To address this, we constructed an environment chamber that enables the controlled deposition of size-regulated dust particles in coatings with varying continuity and thickness. TIR spectra of coated substrates acquired in a simulated asteroid environment are used to investigate the extent to which dust coatings of different thicknesses and arrangements contribute to orbital spectral signatures of airless body surfaces.

Linear Modeling of Spectra of Fine Particulate Materials: Implications for Compositional Analyses of Primitive Asteroids

AbstractIn this study, we applied a sum to one constraint weighted least squares (STO WLS) model to thermal infrared (TIR) spectra of a suite of primitive asteroid analogs spectrally and volumetrically dominated by fine particulates (<38 μm). Since coarse particulate emissivity spectra combine linearly, deriving compositions from these are fairly straightforward. Across the TIR it is not as straightforward for fine particulate emissivity spectra due to the nonlinear behavior that arises from volumetric scattering between particles when the particle size becomes comparable to the wavelength of light. Using a WLS model, mixed spectra may be deconvolved into areal percentages of each end member which we assume corresponds to their volume percentages. We used a spectral library of pure mineral spectra to model TIR spectra of a suite of physical mixtures and meteorites obtained under ambient (Earth‐like) and simulated asteroid environment (SAE) conditions collected for the OSIRIS‐REx team (Donaldson Hanna et al., 2021, https://doi.org/10.1029/2020JE006624). The STO WLS model underestimated the modal abundances of the dominant mineral phases by ∼25.0 ± 0.1% on average over the full spectral range and ∼22.0 ± 0.4% over a limited spectral range in all of the ambient and SAE physical mixture and meteorite spectra. Minor phases present in the mixtures and meteorites (abundances ≤5%) were typically not modeled. Also, phases not present in the mixtures were commonly selected (∼2 phases on average with an average abundance of ∼25.2 ± 1.9%) to get the best mathematical fit.

A Spectral Investigation of Aqueously and Thermally Altered CM, CM‐An, and CY Chondrites Under Simulated Asteroid Conditions for Comparison With OSIRIS‐REx and Hayabusa2 Observations

AbstractVolatile‐rich asteroids are crucial to understanding the transport of water and organics to the terrestrial planet forming region in the early Solar System. Observations of two such asteroids by Hayabusa2 and Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS‐REx) suggest a relationship between these bodies and CI, CM, and CY chondrites. To confirm this, meteorite spectra need to be collected under appropriate conditions for comparison with asteroid observations. We report midinfrared (MIR) emissivity spectra (5.5–50 μm) obtained under ambient and simulated asteroid environment conditions and near‐infrared (NIR) reflectance spectra (2–5 μm) of CM and CY chondrite fine‐particulate (<35 μm) powders for which bulk mineralogy was determined using X‐ray diffraction. Reflectance spectra show a 3 μm feature associated with ‐OH/H2O that shifts from shorter (∼2.72 μm) to longer (∼2.90 μm) wavelengths and develops a rounder shape and reduced band area with increasing thermal metamorphism. In the MIR, the transparency feature (TF) and features in the Si‐O bending region (>15 μm) can be used to infer the relative degree of aqueous alteration, and to resolve the effects of aqueous and thermal alteration, when combined with NIR spectral parameters. The MIR spectra of metamorphosed CY chondrites are distinct from CM chondrite spectra, including a plateau around the Christiansen feature (∼8.00–12.50 μm) and features at longer wavelengths in the Si‐O bending region (e.g., ∼25.50 μm compared to ∼24.30 μm in the CM spectra). We additionally report potential implications of the spectra and parameters determined in this study for the results from Hayabusa2 and OSIRIS‐REx.

Thermal emission measurements of ordinary chondrite mineral analogs in a simulated asteroid environment: 1. Constituent mineral phases

Telescopic surveys suggest that S-type asteroids are the dominant small body type in the near-Earth object population and are among the most abundant in the inner main asteroid belt. Given the link between S-type asteroids and the ordinary chondrites, regoliths of ordinary chondrite mineralogy may represent the most common regolith type on small bodies in these populations, and therefore it is important to understand the thermal emission properties of ordinary chondrite mineral analogs radiating into asteroid-like environments. Thermal infrared spectra of particulate surfaces in airless environments are substantially modified due to near-surface thermal gradients formed between the immediate surface undergoing radiative cooling and underlying materials that are warmed by the absorption of solar radiation. To advance our understanding of how the thermal emission properties of materials relevant to ordinary chondrite composition may be modified in an airless environment, we analyze a suite of analogous single mineral phases in a simulated asteroid surface environment. A companion paper presents and discusses analyses of modal mixtures of these minerals designed to match modal abundances of ordinary chondrites as reported in the literature. We probe the thermal emission of these materials by investigating relationships between their sample temperatures, emissivity spectra, brightness temperatures, and the environmental and experimental conditions. We focus attention on the radiance spectra of the samples as derived by two data reduction methods and their corresponding brightness temperature spectra to infer the intensity of near-surface thermal gradients formed in the samples. We demonstrate that the Christiansen feature position is sensitive to the sample cup temperature with data collected in a simulated asteroid environment under constant illumination condition. Through the analysis of particulate samples of three particle size ranges (<25 μm, 25–125 μm, and 125–250 μm) at ambient and cold, vacuum conditions, we demonstrate that thermal gradients form as a result of the physical, environmental, and optical properties of the target surface. Using temperature variations observed in high spectral resolution brightness temperature spectra as a proxy for the near-surface thermal gradients, we observe relationships between the intensity of the thermal gradient and the sample particle size. Modifications of iron metal spectra due to the changing environmental conditions are examined and compared with the silicate data. Implications for the measurement of thermal infrared spectra of metal-bearing planetary materials, such as the ordinary chondrites, are discussed.

A contact dynamics code implementation for the simulation of asteroid evolution and regolith in the asteroid environment

Over the last decades, simulations by discrete elements methods (DEM) have proven to be a reliable analysis tool in various domains of science and engineering. By providing access to the local physical mechanisms, DEM allows the exploration of microscopic based phenomena related to particles properties and interactions in various conditions and to revisit constitutive equations consequently. The growing computer power and memory now allow us to handle large collections of grains of various shapes and sizes by DEM simulations and in particular, it offers new perspectives in the exploration of the behavior of asteroids seen as self-gravitating and cohesive granular aggregates. In this paper we describe the Contact Dynamics (CD) method, a class of DEM based on non-smooth mechanics, and its implementation in the open-source software LMGC90. In contrast to more classical approach, Hard- and Soft-Sphere DEM, the CD method is based on an implicit time integration of the equations of motion and on a non-regularized formulation of mutual exclusion between particles. This numerical strategy is particularly relevant to the study of dense granular assemblies (even of large size) because it does not introduce numerical artifacts due to contact stiffness. So that it can be used for Small Body research, we implement a parallelized kd-tree and monitor the performance of the code as it simulates a number of granular systems. We provide examples of the simulation of the accretion of self-gravitating aggregates as well as their rotational disruption. We use the routines at our disposal in the code to monitor their behavior through the entire evolution and find agreement with previous research.

Autonomous Exploration of a Small Near-Earth Asteroid

Asteroid exploration missions must deal with large uncertainties in a target body’s gravity and shape as well as ephemeris errors upon rendezvous. Navigation and guidance are typically performed using ground-based operations, which can be costly. This paper studies the possibility of removing the ground in the process through onboard navigation with optical measurements and accelerometer-based measurements. The paper first describes the dynamics and measurement models used to simulate a spacecraft’s interaction with the asteroid environment, followed by implementation details of navigation and guidance subsystems. The paper then presents a covariance analysis of this problem using simplified dynamics, focusing on the information content of the optical and measurements. Guided by this, an end-to-end autonomous exploration scheme with onboard navigation and event-driven orbit control is analyzed through simulation, introducing realistic errors between the truth and filter dynamics. The basic operations of this scheme are built around near-inertial hovering and include approach from the end of an interplanetary phase, reconnaissance at various viewing geometries, close gravity estimation, and orbit insertion. The feasibility of the proposed autonomous navigation and orbit control is evaluated using a Monte Carlo analysis and is shown to be robust.

Seismic waves in the asteroid environment

Through numerical simulations, we investigate impact generated seismic wave transmission in granular media under extremely low pressure. This mimics the conditions in the interior of asteroids and other small planetary bodies. We find a dependency not only on the overburden pressure on the medium, but also on the velocity of the impact that generates the wave. This is, at extremely low values of overburden pressure, the wave speed depends no only on the imposed pressure, but also on the increment in pressure created by the passing of the wave. We study crystalline and random packings and find very similar behaviour though with different wave speeds as expected. We then relate our results to different mission-related events on asteroids.

Thermal emission measurements of ordinary chondrite mineral analogs in a simulated asteroid environment: 2. Representative mineral mixtures

We investigate a suite of synthetic mineral mixtures designed to act as bulk mineralogical analogs to H, L, and LL ordinary chondrite meteorites in order to probe how the thermal emission characteristics of such materials change between ambient and simulated asteroid environmental conditions. Due to the parent body link with certain S-type asteroids, studying these analog mixtures in an environment that is relevant to actual asteroid surfaces advances our understanding of the thermal emission properties of one of the most common regolith types among the main-belt and near-Earth asteroid populations. The observed changes in spectral emissivity features due to cold, vacuum conditions are not as large as previously observed for single mineral (silicate) samples. We interpret this difference to be the result of metallic and opaque components weakening near-surface thermal gradients in the mixtures. As such, we predict that near-surface thermal gradients on ordinary chondrite parent bodies (e.g., S-type asteroids) are likely much weaker than would be inferred from cold, vacuum measurements of individual mineral components. We tested whether the increased spectral contrast observed in fine-grained (<25 μm) samples measured in a cold, vacuum environment increases the efficacy of least squares linear unmixing methods. It is found that the accuracy of such models does not improve relative to measurements made under ambient conditions, thus linear unmixing models are not expected to yield accurate estimates of the modal mineralogy of airless planetary surfaces if they are dominated by fine-grained regolith. Mixtures with coarse particle sizes (125–250 μm) that were modeled using the coarse particle size endmembers yielded results that were largely independent of the environmental conditions, but with larger errors in spectral fits for samples measured in a simulated asteroid environment. At simulated asteroid environmental conditions, the bulk silicate composition and metal content play a more important role in determining the thermal state and brightness temperature of the sample than at ambient conditions. Modest changes in metal content (10–25 wt%) lead to large differences in the brightness temperature of a sample. Under simulated asteroid conditions, an ~10 K increase in maximum brightness temperature that tracks with increased iron content is observed at fine particle sizes (<25 μm) between each of the analog ordinary chondrite groups. Based on these results, it may be difficult to distinguish H, L, and LL compositions of suspected ordinary chondrite parent bodies using only Earth- or space-based thermal emission spectra. This is inferred from the spectral similarity of the analog mixtures and the absence of significant variation in spectral emissivity associated with reported differences in bulk metal content for ordinary chondrites.

Mid-infrared reflectance spectroscopy of carbonaceous chondrites and Calcium–Aluminum-rich inclusions

We obtained mid-infrared reflectance spectra of powdered size fractions (0–25 ​μm, 25–63 ​μm, 63–125 ​μm and 125–250 ​μm) of 5 carbonaceous chondrites HaH 280 (CK4), Allende (CV3), NWA 10574 (CM2) and Murchison (CM2), and C2 (ungrouped) Tagish Lake. In addition, in-situ micro-FTIR reflectance spectra of CAIs in Allende, Ornans and Vigarano have been made.These spectra are part of a database for the comparison with remote sensing data of asteroids and planetary bodies, but also for laboratory studies of meteorites.Carbonaceous chondrites HaH 280 (CK4), Allende (CV3) and NWA 10574 (CM2) show mid-IR spectra with Reststrahlen bands (RB) dominated by forsterite and pyroxene features. The transparency features (TF) are at 12.1 ​μm–12.9 ​μm and the Christiansen features (CF) at 8.5 ​μm–9.3 ​μm.Murchison (CM2) and ungrouped Tagish Lake (C2) show mainly phyllosilicate features in their spectra. The CF is between 8.6 ​μm and 9.0 ​μm.Micro-FTIR spectra of CAIs from Allende, Vigarano, and Ornans have spinel features between 14.1 ​μm and 14.3 ​μm. In addition, melilite was identified in the Vigarano and Ornans samples with characteristic features at 11.7 ​μm and 12.4 ​μm.Nepheline and sodalite features have been identified around 14 ​μm in the Allende CAI as alteration phases resulting from thermal metamorphism.A band shift in spinel with increasing Fe content from thermal metamorphism could be spectral indicator for parent body metamorphism.A comparison with other bulk samples from the same meteorites/type shows high similarity.Comparison of the finest size fractions modelled in emissivity with remote sensing data of asteroids shows some similarity between a linear mixture of Allende and Murchison and the spectra of asteroid 253 Mathilde. However, the main 10 ​μm plateau is clearly shifted by 0.5 ​μm between asteroid and meteorite spectra. Also, the general band shapes are different. Differences between asteroidal environment (e.g. fairy castle structure) and laboratory make direct comparisons difficult.

Style and intensity of hydration among C-complex asteroids: A comparison to desiccated carbonaceous chondrites

Here we report a comparison between reflectance spectroscopy of meteorites under asteroidal environment (high vacuum and temperature) and Main Belt and Near Earth Asteroids spectra. Focusing on the –OH absorption feature around 3 μm, we show that the asteroidal environment induces a reduction of depth and width of the band, as well as a shift of the reflectance minimum. We then decompose the –OH feature into several components with a new model using Exponentially Modified Gaussians. Unlike previous studies, we confirme the link between these components, the aqueous alteration history and the amount of water molecules inside of the sample, using the shape of this spectral feature only. We then apply this deconvolution model to asteroids spectra which were obtained with a space-borne telescope and two space probes, and find a strong similarity with the components detected on meteorites, and among asteroids from a same type. Based on the conclusions drawn from our meteorites experiment, we suggest to use the 3-μm band as a tracer of the alteration history of the small bodies. Using the 3-μm band only, we show that Ryugu has been heavily altered by water, which is consistent with its parent body being covered with water ice, then went through a high temperature sequence, over 400 °C. We also point out that the 3-μm band of Bennu shows signs of its newly discovered surface activity.

Dynamical Environment and Surface Characteristics of Asteroid (16) Psyche

Abstract Radar observations show that (16) Psyche is one of the largest and most massive asteroids of the M-class located in the main belt, with a diameter of approximately 230 km. This fact makes Psyche a unique object since observations indicated an iron-nickel composition. It is believed that this body may be what was left of a metal core of an early planet that would have been fragmented over millions of years due to violent collisions. In this work we study a variety of dynamical aspects related to the surface, as well as, the environment around this asteroid. We use computational tools to explore the gravitational field generated by this body, assuming constant values for its density and rotation period. We then determine a set of physical and dynamical characteristics over its entire surface. The results include the geometric altitude, geopotential altitude, tilt, slope, among others. We also explore the neighborhood around the asteroid (16) Psyche, so that the location and linear stability of the equilibrium points were found. We found four external equilibrium points, two of them linearly stable. We confirmed the stability of these points by performing numerical simulations of massless particles around the asteroid, which also showed an asymmetry in the size of the stable regions. In addition, we integrate a cloud of particles in the vicinity of (16) Psyche in order to verify in which regions of its surface the particles are most likely to collide.

Simulated asteroid materials based on carbonaceous chondrite mineralogies

AbstractA set of high‐fidelity simulated asteroid materials, or simulants, was developed based on the mineralogy of carbonaceous chondrite meteorites. Three varieties of simulant were developed based on CI1 chondrites (typified by Orgueil), CM2 chondrites (typified by Murchison), and CR2/3 chondrites (multiple samples). The simulants were designed to replicate the mineralogy and physical properties of the corresponding meteorites and anticipated asteroid surface materials as closely as is reasonably possible for bulk amounts. The simulants can be made in different physical forms ranging from larger cobbles to fine‐grained regolith. We analyzed simulant prototypes using scanning electron microscopy, X‐ray fluorescence, reflectance spectroscopy at ambient conditions and in vacuum, thermal emission spectroscopy in a simulated asteroid environment chamber, and combined thermogravimetry and evolved gas analysis. Most measured properties compare favorably to the reference meteorites and therefore to predicted volatile‐rich asteroid surface materials, including boulders, cobbles, and fine‐grained soils. However, there were also discrepancies, and mistakes were made in the original mineral formulations that will be updated in the future. The asteroid simulants are available to the community from the nonprofit Exolith Lab at UCF, and the mineral recipes are freely published for other groups to reproduce and modify as they see fit.

The operational environment and rotational acceleration of asteroid (101955) Bennu from OSIRIS-REx observations

During its approach to asteroid (101955) Bennu, NASA’s Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) spacecraft surveyed Bennu’s immediate environment, photometric properties, and rotation state. Discovery of a dusty environment, a natural satellite, or unexpected asteroid characteristics would have had consequences for the mission’s safety and observation strategy. Here we show that spacecraft observations during this period were highly sensitive to satellites (sub-meter scale) but reveal none, although later navigational images indicate that further investigation is needed. We constrain average dust production in September 2018 from Bennu’s surface to an upper limit of 150 g s–1 averaged over 34 min. Bennu’s disk-integrated photometric phase function validates measurements from the pre-encounter astronomical campaign. We demonstrate that Bennu’s rotation rate is accelerating continuously at 3.63 ± 0.52 × 10–6 degrees day–2, likely due to the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect, with evolutionary implications.

Equilibria and orbits in the dynamical environment of asteroid 22 Kalliope

Abstract This paper studies the orbital dynamics of the potential of asteroid 22 Kalliope using observational data of the irregular shape. The zero-velocity surface are calculated and showed with different Jacobian values. All five equilibrium points are found, four of them are outside and unstable, and the other one is inside and linearly stable. The movement and bifurcations of equilibrium points during the variety of rotation speed and density of the body are investigated. The Hopf bifurcations occurs during the variety of rotational speed from ω=1.0ω 0 to 0.5ω 0, and the Saddle-Node bifurcation occurs during the variety of rotational speed from ω=1.0ω 0 to 2.0ω 0. Both unstable and stable resonant periodic orbits around Kalliope are coexisting. The perturbation of an unstable periodic orbit shows that the gravitational field of Kalliope is strongly perturbed.

Hayabusa2-Ryugu proximity operation planning and landing site selection

This paper presents the robust planning of the Hayabusa2-Ryugu proximity operation and landing site selection process considering unknown asteroid environment and the spacecraft constraints. The proximity operation scenario is described together with the relationship between the selection process and the in-situ observation. The mission constraints are summarized for the possible asteroid environment, including the rotation state, thermal condition and gravity.

Parametric Study of Ballistic Lander Deployment to Small Bodies

This paper investigates the sensitivities of spherical lander deployment to small bodies. Previous work established methods to simulate the motion of such landers in the gravitationally and topographically complex small-body environment. These methods are extended, primarily through the inclusion of a “persistent” rock model that accounts for the observed distribution of rocks and boulders on the small-body surface. The resulting framework is applied to investigate the effects of relevant environmental and hardware parameters on trends in the deployment of a lander. In the dynamically favorable environment of asteroid Itokawa, variations in the surface interaction, rock distribution, and lander mass distribution scale the settling time, slope, and surface dispersion of a given deployment scenario. In the more challenging environment of asteroid 1999 Alpha, these parameters determine the success rate with which landers are delivered to the surface, and they should be carefully considered during deployment design. The current results underscore the importance of high-fidelity modeling, may provide guidelines for the hardware and mission operations design of lander spacecraft, and may prioritize particular studies and observations of the small-body (sub)surface.

Numerical simulations of oscillation-driven regolith motion: Brazil-nut effect

Many if not most small asteroids are rubble piles covered by regolith, and small perturbations may be enough to disturb their surfaces in complex ways due to microgravity. Experiments to study low-gravity regolith dynamics are challenging, and properly validated numerical simulations can provide valuable insights. In this paper, we investigate numerically size segregation among regolith grains, which is likely to occur after repeated shaking events. In particular, we are interested in the so-called Brazil-nut effect (BNE), i.e. the migration of a large intruder towards the top of a vertically shaken granular system. We go a step forward in simulating this effect by implementing horizontal periodic boundary conditions (PBC) in the N-body code pkdgrav, with the aim of making the simulations more representative of the expected asteroid environment. We study the influence of PBC on the BNE in Earth gravity and compare them with a walled case. We also investigate the influence of static and rolling friction on the BNE. With walls, we observe the well-known convection mechanism driving the BNE. However, we find that a different mechanism, consisting of void filling, is responsible for the BNE with PBC, and we discuss its relevance in light of previous studies. By running simulations in 10−4g, we show that this void-filling mechanism remains relevant in a low-gravity environment. However, we find that depending on the gravity level, the void-filling mechanism is differently influenced by the friction properties of particles. We speculate that this is likely due to a change in the granular flow time-scales.

The dynamical environment of asteroid 21 Lutetia according to different internal models

One of the most accurate models currently used to represent the gravity field of irregular bodies is the polyhedral approach. In this model, the mass of the body is assumed to be homogeneous, which may not be true for a real object. The main goal of the present paper is to study the dynamical effects induced by three different internal structures (uniform, three- and four-layers) of asteroid (21) Lutetia, an object that recent results from space probe suggest being at least partially differentiated. The Mascon gravity approach used in the present work, consists of dividing each tetrahedron into eight parts to calculate the gravitational field around the asteroid. The zero-velocity curves show that the greatest displacement of the equilibrium points occurs in the position of the E4 point for the four-layers structure and the smallest one occurs in the position of the E3 point for the three-layers structure. Moreover, stability against impact shows that the planar limit gets slightly closer to the body with the four-layered structure. We then investigated the stability of orbital motion in the equatorial plane of (21) Lutetia and propose numerical stability criteria to map the region of stable motions. Layered structures could stabilize orbits that were unstable in the homogeneous model.