Search

1. Introduction During the last five years, machine learning and deep learning have been used more commonly in the field of asteroid dynamics. Artificial neural networks have been recently used for identifying members of asteroid families [6]. This is the first attempt to use deep learning for the automatic classification of images of asteroids resonant arguments. The population of asteroids inside the M1:2 mean motion resonance with Mars was studied by [4]. The V-shaped region at the resonance center in the proper (a, e) plane (see figure (1)) is associated with the M1:2 resonance. [4] defines two main resonant arguments. σ is given by: where λ = M + Ω + ω is the mean longitude, ϖ = Ω + ω, with Ω the longitude of the node, ω the argument of pericenter, and where the suffix M identifies the planet Mars. σ1 is defined as: The orbital behavior of asteroids in the affected region can be identified by studying the time dependence of these two angles. Asteroids for which the critical arguments cover the whole range of values, from 0◦ to 360◦, are on circulating orbits. If the argument oscillates around an equilibrium point, we have a librating orbit. Whether the argument alternates phases of libration and circulations we have a switching orbit, as defined in this work. The main equilibrium point for the σ1 argument is near 0◦. Pure σ librators tend to be much rarer than pure σ1 ones. Since in this work we are interested in treating a multi-class problem we focus our study on the case of the σ1 resonant argument. 2. Artificial Neural Networks (ANN) Artificial neuron networks mimic the neuron's web in a biological brain. Each artificial neuron can transmit a signal to other neurons. This signal can be processed, and the signal coming out of each neuron is computed as a non-linear function of the inputs. A basic architecture for ANN consists of an input and an output layers, with the possible presence of one or more hidden layers between them to improve the model precision. Each neuron will perform a weighted sum, WS, given by: where n is the number of input to process, Xi are the signals from other neurons, and wi are the weights. ANN will optimize the values of the weights during the learning process. On the weighted sum WS, ANN will apply an activation function. For images classifications, one of the most used activation function is the “relu”, defined as: which will produce as an outcome the weighted sum itself WS, if that is a positive number, or 0, if WS has a negative value. As a next step, the loss function must be applied to all the weights in the network through a back-propagation algorithm. A loss function is usually calculated by computing the differences between the predicted and real output values. Interested readers can find more information in the Keras documentation (https://keras.io/, [5]). 3 Applications of ANN to M1:2 Here, we used the Keras implementation of ANN, which is based on the Tensorflow Python software package [2]. The process used in this work is the following: 1. The asteroid orbits are integrated under the gravitational influences of the planets.2. We compute the resonant arguments.3. Images of the time dependence of resonant arguments are drawn.4. The ANN trains on the training label image data.5. Predictions on the test images are obtained, and images of the test data, with their classification, are produced. To identify resonant argument images, we created a four-layer model with a flatten, an inner, a hidden, and an output layers. The flatten layer will transform the image matrices into arrays. The inner layer will look for simpler patterns in the arguments images, while the hidden layer will search for more complex features. The output layer, with three nodes, will perform the final classification for the three possible classes. To quantitatively classify the outcome of ANN, it is often useful to compute values of metrics. [3] defines accuracy as: Our model performs quite well: Accuracy values were all above 0.996. 4. ML identification of resonant groups Using ANN and ML, we obtained labels for 6440 asteroids in the M1:2 resonance region. We then used the ML Hierarchical Clustering Method (ML-HCM) of [1] to identify asteroid groups among the resonant population of M1:2 resonators. Our analysis produced seven possible groups, all associated with the Massalia, Nysa, and Vesta families. This confirms the analysis of [4]. 5. Summary and Conclusions The use of ANN allowed us to classify the orbital type of all numbered asteroids affected by the M1:2 resonance. The identification of clusters in the population of asteroids in librating and switching orbits suggested that three asteroid families, those of Massalia, Nysa, and Vesta, are the most dynamically affected by this resonance. Acknowledgements We would like to thank the Brazilian National Research Council (CNPq, grant 301577/2017-0). More information on this work can be obtained from Carruba et al. (2021), MNRAS, 504, 692. References[1] CARRUBA, V., ALJBAAE, S., AND LUCCHINI, A. Machine-learning identification of asteroid groups. MNRAS 488, 1 (Sept. 2019), 1377–1386.[2] CHOLLET, F., AND OTHERS. Keras: The Python Deep Learning library, (June 2018).[3] FAWCETT, T. An introduction to ROC analysis. Pattern Recognition Letters 27, 8 (Jun. 2006), 861 –874.[4] GALLARDO, T., VENTURINI, J., ROIG, F., AND GIL-HUTTON, R. Origin and sustainability of the population of asteroids captured in the exterior resonance 1:2 with Mars. Icarus 214, 2 (Aug. 2011), 632–644.[5] LECUN, Y., BENGIO, Y., AND HINTON, G. Deep learning. Nature 521, 7553 (May 2015), 436–444.[6] VUJIČIĆ, D., PAVLOVIĆ, D., D., M., Ð ORÐEVIĆ, S., S., R., AND D., S. Classification of asteroid families with artificial neural networks. Serb. Astron. J. 200 (Dec. 2020), 1–8.

1. Introduction Linear secular resonances occur when there is a commensurability between the frequency of precession of an asteroid perihelion, g, or node, s, and that of a planet. The ν6 involves a relationship between the frequency g of an asteroid and the g6 frequency of Saturn. Since it is a pericenter resonance, it can increase most asteroids’ eccentricities to planet-crossing levels. It can, therefore, destabilize most of the bodies that interact with it, and it is a major source of NEAs through Yarkovsky effect [2]. Despite this fact, stable orbital configurations exist inside the ν6 resonance. In such configurations, the resonant angle σ = ϖ −ϖ6, with ϖ the longitude of pericenter of the asteroid and ϖ6 that of Saturn, can oscillate around either 0◦ or 180◦. In the first case, we have an “aligned libration”, since the pericenters of both Saturn and the asteroid are pointing in the same direction. For the second case, we have an “anti-aligned libration”. [4] identified the first case of an asteroid family completely made of asteroids in anti-aligned libration states, that of 1222 Tina. [6] extended this analysis to the whole main-belt, and found the first seven asteroids in aligned states of the same resonance. Here, we extended the previous analysis using the largest database of asteroid proper yet obtained. 2. Identification of the resonant population using large databases To identify the population of ν6 resonators, first, we need to select the asteroids most likely to be affected by this resonance. For this purpose, we use the criterion described in [6] and the approach outlined in [3]. We identified 15 asteroids on aligned orbital configurations, and 1713 on anti-aligned ones (see figure (1)). We then proceeded searching for asteroid groups among the newly identified anti-aligned population using the Hierarchical Clustering Method (HCM) [1]. Our results are shown in figures (2). We identify a new group around the asteroid 12988 Tiffanykapler. 3. 12988 Tiffanykapler: the first young family in the ν6 secular resonance Young asteroid families can be dated using methods based on numerical integrations of family members in the past, like the Backward Integration Method (BIM, [7]) and the Close Encounters Method (CEM, [5]). In the BIM method, from time-reversal numerical simulations, past discrepancies in the longitudes of node Ω of family members with regard to those of the claimed parent body are obtained. These differences should converge to values approaching zero at the time of family formation. The CEM approach works by integrating into the past multiple clones of the parent body and of the other family members. Close encounters that occur at low relative distances and speeds between two clones are recorded, and the median value of these times is used to estimate the asteroid pair’s age. The results of both methods are shown in figure (3). The BIM method suggests a possible solution for the 12988 group in the time range from 3.3 to 6.5 Myr. The weighted average of the age determination of all asteroid pairs in the family, one example of which is shown in the right panel of figure (3), provides an age estimate for the family of 3.05 ± 1.15 Myr. As discussed in [4], at the simplest level of perturbation theory the quantity: is preserved for asteroids in the ν6 resonance in the conservative case. The preservation of the original values of K2' permits to estimate the initial ejection velocity field with a method not generally available for non-resonant families. Our analysis yields a value of the ejection velocity parameter VEJ = 15+6-3 m/s. 4. Summary and Conclusions In this work, we were able to obtain a sample of 15 asteroids on aligned orbits and 1669 asteroids on anti-aligned orbits, the largest database so far for this asteroidal population. Two new asteroid groups were identified for the first time in this work: those of Tiffanykapler in the inner main-belt and 138605 QW177 in the outer belt. Tiffanykapler is the first young asteroid family in a linear resonant configuration ever to be found. Combining methods based on backward numerical simulations and constraints from resonant dynamics, we found that the family has an age of 3.05 ± 1.15 Myr and an ejection velocity field parameter of VEJ = 15+6-3 m/s. Finally, using resonant proper elements ([4]), we also identified a highly eccentric population of asteroids near the Tina family, that are likely to be part of its halo. It is the first example of a “resonant halo”. Acknowledgements We thank the Brazilian National Research Council (CNPq, grant 301577/2017-0), and the Foundation for Research Support of São Paulo state(FAPESP, grant 2016/024561-0). More information on this work is available on Carruba et al. 2022, MNRAS, under review, available on ArXiv: 2203.15763. References [1] BENDJOYA, P., AND ZAPPALÀ, V. Asteroid Family Identification. In Asteroids III. Arizona Univ. Press, 2002, pp. 613–618. [2] BOTTKE, W. F., JEDICKE, R., MORBIDELLI, A., PETIT, J.-M., AND GLADMAN, B. Understanding the Distribution of Near-Earth Asteroids. Science 288, 5474 (June 2000), 2190–2194. [3] CARRUBA, V., A LJBAAE, S., DOMINGOS, R. C., AND BARLETTA, W. Artificial neural network classification of asteroids in the M1:2 mean-motion resonance with Mars. MNRAS 504, 1 (June 2021), 692–700. [4] CARRUBA, V., AND MORBIDELLI, A. On the first ν6 anti-aligned librating asteroid family of Tina. MNRAS 412, 3 (Apr. 2011), 2040–2051. [5] CARRUBA, V., S POTO, F., BARLETTA, W., ALJBAAE, S., FAZENDA, Á. L., AND MARTINS, B. The population of rotational fission clusters inside asteroid collisional families. Nature Astronomy 4 (Jan. 2020), 83–88. [6] HUAMAN, M., ROIG, F., CARRUBA, V., DOMINGOS, R. C., AND ALJBAAE, S. The resonant population of asteroids in librating states of the ν6 linear secular resonance. MNRAS 481, 2 (Dec. 2018), 1707–1717. [7] NESVORNÝ, D., BOTTKE, WILLIAM F., J., DONES, L., AND L EVISON, H. F. The recent breakup of an asteroid in the main-belt region. Nature 417, 6890 (June 2002), 720–771.

Artificial neural networks (ANN) have been successfully used in the last years to identify patterns in astronomical images. The use of ANN in the field of asteroid dynamics has been, however, so far somewhat limited. In this work we used for the first time ANN for the purpose of automatically identifying the behaviour of asteroid orbits affected by the M1:2 mean-motion resonance with Mars. Our model was able to perform well above 85% levels for identifying images of asteroid resonant arguments in term of standard metrics like accuracy, precision and recall, allowing to identify the orbital type of all numbered asteroids in the region. Using supervised machine learning methods, optimized through the use of genetic algorithms, we also predicted the orbital status of all multi-opposition asteroids in the area. We confirm that the M1:2 resonance mainly affects the orbits of the Massalia, Nysa, and Vesta asteroid families., Comment: 11 pages, 10 figures, 1 table. Accepted for publication in MNRAS

Made available in DSpace on 2021-06-25T11:58:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-04-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) National Institute for Space Research (INPE) The goal of this paper is to develop a simplified model to describe the gravitational fields of elongated asteroids. The proposed model consists of representing an elongated asteroid using a triple-particle-linkage system distributed in the three-dimensional space and it is an extension of previous planar models. A nonlinear optimization method is used to determine the parameters of our model, minimizing the errors of all the external equilibrium points with respect to the solutions calculated with a more realistic approach, the Mascon model, which are assumed to give the real values of the system. The model considered in this paper is then applied to three real irregular asteroids: 1620 Geographos, 433 Eros, and 243 Ida. The results show that the current triple-particle-linkage three-dimensional model gives better accuracy when compared to the axisymmetric triple-particle-linkage model available in the literature, and provides an advantage in terms of accuracy over the mass point model, while keeping computational time low. This model is also used to carry out simulations to characterize regions with solutions that remain bounded or that escape from around each asteroid under analysis. We investigated initial inclinations of 0 degrees (direct orbits) and 180 degrees (retrograde orbits). We considered the gravitational field of the asteroid, the gravitational attraction of the Sun, and the SRP. Our results are then compared to the results obtained using the Mascon gravitational model, based on the polyhedral shape source. We found good agreement between the two models. INPE, Natl Inst Space Res, Div Space Mech & Control, Sao Paulo, Brazil Sao Paulo State Univ, UNESP, Sao Joao Da Boa Vista, Brazil Sao Paulo State Univ, UNESP, Sao Joao Da Boa Vista, Brazil CNPq: 140501/2017-7 CNPq: 150678/2019-3 CNPq: 422282/2018-9 CNPq: 301338/2016-7 FAPESP: 2016/24561-0 FAPESP: 2016/18418-0 CAPES: 88887.374148/2019-00

We provide a generalized discussion on the dynamics of a spacecraft around the equal-mass binary asteroid (90) Antiope, under the influence of solar radiation pressure at the perihelion and aphelion distances of the asteroid from the Sun. The polyhedral shape of the components of this asteroid is used to accurately model the gravitational field. Five unstable equilibrium points are determined and classified into two cases that allow classifying of the motion associated with the target as always unstable. The dynamical effects of the mass ratio of our binary system are investigated. We tested massless particles initially located at the periapsis distance on the equatorial plane of the primary of our binary asteroid. Bounded orbits around our system are not found for the longitudes λ ∈ {60, 90, 120, 240, 270, 300}. We also discuss the orbital dynamics in the full potential field of (90) Antiope. The tested motions are mainly dominated by the binary’s gravitational field; no significant effects of the SRP are detected. For λ = 180°, less perturbed orbits are identified between 420 and 700 km from the centre of the system, that corresponds to orbits with Δa < 30 km and Δe < 0.15. All the orbits with initial periapsis distance smaller than 350 km either collide with components of our asteroid or escape from the system.

Made available in DSpace on 2022-05-01T08:15:12Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-08-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Chaotic motion affecting small bodies in the Solar system can be caused by close encounters or collisions or by resonance overlapping. Chaotic motion can be detected using approaches that measure the separation rate of trajectories that starts infinitesimally close or changes in the frequency power spectrum of time series, among others. In this work, we introduce an approach based on the autocorrelation function of time series, the ACF index (ACFI). Autocorrelation coefficients measure the correlation of a time series with a lagged copy of itself. By measuring the fraction of autocorrelation coefficients obtained after a given time lag that are higher than the 5% null hypothesis threshold, we can determine how the time series autocorrelates with itself. This allows identifying unpredictable time series, characterized by low values of ACFI. Applications of ACFI to orbital regions affected by both types of chaos show that this method can correctly identify chaotic motion caused by resonance overlapping, but it is mostly blind to close encounters induced chaos. ACFI could be used in these regions to select the effects of resonance overlapping. School of Natural Sciences and Engineering São Paulo State University (UNESP) Division of Space Mechanics and Control National Space Research Institute (INPE), C.P. 515 São Paulo State University (UNESP) Universidad Tecnológica del Perú (UTP), Cercado de Lima School of Natural Sciences and Engineering São Paulo State University (UNESP) São Paulo State University (UNESP) CNPq: 121889/2020-3 FAPESP: 2016/024561-0 CNPq: 301577/2017-0 CAPES: 88887.374148/2019-00

The asteroids’ brightness is not generally constant, but presents time variations that depend on the asteroid shape, albedo, rotation period, and other factors. In 1901, Von Oppolzer first noted changes in the brightness of (433) Eros (von Oppolzer 1901), and the first correct period for this asteroid was published in Bailey & Pickering (1913). Today, lightcurves, time-series data for brightness variations, are available for more than 10,000 asteroids, and periods are known for more than 8,300 bodies (Warner et al. 2009). Data from asteroid lightcurves can be used, through lightcurve inversion methods, to infer information on the asteroid shapes, rotation periods, and spin axis directions. The Database of Asteroid Models from Inversion Techniques (DAMIT, (Durech et al. 2010)) currently has models for 3303 asteroids. Asteroid photometric lightcurves in a “FITS-like”, self-describing, style are publicly available for several bodies at the Asteroid Lightcurve Data Exchange Format (ALCDEF), website (http://alcdef.org (Stephens & Warner 2018; Warner et al. 2011; Stephens et al. 2010)). Asteroid lightcurves data are, in essence, a time series, and, as such, may be considered part of the discipline that Griffin et al. (2012) call “time-domain astronomy”. In statistical literature, dominant methods for studying time series are time-domain parametric modelling. Popular introductory (Brockwell & Davis 2016) and graduate-level (Shumway & Stoffer 2017) textbooks mostly focus on auto-regressive time-domain models, with only brief mentions of Fourier frequency-domain methods. Yet, while the latter methods have been used for several decades to study asteroid lightcurves and obtain asteroid periods (see for instance Lenz & Breger (2005); Szabó et al. (2016) and references therein), auto-regressive models, like the ARIMA methods, have not received as much attention. ARIMA stands for Auto-regressive (AR), integrated (I), moving average (MA). The AR part indicates that the variable of interest is regressed on its own lagged values. The MA indicates that the regression error is a linear combination of error terms that occurred at present and various past times. The I means that the variable values have been replaced by differences in their values and the previous ones. In this work, we attempt to use ARIMA methods to model observed lightcurves of main-belt asteroids, as available at the ALCDEF database. The ideal lightcurve shape would display “smooth, double-waved, quasi-sinusoidal” form Cellino et al. (1989). This kind of perfect shape is, however, very rare. Some features deforming the lightcurve are very common, and, for the same asteroid, can be caused by changes of the aspect angle, the angle between the asteroid spin axis and the direction of observation of the body from Earth, at different observing epochs. Cellino et al. (1989) introduced four categories for classifying irregularities in the shape of lightcurves: (i) Irregular morphology of one or more extrema (ii) Different levels of the extrema (iii) Different time intervals between the extrema (iv) More or less than two maxima or minima per cycle More recently, Harris et al. (2014) identified cases of very complex lightcurves with six maxima, for asteroids (5404) Uemura and 2010 RC130, which were later also retrieved by Szabó et al. (2016) for the asteroids (29628) 1998 TX30 and (37201) 2000WS94 observed during the K2 Kepler space telescope mission. For this work, we will define three categories of lightcurves: (i) Regular lightcurves, with no prominent irregularities as defined by Cellino et al. (1989). Examples of asteroids with these kinds of lightcurves in the ALCDEF database are (8) Flora, (16) Psyche, and (593) Titania. (ii) Complex lightcurves, with at least one shape irregularity. Examples are (21) Lutetia, (39) Laetitia, and (43) Ariadne. (iii) Very complex lightcurves, as defined by Harris et al. (2014). Examples are (5404) Uemura and (37201) 2000WS94. Figure (1) displays the ARIMA best-fits for (43) Ariadne and (5404) Uemura. ARIMA models were able to fit even very complex lightcurves with six maxima, like those of (5404) Uemura and (37201) 2000 WS94. Most models obtained in this work achieved a precision, measured in terms of mean relative error, of less than 1%, and future forecast of lightcurve data on timescales of a few hours is possible for most studied asteroids. Article submitted to MNRAS. This is publication from the MASB (Machine Learning applied to Small bodies https://valeriocarruba.github.io/Site-MASB/) research group. References Bailey, S. I. and Pickering, E. C. (1913). Observations of Eros and other asteroids. Annals of Harvard College Observatory, 72(5):165–189. Brockwell, P. J. and Davis, R. A. (2016). Introduction to Time Series and Forecasting. Springer, New York City, NY, USA. Cellino, A., Zappala, V., and Farinella, P. (1989). Asteroid shapes and lightcurve morphology. ICARUS, 78(2): 298–310. Durech, J., Sidorin, V., and Kaasalainen, M. (2010). DAMIT: a database of asteroid models. A&A, 513:A46. Griffin, E., Hanisch, R., and Seaman, R., editors (2012). New Horizons in Time Domain Astronomy (IAU S285), volume 285 of 285. Harris, A. W., Pravec, P., Galád, A., Skiff, B. A., Warner, B. D., Világi, J., Gajdoš, Š., Carbognani, A., Hornoch, K., Kušnirák, P., Cooney, W. R., Gross, J., Terrell, D., Higgins, D., Bowell, E., and Koehn, B. W. (2014). On the maximum amplitude of harmonics of an asteroid lightcurve. ICARUS, 235:55–59. Lenz, P. and Breger, M. (2005). Period04 User Guide. Communications in Asteroseismology, 146:53–136. Shumway, R. H. and Stoffer, D. S. (2017). Time Series Analysis and Its Applications with R Examples. Springer, New York City, NY, USA. Stephens, R. and Warner, B. D. (2018). The ALCDEF Database and the NASA SBN/PDS: The Perfect Merger. In AAS/Division for Planetary Sciences Meeting Abstracts #50, volume 50 of AAS/Division for Planetary Sciences Meeting Abstracts, page 417.03. Stephens, R. D., Warner, B. D., and Harris, A. W. (2010). A Proposed Standard For Reporting Asteroid Lightcurve Data. In AAS/Division for Planetary Sciences Meeting Abstracts #42, volume 42 of AAS/Division for Planetary Sciences Meeting Abstracts, page 39.14. Szabó, R., Pál, A., Sárneczky, K., Szabó, G. M., Molnár, L., Kiss, L. L., Hanyecz, O., Plachy, E., and Kiss, C. (2016). Uninterrupted optical light curves of main-belt asteroids from the K2 mission. A&A, 596:A40. von Oppolzer, E. (1901). Notiz betr. Planet (433) Eros. Astronomische Nachrichten, 154(14):297.

Made available in DSpace on 2021-06-25T11:16:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-06-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Linear secular resonances are observed when there is a ratio between the precession period of the longitudes of pericenter or nodes of a minor body and a planet. Nonlinear secular resonances occur for higher-order combinations of frequencies. They can change the shape of asteroid families in the (a, e, sin (i)) proper elements space. Identifying asteroids in secular resonances requires performing numerical simulations, and then visually inspecting if the resonant argument is librating, which is generally a time-consuming procedure. Here, we use machine learning genetic algorithms to select the most optimal model and training set to best-fit asteroids likely to be in librating states of the z1 and z2 secular resonances. We then identify groups in domains of librating asteroids, as predicted by our algorithms, and verified whether these clusters belong to known collisional families. Using this approach, we retrieved all the asteroid families known to interact with the two resonances and identified 5 fairly robust previously unknown groups. School of Natural Sciences and Engineering São Paulo State University (UNESP) Division of Space Mechanics and Control National Space Research Institute (INPE), C.P. 515 São Paulo State University (UNESP) School of Natural Sciences and Engineering São Paulo State University (UNESP) São Paulo State University (UNESP) FAPESP: 2018/20999-6 CNPq: 30157/2017-0 CAPES: 88887.374148/2019-00

Close encounters or resonances overlaps can create chaotic motion in small bodies in the Solar System. Approaches that measure the separation rate of trajectories that start infinitesimally near, or changes in the frequency power spectrum of time series, among others, can discover chaotic motion. In this paper, we introduce the ACF index (ACFI), which is based on the auto-correlation function of time series. Auto-correlation coefficients measure the correlation of a time-series with a lagged duplicate of itself. By counting the number of auto-correlation coefficients that are larger than 5% after a certain amount of time has passed, we can assess how the time series auto-correlates with each other. This allows for the detection of chaotic time-series characterized by low ACFI values.

Made available in DSpace on 2019-10-06T07:29:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-09-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) National Aeronautics and Space Administration Asteroid families are groups of asteroids that share a common origin. They can be the outcome of a collision or be the result of the rotational failure of a parent body or its satellites. Collisional asteroid families have been identified for several decades using hierarchical clustering methods (HCMs) in proper elements domains. In this method, the distance of an asteroid from a reference body is computed, and, if it is less than a critical value, the asteroid is added to the family list. The process is then repeated with the new object as a reference, until no new family members are found. Recently, new machine-learning clustering algorithms have been introduced for the purpose of cluster classification. Here, we apply supervised-learning hierarchical clustering algorithms for the purpose of asteroid families identification. The accuracy, precision, and recall values of results obtained with the new method, when compared with classical HCM, show that this approach is able to found family members with an accuracy above 89.5 per cent, and that all asteroid previously identified as family members by traditional methods are consistently retrieved. Values of the areas under the curve coefficients below Receiver Operating Characteristic curves are also optimal, with values consistently above 85 per cent. Overall, we identify 6 new families and 13 new clumps in regions where the method can be applied that appear to be consistent and homogeneous in terms of physical and taxonomic properties. Machine-learning clustering algorithms can, therefore, be very efficient and fast tools for the problem of asteroid family identification. Sao Paulo State Univ UNESP, Sch Nat Sci & Engn, BR-12516410 Guaratingueta, SP, Brazil Natl Space Res Inst INPE, Div Space Mech & Control, CP 515, BR-12227310 Sao Jose Dos Campos, SP, Brazil Sao Paulo State Univ UNESP, Sch Nat Sci & Engn, BR-12516410 Guaratingueta, SP, Brazil FAPESP: 2018/20999-6 CNPq: 301577/2017-0

Tumbling asteroids belong to a small group of objects, whose angular velocity vector is unaligned with any of its principal axes of inertia. This leads to challenging efforts to model the trajectory of any spacecraft designed to orbit these bodies. In this work, we deepen a previous study on this topic, concerning the asteroid (99942) Apophis during its close encounter with the Earth in 2029. We analyze the orbital behaviour of a spacecraft orbiting the asteroid during this event, by including the effects of the changes of orientation of the spin axis of the asteroid, depending on two sets of initial conditions. The global dynamics of the spacecraft around the target are analyzed using three approaches, MEGNO, PMap, and Time-Series prediction. We confirm that no spacecraft with natural orbits could survive the high perturbations caused by the close encounter with our planet., Comment: 13 pages, 13 figures

Made available in DSpace on 2020-12-12T02:46:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-06-11 Asteroid families are groups of asteroids that are the product of collisions or of the rotational fission of a parent object. These groups are mainly identified in proper elements or frequencies domains. Because of robotic telescope surveys, the number of known asteroids has increased from ∼eq10000 in the early 1990s to more than 750000 nowadays. Traditional approaches for identifying new members of asteroid families, like the hierarchical clustering method (HCM), may struggle to keep up with the growing rate of new discoveries. Here we used machine learning classification algorithms to identify new family members based on the orbital distribution in proper (a, e, sin (i)) of previously known family constituents. We compared the outcome of nine classification algorithms from stand-alone and ensemble approaches. The extremely randomized trees (ExtraTree) method had the highest precision, enabling to retrieve up to 97 per cent of family members identified with standard HCM. School of Natural Sciences and Engineering São Paulo State University (UNESP) National Space Research Institute (INPE) Division of Space Mechanics and Control São Paulo State University (UNESP) School of Natural Sciences and Engineering São Paulo State University (UNESP) São Paulo State University (UNESP)

Made available in DSpace on 2021-06-25T10:14:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01 The orbital dynamics of a spacecraft orbiting around irregular small celestial bodies is a challenging problem. Difficulties to model the gravity field of these bodies arise from the poor knowledge of the exact shape as observed from the Earth. In order to understand the complex dynamical environment in the vicinity of irregular asteroids, several studies have been conducted using simplified models. In this work, we investigate the qualitative dynamics in the vicinity of an asteroid with an arched shape using a tripole model based on the existence of three mass points linked to each other by rods with given lengths and negligible masses. We applied our results to some real systems, namely, asteroids 8567, 243 Ida and 433 Eros and also Phobos, one of the natural satellites of Mars. Division of Space Mechanics and Control National Institute for Space Research (INPE) Department of Aeronautical Engineering São Paulo University (UNESP) Department of Aeronautical Engineering São Paulo University (UNESP)

Several studies have proposed a way to mitigate a possible threat given by an asteroid approach to the Earth. However, the possibility to deviate or break such bodies depends mainly on their physical characteristics. Our work aims to determine the best region for human interference in the object's trajectory. It means that we will search for the region of minimal internal forces that keep the body as a single unit, which is the best point for the asteroid breakup. We report that the consideration of the body resistance, while it belongs to the strength regime size, shall be the key to find the best location for an interception. We use the Johnson-Kendall-Roberts (JKR) theory to add adhesive contact forces between the target body's micro-sized particle constituents. We also solve the balanced equation for tidal due to Earth for the body, and we consider it with and without adhesion forces. We see that the best approach region happens while the self-gravity is minimized by the Earth's gravity, which occurs when the body is still held in one piece by the inter-particles forces. It means that we do not expect a natural breakup. Nevertheless, these minimum adhesion forces points are the best options to target a spacecraft for a collision that breaks the asteroids if it is necessary to do so.

The Gefion asteroid family is a group of S-type asteroids located between the 8J:-3A and 5J:-2A mean-motion resonances. The 5J:-2A resonance seems to be responsible for the absence of the right side of the V-shape of this family. We aim in this work to present a detailed study on the Gefion family, motivated by the incompatibility found in previous family age estimations and the fact that this family could be seen as one of the most probable sources of L-chondrite meteorites. After eliminating all possible taxonomical and dynamical interlopers, we use a Monte Carlo method to analyze the semi-major axis evolution of several fictitious families under the influence of the Yarkovsky and Yarkovsky-O’Keefe-Radzievsky-Paddack (YORP) effects. We also perform simulations using symplectic integrators to account for the Yarkovsky effect (diurnal and seasonal versions) and the stochastic YORP effect. We make use of the distribution of the component of the ejection velocity field (vW) perpendicular to the orbital plane and the time dependence of the asymmetry of the distribution of the target function of a fictitious family generated with ejection velocity parameter 20+55−15m s−1to obtain an age estimate of 1030+19−67Myr. We find that 6.5% of asteroids from the Gefion family can reach orbits similar to particles in the current near-Earth objects space; 73% of them are among the Amors asteroids, and the remaining ones are among the Apollos. We only found 0.5% from the Gefion family reaching the Mars-crossing space.

Made available in DSpace on 2019-10-06T17:13:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-06-01 The main goal of our work is to study the orbital dynamics of a spacecraft near the (87) Sylvia system. Here, we consider a non-homogeneous mass distribution with a dense core inside the primary asteroid. The Mascon gravity framework using the shaped polyhedral source, from light-curve data, is chosen to calculate the gravitational field. The zero-velocity curves show four unstable equilibrium points. In the absence of any solar or other celestial body perturbations, a numerical analysis of the orbital dynamics in the potential field of Sylvia is done to delineate the region of stable and unstable motions. In our model, the motions of the two moons of Sylvia and of the spacecraft are integrated with the classical equations of motion in the body-fixed frame of reference. An orbit is considered stable if the variation of its periapsis radius does not exceed a threshold value (i.e. 6 km), and the variation of its eccentricity does not exceed 0.05, although the orientation of these orbits may change. We found that the first stable orbit is detected at a distance of 550 km from the centre of Sylvia. No collision occurs with the central body beyond 350 km. The collisions with Remus occur between 300 and 900 km, while with Romulus they occur between 900 and 1450 km. Moreover, the orbits escape from the system when the distance is smaller than 350 km. Finally, we found that the stability region around our system decreases when the initial eccentricity increases. Division of Space Mechanics and Control INPE, C.P. 515 School of Natural Sciences and Engineering São Paulo State University (UNESP) DLR Institute of Planetary Research, Rutherfordstr. 2 SYRTE Observatoire de Paris PSL Research University, 61 avenue de l'Observatoire School of Natural Sciences and Engineering São Paulo State University (UNESP)

Made available in DSpace on 2020-12-12T02:49:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-11-15 California Institute of Technology Jet Propulsion Laboratory National Aeronautics and Space Administration National Research Council Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Asteroid groups may either form because of collisions or the rotational failure of a parent body. Collisional asteroid families tend to be more spread in proper element domains, while young spin clusters are usually much more compact. Recently, it has been shown that young spin clusters may form at higher rates in extremely young asteroid families (families younger than ≃3 Myr) than in more evolved groups. Among asteroid families, the Koronis family is a natural laboratory to test this phenomenon. While the family itself is very evolved, with an estimated age of more than 2 Byr, two young sub-families are known to be located among Koronis members: the extremely young family of Karin, with an age of 5.75±0.05 Myr, and the relatively young sub-family of Koronis(2), with an age of 10±5 Myr. This fact allows studying the occurrence of young spin clusters in extremely young, young and evolved asteroid populations, all sharing the same physical properties. Using methods based on backward numerical integrations, we identify one possible pair candidate in the Karin family, and retrieved the pair 1741–258640 recently found in other works. No convincing spin pair candidate was found in the Koronis(2) sub-family. This suggests that the occurrence of young spin clusters in families older than ≃ 3 Myr may be a rarer event than what previously thought. São Paulo State University (UNESP) School of Natural Sciences and Engineering National Space Research Institute (INPE) Division of Space Mechanics and Control, C.P. 515 Federal University of São Paulo (UNIFESP) Science and Technology Institute São Paulo State University (UNESP) School of Natural Sciences and Engineering FAPESP: 16/04476-8 CNPq: 301577/2017-0

Made available in DSpace on 2019-10-06T17:01:43Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-12-01 We discuss the asteroid population evolving close by or into the υ6 secular resonance in the main asteroid belt. Using the analytical method of Yoshikawa, we estimate the actual domain of the υ6 resonance, which currently contains 4 137 asteroids identified from the AstDys catalogue.We perform numerical integrations of the obits of these asteroids, considering the gravitational perturbation of all the planets, and identify those showing pure libration states. For the first time, seven asteroids are found to librate in aligned states, all located at the central main belt. We analyse the stability of this new population by extending our numerical integrations both into the past and into the future, to find that all of them are stable, but only four of them display long-term aligned librations. We also identified the asteroid families located close to and within the domain of the υ6 secular resonance, with a particular focus on the Svea family, which has 54 per cent of its members librating in anti-aligned states. This is the third family identified to be largely affected by the υ6 resonance, together with the families of Tina and Euphrosyne. Observatório Nacional (ON), Rua Gal. Jose Cristino 77 São Paulo State University (UNESP) School of Natural Sciences and Engineering São Paulo State University (UNESP), Campus of São São Paulo State University (UNESP) School of Natural Sciences and Engineering São Paulo State University (UNESP), Campus of São

The Nele group, formerly known as the Iannini family, is one of the youngest asteroid families in the main belt. Previously, it has been noted that the pericenter longitudes $\varpi$ and nodal longitudes $\Omega$ of its largest member asteroids are clustered at the present time, therefore suggesting that the collisional breakup of parent body must have happened recently. Here we verify this conclusion by detailed orbit-propagation of a synthetic Nele family and show that the current level of clustering of secular angles of the largest Nele family members requires an approximate age limit of $4.5$ Myr. Additionally, we make use of an updated and largely extended Nele membership to obtain, for the first time, an age estimate of this family using the Backward Integration Method (BIM). Convergence of the secular angles in a purely gravitational model and in a model including the non-gravitational forces caused by the Yarkovsky effect are both compatible with an age younger than $7$ Myr. More accurate determination of the Nele family age would require additional data about the spin state of its members., Comment: 11 pages, 12 figures, accepted for publication on MNRAS

Made available in DSpace on 2018-11-28T13:17:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-07-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) National Aeronautics and Space Administration Non-linear secular resonances of g-type, i.e. involving the frequency of precession g of the asteroid pericentre, can affect the proper eccentricities of asteroids in resonant or near-resonant configurations. We first identified objects that could potentially be affected by non-linear secular resonances of this type. We then numerically integrated these objects and checked for their resonant argument. We identified a population of 1517 asteroids in g -2g(6) + g(5) librating states, and of 128 objects in g -3g(6) + 2g(5) resonant configurations. While secular resonances are rather extended structures and many objects from different and unrelated parts of the main belt could be encountered within, we found that g-2g(6) + g(5) librators are predominantly of the S taxonomical type (56 per cent of the total), but with a significant fraction of other spectral types. No spectral type dominates in the population of g -3g(6) + 2g(5) resonators. Several asteroid families are affected by the g -2g(6) + g(5) secular resonance. The Astraea group is cut into two by this resonance, while the Tirela and Brasilia groups are on the resonance centre and on the left side, respectively. The g -2g(6) + g(5) secular can significantly affect the shape of families inside the resonance, such as Astraea. It can also increase the flux of asteroids to nearby powerful mean-motion resonances, such as the 5J:-2A and the 2J:-1A. As expected, the long-term effect of g-type resonances on inclinations is essentially negligible. Sao Paulo State Univ UNESP, Sch Nat Sci & Engn, BR-12516410 Guaratingueta, SP, Brazil Sao Paulo State Univ UNESP, Campus Sao Joao da Boa Vista, BR-13876750 Sao Paulo, SP, Brazil Sao Paulo State Univ UNESP, Sch Nat Sci & Engn, BR-12516410 Guaratingueta, SP, Brazil Sao Paulo State Univ UNESP, Campus Sao Joao da Boa Vista, BR-13876750 Sao Paulo, SP, Brazil FAPESP: 2016/04476 - 8 FAPESP: 2013/15357 - 1 CNPq: 305453/2011 - 4 CNPq: 310317/2016 - 9

Made available in DSpace on 2018-12-11T17:36:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-01-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) The Maria asteroid family is a group of S-type asteroids. Its location adjacent to the left side of the 3J:-1A mean-motion resonances could be the reason for the absence of the left side of the 'V' shape in the (a, 1/D) domain. This family can be considered as a likely source of ordinary chondrite-like material. In this work, we make use of the time dependence of the asymmetric coefficient AS describing the degree of asymmetry of the C distribution of a fictitious Maria family generated with the value of the ejection velocity parameter VEJ = 35ms-1 to obtain an age estimate of 1750 +537 -231 Myr, in good agreement with the family age found in the literature. Analysing the contribution to the near-Earth object (NEO) population, we found that about 7.6 per cent of presently known near-Earth asteroids (NEAs) have orbits similar to asteroids from the Maria family. Only ~1.7 per cent of our simulated family can stay in NEO space for more than 10 Myr, while only five asteroids become NEOs in the last 500 Myr of the simulation. São Paulo State University (UNESP) School of Natural Sciences and Engineering Jet Propulsion Laboratory/Caltech, 4800 Oak Grove Dr., MS 183-601 Universidade Estadual Paulista (UNESP) Observatório Nacional (ON), Rua Gal. Jose Cristino 77 São Paulo State University (UNESP) School of Natural Sciences and Engineering Universidade Estadual Paulista (UNESP)

The Hoffmeister family is a C-type group located in the central main belt. Dynamically, it is important because of its interaction with the ${\nu}_{1C}$ nodal secular resonance with Ceres, that significantly increases the dispersion in inclination of family members at lower semi-major axis. As an effect, the distribution of inclination values of the Hoffmeister family at semi-major axis lower than its center is significantly leptokurtic, and this can be used to set constraints on the terminal ejection velocity field of the family at the time it was produced. By performing an analysis of the time behaviour of the kurtosis of the $v_W$ component of the ejection velocity field (${\gamma}_2(v_W)$), as obtained from Gauss' equations, for different fictitious Hoffmeister families with different values of the ejection velocity field, we were able to exclude that the Hoffmeister family should be older than 335 Myr. Constraints from the currently observed inclination distribution of the Hoffmeister family suggest that its terminal ejection velocity parameter $V_{EJ}$ should be lower than 25~m/s. Results of a Yarko-YORP Monte Carlo method to family dating, combined with other constraints from inclinations and ${\gamma}_2(v_W)$, indicate that the Hoffmeister family should be $220^{+60}_{-40}$~Myr old, with an ejection parameter $V_{EJ}= 20\pm5$~m/s., Comment: 8 pages, 7 figures. Accepted for publication in MNRAS. arXiv admin note: text overlap with arXiv:1606.05189

Here we study the dynamical effects of the solar radiation pressure (SRP) on a spacecraft that will survey the near-Earth rotating asteroid (101955) Bennu when the projected shadow is accounted for. The spacecraft's motion near (101955) Bennu is modelled in the rotating frame fixed at the centre of the asteroid, neglecting the sun gravity effects. We calculate the solar radiation pressure at the perihelion, semi-major axis and aphelion distances of the asteroid from the Sun. The goals of this work are to analyse the stability for both homogeneous and inhomogeneous mass distribution and study the effects of the solar radiation pressure in equatorial orbits close to the asteroid (101955) Bennu. As results, we find that the mascon model divided into ten equal layers seems to be the most suitable for this problem. We can highlight that the centre point $E$8, which was linearly stable in the case of the homogeneous mass distribution, becomes unstable in this new model changing its topological structure. For a Sun initial longitude $\psi_0 = -180^o$, starting with the spacecraft longitude $\lambda = 0$, the orbits suffer fewer impacts and some (between 0.4 and 0.5 km), remaining unwavering even if the maximum solar radiation is considered. When we change the initial longitude of the Sun to $\psi_0 = -135^o$, the orbits with initial longitude $\lambda = 90^0 $ appear to be more stable. Finally, when the passage of the spacecraft in the shadow is accounted for, the effects of solar radiation pressure are softened, and we find more stable orbits., Comment: Accepted 2017 May 10. Received 2017 April 29; in original form 2017 January 13

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., Comment: 10 pages, 7 figures, and 4 Tables. Accepted for publication in MNRAS

International audience; Many asteroid families are identified and well characterized all over the main asteroid belt. Interestingly, however, none of them are older than 4 Gyr. Many mechanisms have been proposed to disperse such old primordial asteroid families that presumably have existed, but only very few have really worked. Here we present a plausible mechanism for dispersing primordial asteroid families that is based on the 5-planet instability model known as jumping Jupiter. Using two different evolutions for the jumping-Jupiter model, we have numerically integrated orbits of eight putative primordial families. Our results show that the most important effect on the asteroid families' eccentricity and inclination dispersal is that of the secular resonances, in some cases associated with the mean motion resonances. As for the semimajor axes spreading we find that the principal effect is that of close encounters with the fifth giant planet whose orbit briefly overlaps with (part of) the main belt. Therefore, the existence of a fifth giant planet with the mass comparable with that of Uranus' or Neptune's could contribute in important ways to dispersal of the primordial asteroid families. To have that effect, the interloper planet should go into and considerably interact with the asteroids during the instability phase.

Ceres is the largest and most massive body in the asteroid main belt. Observational data from the Dawn spacecraft reveal the presence of at least two impact craters about 280~km in diameter on the Ceres surface, that could have expelled a significant number of fragments. Yet, standard techniques for identifying dynamical asteroid families have not detected any Ceres family. In this work, we argue that linear secular resonances with Ceres deplete the population of objects near Ceres. Also, because of the high escape velocity from Ceres, family members are expected to be very dispersed, with a considerable fraction of km-sized fragments that should be able to reach the pristine region of the main belt, the area between the 5J:-2A and 7J:-3A mean-motion resonances, where the observed number of asteroids is low. Rather than looking for possible Ceres family members near Ceres, here we propose to search in the pristine region. We identified 156 asteroids whose taxonomy, colors, albedo could be compatible with being fragments from Ceres. Remarkably, most of these objects have inclinations near that of Ceres itself., Comment: 12 pages, 6 figures, 1 table. Accepted for publication in MNRAS

$v_W$ leptokurtic asteroid families are families for which the distribution of the normal component of the terminal ejection velocity field $v_W$ is characterized by a positive value of the ${\gamma}_2$ Pearson kurtosis, i.e., they have a distribution with a more concentrated peak and larger tails than the Gaussian one. Currently, eight families are known to have ${\gamma}_2(v_W) > 0.25$. Among these, three are highly inclined asteroid families, the Hansa, Barcelona, and Gallia families. As observed for the case of the Astrid family, the leptokurtic inclination distribution seems to be caused by the interaction of these families with node secular resonances. In particular, the Hansa and Gallia family are crossed by the $s-s_V$ resonance with Vesta, that significantly alters the inclination of some of their members. In this work we use the time evolution of ${\gamma}_2(v_W)$ for simulated families under the gravitational influence of all planets and the three most massive bodies in the main belt to assess the dynamical importance (or lack of) node secular resonances with Ceres, Vesta, and Pallas for the considered families, and to obtain independent constraints on the family ages. While secular resonances with massive bodies in the main belt do not significantly affect the dynamical evolution of the Barcelona family, they significantly increase the ${\gamma}_2(v_W)$ values of the simulated Hansa and Gallia families. Current values of the ${\gamma}_2(v_W)$ for the Gallia family are reached over the estimated family age only if secular resonances with Vesta are accounted for., Comment: 7 pages, 5 figures, 2 tables. Accepted for publication in MNRAS

The Erigone family is a C-type group in the inner main belt. Its age has been estimated by several researchers to be less then 300 My, so it is a relatively young cluster. Yarko-YORP Monte Carlo methods to study the chronology of the Erigone family confirm results obtained by other groups. The Erigone family, however, is also characterized by its interaction with the $z_2$ secular resonance. While less than 15% of its members are currently in librating states of this resonance, the number of objects, members of the dynamical group, in resonant states is high enough to allow to use the study of dynamics inside the $z_2$ resonance to set constraints on the family age. Like the ${\nu}_{6}$ and $z_1$ secular resonances, the $z_2$ resonance is characterized by one stable equilibrium point at $\sigma = 180^{\circ}$ in the $z_2$ resonance plane $(\sigma, \frac{d\sigma}{dt})$, where $\sigma$ is the resonant angle of the $z_2$ resonance. Diffusion in this plane occurs on timescales of $\simeq 12$ My, which sets a lower limit on the Erigone family age. Finally, the minimum time needed to reach a steady-state population of $z_2$ librators is about 90 My, which allows to impose another, independent constraint on the group age., Comment: This paper has 11 pages, 12 figures, and 1 table. Accepted for publication in MNRAS

Made available in DSpace on 2018-12-11T17:25:26Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-01 In the last two decades, new computational tools have been developed in order to aid space missions to orbit around irregular small bodies. One of the techniques consists in rebuilding their shape in tetrahedral polyhedron. This method is well suited to determine the shape and estimate certain physical features of asteroids. However, a large computational effort is necessary depending on the quantity of triangular faces chosen. Another method is based on a representation of the central body in terms of mascons (discrete spherical masses). The main advantage of the method is its simplicity which makes the calculation faster. Nevertheless, the errors are non-negligible when the attraction expressions are calculated near the surface of the body. In this work, we carry out a study to develop a new code that determines the centre of mass of each tetrahedron of a shaped polyhedral source and evaluates the gravitational potential function and its first-and second-order derivatives. We performed a series of tests and compared the results with the classical polyhedron method. We found good agreement between our determination of the attraction expressions close to the surface, and the same determination by the classical polyhedron method. However, this agreement does not occur inside the body. Our model appears to be more accurate in representing the potential very close to the body's surface when we divide the tetrahedron in three parts. Finally, we have found that in terms of CPU time requirements, the execution of our code is much faster compared with the polyhedron method. Univ. Estadual Paulista-UNESP, Grupo de Dinâmica Orbital and Planetologia Univ. Estadual Paulista-UNESP, Grupo de Dinâmica Orbital and Planetologia

The Cybele region, located between the 2J:-1A and 5J:-3A mean-motion resonances, is adjacent and exterior to the asteroid main belt. An increasing density of three-body resonances makes the region between the Cybele and Hilda populations dynamically unstable, so that the Cybele zone could be considered the last outpost of an extended main belt. The presence of binary asteroids with large primaries and small secondaries suggested that asteroid families should be found in this region, but only relatively recently the first dynamical groups were identified in this area. Among these, the Sylvia group has been proposed to be one of the oldest families in the extended main belt. In this work we identify families in the Cybele region in the context of the local dynamics and non-gravitational forces such as the Yarkovsky and stochastic YORP effects. We confirm the detection of the new Helga group at $\simeq$3.65~AU, that could extend the outer boundary of the Cybele region up to the 5J:-3A mean-motion resonance. We obtain age estimates for the four families, Sylvia, Huberta, Ulla and Helga, currently detectable in the Cybele region, using Monte Carlo methods that include the effects of stochastic YORP and variability of the Solar luminosity. The Sylvia family should be $T = 1220 \pm 40$ Myr old, with a possible older secondary solution. Any collisional Cybele group formed prior to the late heavy bombardment would have been most likely completely dispersed in the jumping Jupiter scenario of planetary migration., This paper has 13 pages, 14 figures, and 4 tables. Accepted for publication in MNRAS

The Rafita asteroid family is an S-type group located in the middle main belt, on the right side of the 3J:-1A mean-motion resonance. The proximity of this resonance to the family left side in semi-major axis caused many former family members to be lost. As a consequence, the family shape in the $(a,1/D)$ domain is quite asymmetrical, with a preponderance of objects on the right side of the distribution. The Rafita family is also characterized by a leptokurtic distribution in inclination, which allows the use of methods of family age estimation recently introduced for other leptokurtic families such as Astrid, Hansa, Gallia, and Barcelona. In this work we propose a new method based on the behavior of an asymmetry coefficient function of the distribution in the $(a,1/D)$ plane to date incomplete asteroid families such as Rafita. By monitoring the time behavior of this coefficient for asteroids simulating the initial conditions at the time of the family formation, we were able to estimate that the Rafita family should have an age of $490\pm200$ Myr, in good agreement with results from independent methods such as Monte Carlo simulations of Yarkovsky and Yorp dynamical induced evolution and the time behaviour of the kurtosis of the $\sin{(i)}$ distribution. Asteroids from the Rafita family can reach orbits similar to 8\% of the currently known near Earth objects. $\simeq$1\% of the simulated objects are present in NEO-space during the final 10 Myr of the simulation, and thus would be comparable to objects in the present-day NEO population., Accepted 2017 January 19. Received 2017 January 17; in original form 2016 September 5

International audience

International audience

% context :The precise and accurate modelling of a terrestrial planet like Venus is an exciting and challenging topic, all the more interesting since it can be compared with that of the Earth for which such a modelling has already been achieved at the milliarcsecond level % aims: We want to complete a previous study (Cottereau and Souchay, 2009), by determining at the milliarcsecond level the polhody, i.e. the torque-free motion of the axis of angular momentum of a rigid Venus in a body-fixed frame, as well as the nutation of its third axis of figure in space, which is fundamental from an observational point of view. results :In a first part we have computed the polhody, i.e. the respective free rotational motion of the axis of angular momentum of Venus with respect to a body-fixed frame. We have shown that this motion is highly elliptical, with a very long period of 525 cy to be compared with 430 d for the Earth. This is due to the very small dynamical flattening of Venus in comparison with our planet. In a second part we have computed precisely the Oppolzer terms which allow to represent the motion in space of the third Venus figure axis with respect to Venus angular momentum axis, under the influence of the solar gravitational torque. We have determined the corresponding tables of coefficients of nutation of the third figure axis both in longitude and in obliquity due to the Sun, which are of the same order of amplitude as for the Earth. We have shown that the coefficients of nutation for the third figure axis are significantly different from those of the angular momentum axis on the contrary of the Earth. Our analytical results have been validated by a numerical integration which revealed the indirect planetary effects., Comment: 14 pages, 11 figures, accepted for publication in section 11. Celestial mechanics and astrometry of Astronomy and Astrophysics (27/02/2010)

We aim at providing a preliminary approach on the dynamics of a spacecraft in orbit about the asteroid (99942) Apophis during its Earth close approach. The physical properties from the polyhedral shape of the target are derived assigning each tetrahedron to a point mass in its center. That considerably reduces the computation processing time compared to previous methods to evaluate the gravitational potential. The surfaces of section close to Apophis are build considering or not the gravitational perturbations of the Sun, the planets, and the SRP. The Earth is the one that most affects the invisticated region making the vast majority of the orbits to collide or escape from the system. Moreover, from numerical analysis of orbits started on March 1, 2029, the less perturbed region is characterized by the variation of the semimajor axis of 40-days orbits, which do not exceed 2 km very close to the central body ($a < 4$ km, $e < 0.4$). However, no regions investigated could be a possible option for inserting a spacecraft into natural orbits around Apophis during the close approach with our planet. Finally, to solve the stabilization problem in the system, we apply a robust path following control law to control the orbital geometry of a spacecraft. At last, we present an example of successful operation of our orbit control with a total $\bigtriangleup v$ of 0.495 m/s for 60 days. All our results are gathered in the CPM-ASTEROID database, which will be regularly updated by considering other asteroids., 24 pages, 20 figures