arXiv subjects

Elisa Maria Alessi

Publications and source records attributed to Elisa Maria Alessi.

At least 19 recordsLinked to original sources

arXiv2026

Twin Impact Lunar Telescope network: Lunar Impact Flash observations of the 2025 Geminids

Meteoroid impacts on the Moon, observed from Earth as flashes typically lasting a few tens of milliseconds, have been monitored for three decades for determining meteoroids' size and mass frequency distribution in the cm to dm range. Studies link these observed impact events to fresh craters advancing our understanding of energy partitioning during an impact. Currently we are transitioning to a new era where lunar impact flashes (LIFs) can be used to supplement upcoming lunar seismology to study the internal lunar structure. Here we present results from the first station of a telescope network under development for continuous LIF monitoring. Observations were carried out during the Geminids 2025 campaign, initiated by the LUMIO Science Team in the framework of their public engagement activities. We detected 53 potential impact flashes and confirmed 11 of them through multiframe observations, and independent detections by other observers. We present evidence suggesting that some of the yet unconfirmed events may be real. Our confirmed events range between magnitude +7.5 and +10.4, primarily in the V and R band. We obtained a high rate of observations per hour, highlighting the importance of high ZHR meteoroid streams for observing LIFs. We also discuss the scientific value of potential LIFs that remain unconfirmed in optical data alone. Even without multi station confirmation, these events can correlate to seismic signals in future lunar seismic networks, thereby providing useful physical constraints on impact processes. This approach would also allow stations equipped with a single telescope/camera to meaningfully contribute to the network.

astro-ph.EP↗

arXiv2026

Observational planning for the 2026 August 5 Falcon 9 Upper Stage lunar impact

On 2026 August 5, at approximately 06:35 UT, a spent Falcon 9 upper stage will impact the lunar surface near Einstein Crater. This event will occur on sunlit terrain near the eastern limb as seen from Earth. The impact flash and resultant ejecta plume from this event are potentially observable from ground- and space-based observational facilities. This event provides an opportunity to attempt the recording of an artificial impact in real-time; although many of the properties of the event (such as visual magnitude) are imprecisely predicted at present. Moreover, this event provides an opportunity to test a pipeline for localising impacts on the lunar surface for future seismic experiments, investigating the dust and plume dynamics from impact events on the Moon, and considering hazards from artificial space debris impacts. Both professional and amateur astronomers are encouraged to attempt observations of this event.

astro-ph.EP↗

arXiv2026

Regularity and reentry basins of low Earth orbits in the $J_{2}$-solar radiation pressure problem

We investigate the long-term dynamical structure of low Earth orbits (LEOs) using the Smaller Alignment Index (SALI), a fast numerical indicator of chaos, within a closed-form averaged model that incorporates the effects of solar radiation pressure and Earth's oblateness. Our analysis reveals that the area-to-mass ratio is a key parameter governing the onset and extent of chaotic behavior in LEOs. We map the system's chaotic regions, study the behavior of reentry trajectories and characterize their temporal laws over a timescale constrained by the $25$-year mitigation guideline. Within this physically relevant timescale, we show that most of the reentry trajectories exhibit regular motion. Reentry basins, constructed according to different mitigation guidelines up to $25$ years, display fractal-like structures for less-stringent guidelines. The degree of this fractality is quantitatively assessed using the uncertainty exponent method. In most cases, for large area-to-mass ratios, reentry occurs on relatively short timescales (a few years) - short enough that no fractal behavior is observed in the basin boundaries. This numerical dynamical study offers insights into the development of dynamically informed deorbiting strategies.

nlin.CD↗

arXiv2026

The steady-state population of Earth's co-orbitals of lunar provenance

The population of natural objects in a 1:1 mean motion resonance with Earth are known as Earth's co-orbitals. Main belt objects can dynamically evolve into Earth co-orbitals but taxonomic studies of some of them have suggested that they are more likely to be lunar material. While it has long been known that lunar ejecta can achieve Earth co-orbital status, in this work we calculate their expected steady-state size-frequency distribution from the impact rate of asteroids and comets on the Moon's surface, the ejecta's size-frequency and speed distribution, and dynamical integration of the particles for millions of years, among other factors. We also classify known and synthetic co-orbitals by their regime (quasi-satellite, horseshoe, tadpole, or compound) and compute the probability of transitions between them. Our nominal solution predicts that there are $\gtrsim 70$ Earth co-orbitals in the steady-state population larger than $10$ m in diameter with a lunar provenance but there are orders-of-magnitude systematic uncertainty on the value. We used NEOMOD3 to calculate that about 1600 are expected in the co-orbital population with a main belt provenance and they have higher eccentricity and inclination than those from the Moon. New taxonomic classifications for more Earth co-orbitals will reduce the uncertainties on e.g. crater scaling relations that will, in turn, reduce the uncertainties in the calculation of the steady-state population of Earth's co-orbitals with a lunar origin. The mineralogy and abundance of Earth's co-orbitals is also of interest to commercial asteroid mining ventures because they are the lowest $Δv$ targets in the asteroid population.

astro-ph.EP↗

arXiv2025

Fuzzy Jump Models for Soft and Hard Clustering of Multivariate Time Series Data

Statistical jump models have been recently introduced to detect persistent regimes by clustering temporal features and discouraging frequent regime changes. However, they are limited to hard clustering and thereby do not account for uncertainty in state assignments. This work presents an extension of the statistical jump model that incorporates uncertainty estimation in cluster membership. Leveraging the similarities between statistical jump models and the fuzzy c-means framework, our fuzzy jump model sequentially estimates time-varying state probabilities. Our approach offers high flexibility, as it supports both soft and hard clustering through the tuning of a fuzziness parameter, and it naturally accommodates multivariate time series data of mixed types. Through a simulation study, we evaluate the ability of the proposed model to accurately estimate the true latent-state distribution, demonstrating that it outperforms competing approaches under high cluster assignment uncertainty. We further demonstrate its utility on two empirical applications: first, by automatically identifying co-orbital regimes in the three-body problem, a novel application with important implications for understanding asteroid behavior and designing interplanetary mission trajectories; and second, on a financial dataset of five assets representing distinct market sectors (equities, bonds, foreign exchange, cryptocurrencies, and utilities), where the model accurately tracks both bull and bear market phases.

stat.ME↗

arXiv2025

The steady state population of Earth's minimoons of lunar provenance

This work examines the plausibility of a lunar origin of natural objects that have a negative total energy (ET) with respect to the geocenter while within 3 Earth Hill radii (RH), a population that we will refer to as 'bound'. They are a super-set of the population of 'minimoons' which require that the object make at least one orbit around Earth in a synodic frame rotating with Earth and that its geocentric distance be <RH at some point while ET<0. Only two minimoons have been discovered to date, 2006 RH120 and 2020 CD3, while 2024 PT5 and 2022 NX1 meet our condition for 'bound'. The likely source region of co-orbital objects is either the main belt, lunar ejecta, or a combination of both. Earlier works found that dynamical evolution of asteroids from the MB could explain the observed minimoon population, but spectra of 2020 CD3 and 2024 PT5 and Earth co-orbital (469219) Kamo'oalewa are more consistent with lunar basalts than any MB asteroid spectra. This work calculates the steady-state size-frequency distribution of the bound population given our understanding of the lunar impact rate, the energy of the impactors, crater-scaling relations, and the relationship between the ejecta mass and speed. We integrate the trajectory of lunar ejecta and calculate the statistics of 'prompt' bounding that take place immediately after ejection, and 'delayed' bounding that occurs after the objects have spent time on heliocentric orbits. A sub-set of the delayed bound population composes the minimoon population. We find that lunar ejecta can account for the observed population of bound objects but uncertainties in the crater formation and lunar ejecta properties induce a many orders of magnitude range on the predicted population. If the bound objects can be distinguished as lunar or asteroidal based on their spectra it may be possible to constrain crater formation processes.

astro-ph.EP↗

arXiv2024

On the role of the fast oscillations in the secular dynamics of the lunar coplanar perturbation on Galileo satellites

Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation, assuming that the Moon lies on the ecliptic plane. The secular Hamiltonian defined in that way is characterized by two timescales. We compare the location and stability of the fixed points associated with the secular Hamiltonian averaged with respect to the fast variable with the corresponding periodic orbits of the full system. Focusing on the orbit of the Galileo satellites, it turns out that the two dynamics cannot be confused, as the relative difference depends on the ratio between the semi-major axis of Galileo and the one of the Moon, that is not negligible. The result is relevant to construct rigorously the Arnold diffusion mechanism that can drive a natural growth in eccentricity that allows a satellite initially on a circular orbit in Medium Earth Orbit to reenter into the Earth's atmosphere.

astro-ph.EP↗

arXiv2024

On the Arnold diffusion mechanism in Medium Earth Orbit

Space debris mitigation guidelines represent the most effective method to preserve the circumterrestrial environment. Among them, end-of-life disposal solutions play a key role. A growing effort is devoted to exploit natural perturbations to lead the satellites towards an atmospheric reentry, reducing the disposal cost, also if departing from high-altitude regions. In the case of the Medium Earth Orbit region, home of the navigation satellites (like Galileo), the main driver is the gravitational perturbation due to the Moon, that can increase the eccentricity in the long term. In this way, the pericenter altitude can get into the atmospheric drag domain and the satellite can eventually reenter. In this work, we show how an Arnold diffusion mechanism can trigger the eccentricity growth. Focusing on the case of Galileo, we consider a hierarchy of Hamiltonian models, assuming that the main perturbations on the motion of the spacecraft are the oblateness of the Earth and the gravitational attraction of the Moon. First, the Moon is assumed to lay on the ecliptic plane and periodic orbits and associated stable and unstable invariant manifolds are computed for various energy levels, in the neighborhood of a given resonance. Along each invariant manifold, the eccentricity increases naturally, achieving its maximum at the first intersection between them. This growth is, however, not sufficient to achieve reentry. By moving to a model where the inclination of the Moon is taken into account, the problem becomes non-autonomous and the satellite is able to move along different energy levels. Under the ansatz of transversality of the manifolds in the autonomous case, checked numerically, Poincaré-Melnikov techniques are applied to show how diffusion can be attained, by constructing a sequence of homoclinic orbits that connect invariant tori at different energy levels.

math.DS↗

arXiv2023

Asteroids co-orbital motion classification based on Machine Learning

In this work, we explore how to classify asteroids in co-orbital motion with a given planet using Machine Learning. We consider four different kinds of motion in mean motion resonance with the planet, nominally Tadpole, Horseshoe and Quasi-satellite, building 3 datasets defined as Real (taking the ephemerides of real asteroids from the JPL Horizons system), Ideal and Perturbed (both simulated, obtained by propagating initial conditions considering two different dynamical systems) for training and testing the Machine Learning algorithms in different conditions. The time series of the variable theta (angle related to the resonance) are studied with a data analysis pipeline defined ad hoc for the problem and composed by: data creation and annotation, time series features extraction thanks to the tsfresh package (potentially followed by selection and standardization) and the application of Machine Learning algorithms for Dimensionality Reduction and Classification. Such approach, based on features extracted from the time series, allows to work with a smaller number of data with respect to Deep Learning algorithms, also allowing to define a ranking of the importance of the features. Physical Interpretability of the features is another key point of this approach. In addition, we introduce the SHapley Additive exPlanations for Explainability technique. Different training and test sets are used, in order to understand the power and the limits of our approach. The results show how the algorithms are able to identify and classify correctly the time series, with a high degree of performance.

astro-ph.EP↗

arXiv2023

End-to-end trajectory concept for close exploration of Saturn's Inner Large Moons

We present a trajectory concept for a small mission to the four inner large satellites of Saturn. Leveraging the high efficiency of electric propulsion, the concept enables orbit insertion around each of the moons, for arbitrarily long close observation periods. The mission starts with a EVVES interplanetary segment, where a combination of multiple gravity assists and deep space low thrust enables reduced relative arrival velocity at Saturn, followed by an unpowered capture via a sequence of resonant flybys with Titan. The transfers between moons use a low-thrust control law that connects unstable and stable branches of the invariant manifolds of planar Lyapunov orbits from the circular restricted three-body problem of each moon and Saturn. The exploration of the moons relies on homoclinic and heteroclinic connections of the Lyapunov orbits around the L$_1$ and L$_2$ equilibrium points. These science orbits can be extended for arbitrary lengths of time with negligible propellant usage. The strategy enables a comprehensive scientific exploration of the inner large moons, located deep inside the gravitational well of Saturn, which is unfeasible with conventional impulsive maneuvers due to excessive fuel consumption.

astro-ph.EP↗

arXiv2022

On the co-orbital asteroids in the solar system: medium-term timescale analysis of the quasi-coplanar objects

The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a heliocentric orbit trapped in a 1:1 mean-motion resonance with a given planet. As such, to model it this work considers the Restricted Three-Body Problem in the circular-planar case with the help of averaging techniques. The domain of each co-orbital regime, that is, the quasi-satellite motion, the horseshoe motion and the tadpole motion, can be neatly defined by means of an integrable model and a simple bi-dimensional map, that is invariant with respect to the mass parameter of the planet, and turns out to be a remarkable tool to investigate the distribution of the co-orbitals objects of interest. The study is based on the data corresponding to the ephemerides computed by the JPL Horizons system for asteroids with a sufficient low orbital inclination with respect to the Sun-planet orbital plane. These objects are cataloged according to their current dynamics, together with the transitions that occur in the given time frame from a given type of co-orbital motion to another. The results provide a general catalog of co-orbital asteroids in the solar system, the first one to our knowledge, and an efficient mean to study transitions.

astro-ph.EP↗

arXiv2021

Revisiting the averaged problem in the case of mean-motion resonances of the restricted three-body problem. Global rigorous treatment and application to the co-orbital motion

A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem of a mean-motion resonance allows to investigate the long-term behavior of the solutions through a suitable approximation that focuses on a particular region of the phase space. In this paper, we intend to bridge a gap between the two approaches in the specific case of mean-motion resonant dynamics, establish the limit of validity of the averaged problem, and take advantage of its results in order to compute trajectories in the synodic reference frame. After the description of each approach, we develop a rigorous treatment of the averaging process, estimate the size of the transformation and prove that the averaged problem is a suitable approximation of the restricted three-body problem as long as the solutions are located outside the Hill's sphere of the secondary. In such a case, a rigorous theorem of stability over finite but large timescales can be proven. We establish that a solution of the averaged problem provides an accurate approximation of the trajectories on the synodic reference frame within a finite time that depend on the minimal distance to the Hill's sphere of the secondary. The last part of this work is devoted to the co-orbital motion (i.e., the dynamics in 1:1 mean-motion resonance) in the circular-planar case. In this case, an interpretation of the solutions of the averaged problem in the synodic reference frame is detailed and a method that allows to compute co-orbital trajectories is displayed.

astro-ph.EP↗

arXiv2021

Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis

We describe the phase space structures related to the semi-major axis of Molniya-like satellites subject to tesseral and lunisolar resonances. In particular, the questions answered in this contribution are: (i) we study the indirect interplay of the critical inclination resonance on the semi-geosynchronous resonance using a hierarchy of more realistic dynamical systems, thus discussing the dynamics beyond the integrable approximation. By introducing ad hoc tractable models averaged over fast angles, (ii) we numerically demarcate the hyperbolic structures organising the long-term dynamics via Fast Lyapunov Indicators cartography. Based on the publicly available two-line elements space orbital data, (iii) we identify two satellites, namely Molniya 1-69 and Molniya 1-87, displaying fingerprints consistent with the dynamics associated to the hyperbolic set. Finally, (iv) the computations of their associated dynamical maps highlight that the spacecraft are trapped within the hyperbolic tangle. This research therefore reports evidence of actual artificial satellites in the near-Earth environment whose dynamics are ruled by manifolds and resonant mechanisms. The tools, formalism and methodologies we present are exportable to other region of space subject to similar commensurabilities as the geosynchronous region.

nlin.CD↗

arXiv2021

Science orbits in the Saturn-Enceladus circular restricted three-body problem with oblate primaries

This contribution investigates the properties of a category of orbits around Enceladus. In a previous investigation, a set of heteroclinic connections were designed between halo orbits around the equilibrium points L1 and L2 of the circular restricted three-body problem with Saturn and Enceladus as primaries. The geometrical characteristics of those trajectories makes them good candidates as science orbits for the extended observation of the surface of Enceladus: they are highly inclined, they approach the moon and they are maneuver-free. However, the low heights above the surface and the strong perturbing effect of Saturn require a study of the influence of the polar flattening of the primaries. Therefore, those solutions are here reconsidered with a dynamical model that includes the effect of the oblateness of Saturn and Enceladus, separately and in combination. The dynamical equivalents of the halo orbits around the equilibrium points L1 and L2 and their stable and unstable hyperbolic invariant manifolds are obtained in the perturbed models, and maneuver-free heteroclinic connections are identified. A comparison with the corresponding solutions of the unperturbed problem shows that qualitative and quantitative features are not significantly altered in the perturbed model. The results confirm the scientific value of the solutions obtained in the classical circular restricted three-body problem and suggests that the simpler model can be used in a preliminary feasibility analysis.

astro-ph.EP↗

arXiv2020

Dynamical taxonomy of the coupled solar radiation pressure and oblateness problem and analytical deorbiting configurations

Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly-averaged equations of motion. The coupled perturbations affect the evolution of the eccentricity, inclination and orientation of the orbit with respect to the Sun--Earth line. Resonant interactions lead to non-trivial orbital evolution that can be exploited in mission design. Moreover, the dynamics in the vicinity of each resonance can be analytically described by a resonant model that provides the location of the central and hyperbolic invariant manifolds which drive the phase space evolution. The classical tools of the dynamical systems theory can be applied to perform a preliminary mission analysis for practical applications. On this basis, in this work we provide a detailed derivation of the resonant dynamics, also in non-singular variables, and discuss its properties, by studying the main bifurcation phenomena associated to each resonance. Last, the analytical model will provide a simple analytical expression to obtain the area-to-mass ratio required for a satellite to deorbit from a given altitude in a feasible timescale.

astro-ph.EP↗

arXiv2020

Investigation on a Doubly-Averaged Model for the Molniya Satellites Orbits

The aim of this work is to investigate the lunisolar perturbations affecting the long-term dynamics of a Molniya satellite. Some numerical experiments on the doubly-averaged model, including the expansion of the lunisolar disturbing functions up to the third order, are carried out in order to detect the terms dominating the long-term evolution. The analysis focuses on the following significant indicators: the amplitude of the harmonic coefficients, the periods of the arguments involved and, in particular, the ratio between the amplitudes and the corresponding frequency. The results show that the second-order lunisolar perturbation gives the dominant contribution to the long-term dynamics. The second part of this work aims to study the resonant regions associated to the dominant terms identified so far by using both the ideal resonance model and an alternative approach. The results obtained show when the standard method does not catch the main features of the dynamical structure of the resonant regions. Finally, the maximum overlapping region is identified in the proximity of the Molniya orbital environment.

astro-ph.EP↗

arXiv2020

Dynamical properties of the Molniya satellite constellation: long-term evolution of orbital eccentricity

The aim of this work is to analyze the orbital evolution of the mean eccentricity given by the Two-Line Elements (TLE) set of the Molniya satellites constellation. The approach is bottom-up, aiming at a synergy between the observed dynamics and the mathematical modeling. Being the focus the long-term evolution of the eccentricity, the dynamical model adopted is a doubly-averaged formulation of the third-body perturbation due to Sun and Moon, coupled with the oblateness effect on the orientation of the satellite. The numerical evolution of the eccentricity, obtained by a two-degree-of-freedom model assuming different orders in the series expansion of the third-body effect, is compared against the mean evolution given by the TLE. The results show that, despite being highly elliptical orbits, the second order expansion catches extremely well the behavior. Also, the lunisolar effect turns out to be non-negligible for the behavior of the longitude of the ascending node and the argument of pericenter. The role of chaos in the timespan considered is also addressed. Finally, a frequency series analysis is proposed to show the main contributions that can be detected from the observational data.

astro-ph.EP↗

arXiv2019

Phase space description of the dynamics due to the coupled effect of the planetary oblateness and the solar radiation pressure perturbations

The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly-averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure perturbations. A two-dimensional differential system is derived by considering the classical theory, supported by the existence of an integral of motion comprising semi-major axis, eccentricity and inclination. Under the single resonance hypothesis, the analytical expressions for the equilibrium points in the eccentricity-resonant angle space are provided, together with the corresponding linear stability. The Hamiltonian formulation is also given. The model is applied considering, as example, the Earth as major oblate body, and a simple tool to visualize the structure of the phase space is presented. Finally, some considerations on the possible use and development of the proposed model are drawn.

astro-ph.EP↗