arXiv subjects

Aaron J. Rosengren

Publications and source records attributed to Aaron J. Rosengren.

At least 19 recordsLinked to original sources

arXiv2026

The Astrodynamics Primer on Cislunar and Translunar Space

The Earth-Moon environment is multiscale and strongly nonuniform, yet it is often discussed as a single cislunar regime. In reality, circumterrestrial space is partitioned by changes in perturbation hierarchy, by gateway topology, and secular and resonant structures that differ qualitatively across the domain. This paper develops a unified spatiographic description of that structure, combining perturbative theory, semi-analytical resonance cartography, restricted multi-body dynamics, and direct numerical mapping. The terrestrial-cislunar transition is sharpened through the Laplace radius, beyond which lunisolar torques overtake the classical oblateness-dominated picture. Earthward of the Moon, cislunar space divides into a secularly dominated inner zone and an outer zone structured by interior lunar mean-motion resonances. Near the Moon, circumlunar space forms a distinct dynamical enclave organized by the EM gateway geometry and the lunar SOI. Beyond the Moon, translunar space forms an outer circumterrestrial province in which the Moon acts as an interior perturber, the Sun remains an exterior perturber, and the resulting dynamics acquire a mixed lunisolar secular and resonant architecture before weakening outward toward heliocentric behavior. These results are synthesized through MEGNO and fate-class cartographies across six numerical map domains. The maps reveal where quasiperiodic confinement survives, where resonance overlap and gateway transport produce sticky residence and organized escape, and where solar forcing becomes a qualitative architectural ingredient. Placed alongside a curated catalog of satellites and debris, the framework provides a dynamical geography of this environments that clarifies the transitions among cislunar, circumlunar, and translunar motion and offers a more precise basis for interpreting stability, transport, and long-term Earth-bound behavior.

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arXiv2025

Cislunar Resonant Transport and Heteroclinic Pathways: From 3:1 to 2:1 to L1

Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is critical for both lunar exploration and for high-Earth-orbiting trajectories. In this study, we investigate the role of mean-motion resonances and their associated heteroclinic connections in enabling natural semi-major axis transport in the Earth-Moon system. Working within the planar circular restricted three-body problem, we compute and analyze families of periodic orbits associated with the interior 4:1, 3:1, and 2:1 lunar resonances. These families exhibit a rich bifurcation structure, including transitions between prograde and retrograde branches and connections through collision orbits. We construct stable and unstable manifolds of the unstable resonant orbits using a perigee-based Poincaré map, and identify heteroclinic connections - both between resonant orbits and with lunar $L_1$ libration-point orbits - across a range of Jacobi constant values. Using a new generalized distance metric to quantify the closeness between trajectories, we establish operational times-of-flight for such heteroclinic-type orbit-to-orbit transfers. These connections reveal ballistic, zero-$Δv$ pathways that achieve major orbit changes within reasonable times-of-flight, thus defining a network of accessible semi-major axes. Our results provide a new dynamical framework for long-term spacecraft evolution and cislunar mission design, particularly in regimes where lunar gravity strongly perturbs distant circumterrestrial orbits.

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arXiv2025

Analytical estimates for heliocentric escape of satellite ejecta

We present a general analytic framework to assess whether impact ejecta launched from the surface of a satellite can escape the gravitational influence of the planet--satellite system and enter heliocentric orbit. Using a patched-conic approach and defining the transition to planetocentric space via the Hill sphere or sphere of influence, we derive thresholds for escape in terms of the satellite-to-planet mass ratio and the ratio of the satellite's orbital speed to its escape speed. We identify three dynamical regimes for ejecta based on residual speed and launch direction. We complement this analysis with the circular restricted three-body problem (CR3BP), deriving a necessary escape condition from the Jacobi integral at $\mathrm{L_{2}}$ and showing that it is consistent with the patched-conic thresholds. Applying our model to the Earth--Moon system reveals that all three outcomes--bound, conditional, and unbound--are accessible within a narrow range of launch speeds. This behavior is not found in other planetary satellite systems, but may occur in some binary asteroids. The framework also shows that the Moon's tidal migration has not altered its propensity to produce escaping ejecta, reinforcing the plausibility of a lunar origin for some near-Earth asteroids.

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arXiv2025

A Bayesian Benchmarking of GBEES Applied to Outer Planet Orbiter Estimation

Moment-based estimation filters have successfully aided spacecraft navigation for decades. However, future missions plan to venture into deep-space regimes with significant round-trip light-time telecommunication delays, operate in unstable, quasi-periodic orbits, and perform highly precise, low-altitude flybys of outer planet moons. These complex trajectories may necessitate ensemble-based filters for accurate estimation over realistic measurement cadences. To mitigate the inherent risk associated with testing novel navigation software, ensemble filters must be accurate, efficient, and robust. Grid-based, Bayesian Estimation Exploiting Sparsity, a high-dimensional Godunov-type finite volume method that propagates the full probability distribution function, demonstrates strong overall performance across all these criteria when compared with the contemporary landscape of filters. These qualities are exhibited via a Bayesian investigation in which the state uncertainty of a Saturn-Enceladus Distant Prograde Orbit is propagated, incorporating infrequent, nonlinear measurement updates. Along with root mean square error, we use the Bhattacharyya coefficient, a non-normal metric for measuring the dissimilarity between distributions, and the Effective Sampling Size, a measure of particle degeneracy, to quantitatively ascertain that in this application, Grid-based, Bayesian Estimation Exploiting Sparsity outperforms the other ensemble filters assessed, though it comes at a nontrivial computational cost.

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arXiv2025

A dynamical coherency gate for state recovery: Statistical requiem for the long arc of cislunar orbital mis-prediction

We present a statistically grounded methodology for recovering physically consistent initial conditions from historical two-line element sets (TLEs), enabling accurate long-arc trajectory reconstruction for distant and highly eccentric Earth satellites. The approach combines numerical averaging of osculating orbital elements with Gaussian-mixture-model (GMM) filtering with robust fallback strategies to isolate a dynamically coherent subset of mean elements at a common reference epoch. From this filtered ensemble, a representative osculating element is reconstructed, yielding a recovered Cartesian state vector with predictive capability far exceeding that of raw TLE-based propagations and existing approaches. We apply this method to the case of OGO-1 (1964-054A), a spacecraft launched into a cislunar orbit and tracked intermittently over five decades. Despite large observational gaps and significant secular evolution, our recovered state, used within an unscented Kalman filter (UKF), accurately reproduces the full trajectory, including its atmospheric reentry in August 2020, to within one day of the true decay time. This result demonstrates the viability of filtered TLE statistics as a proxy for precise orbit determination, particularly in dynamical regimes where resonances and long-period perturbations dominate. The techniques presented here provide a framework for trajectory reconstruction and prediction using only publicly available data and are broadly applicable to the study of high-altitude debris objects and legacy space missions whose original tracking and covariance data are unavailable.

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arXiv2025

Cislunar Mean-Motion Resonances: Definitions, Widths, and Comparisons with Resonant Satellites

Lunar mean-motion resonances (MMRs) significantly shape cislunar dynamics beyond GEO, forming stable-unstable orbit pairs with corresponding intermingled chaotic and regular regions. The resonance zone is rigorously defined using the separatrix of unstable resonant periodic orbits surrounding stable quasi-periodic regions. Our study leverages the planar, circular, restricted three-body problem (PCR3BP) to estimate the (stable) resonance widths and (unstable) chaotic resonance zones of influence of the 2:1 and 3:1 MMRs across various Jacobi constants, employing a Poincaré map at perigee and presenting findings in easily interpretable geocentric orbital elements. An analysis of the semi-major axis versus eccentricity plane reveals broader regions of resonance influence than those predicted by semi-analytical models based on the perturbed Kepler problem. A comparison with high-fidelity 3-dimensional ephemeris propagation of several spacecraft - TESS, IBEX, and Spektr-R - in these regions is made, which shows good agreement with the simplified CR3BP model.

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arXiv2025

Lunar impact ejecta flux on the Earth

The transfer of material between planetary bodies due to impact events is important for understanding planetary evolution, meteoroid impact fluxes, the formation of near-Earth objects (NEOs), and even the provenance of volatile and organic materials at Earth. This study investigates the dynamics and fate of lunar ejecta reaching Earth. We employ the high-accuracy IAS15 integrator withing the REBOUND package to track for 100,000 years the trajectories of 6,000 test particles launched from various lunar latitudes and longitudes. Our model incorporates a realistic velocity distribution for ejecta fragments (tens of meters in size), derived form large lunar cratering events. Our results show that 22.6% of lunar ejecta collide with Earth, following a power-law $C(t) \propto t^{0.315}$ with half of the impacts occurring within ~10,000 years. We also confirm that impact events on the Moon's trailing hemisphere serve as a dominant source of Earth-bound ejecta, consistent with previous studies. Additionally, a small fraction of ejecta remains transiently in near-Earth space, providing evidence that lunar ejecta may contribute to the NEO population. This aligns with recent discoveries of Earth co-orbitals such as Kamo'oalewa (469219, 2016 HO3) and 2024 PT5, both exhibiting spectral properties consistent with lunar material. These findings enhance our understanding of the lunar ejecta flux to Earth, providing insights into the spatial and temporal patterns of this flux and its broader influence on the near-Earth environment.

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arXiv2024

The Sensitivity to initial conditions of the Co-orbital outcomes of Lunar Ejecta

Lunar ejecta, produced by meteoroidal impacts, have been proposed for the origin of the near-Earth asteroid (469219) Kamo'oalewa, supported by its unusually Earth-like orbit and L-type reflectance spectrum (Sharkey et al., 2021). In a recent study (Castro-Cisneros et al. 2023), we found with N-body numerical simulations that the orbit of Kamo'oalewa is dynamically compatible with rare pathways of lunar ejecta captured into Earth's co-orbital region, persistently transitioning between horseshoe and quasi-satellite (HS-QS) states. Subsequently, Jiao et al. (2024) found with hydrodynamic and N-body simulations that the geologically young lunar crater Giordano Bruno generated up to 300 Kamo'oalewa-sized escaping fragments, and up to three of those could have become Earth co-orbitals. However, these results are based upon specific initial conditions of the major planets in the Solar System, close to the current epoch. In particular, over megayear time spans, Earth's eccentricity undergoes excursions up to five times its current value, potentially affecting the chaotic orbital evolution of lunar ejecta and their capture into Earth's co-orbital regions. In the present work, we carry out additional numerical simulations to compute the statistics of co-orbital outcomes across different launch epochs, representative of the full range of Earth's eccentricity values. Our main results are as follows: Kamo'oalewa-like co-orbital outcomes of lunar ejecta vary only slightly across the range of Earth's orbital eccentricity, suggesting no privileged ejecta launching epoch for such objects; the probability of co-orbital outcomes decreases rapidly with increasing launch speed, but long-lived HS-QS states are favored at higher launch speeds.

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arXiv2023

Lunar ejecta origin of near-Earth asteroid Kamo`oalewa is compatible with rare orbital pathways

Near-Earth asteroid, Kamo'oalewa (469219), is one of a small number of known quasi-satellites of Earth; it transitions between quasi-satellite and horseshoe orbital states on centennial timescales, maintaining this dynamics over megayears. The similarity of its reflectance spectrum to lunar silicates and its Earth-like orbit both suggest that it originated from the lunar surface. Here we carry out numerical simulations of the dynamical evolution of particles launched from different locations on the lunar surface with a range of ejection velocities in order to assess the hypothesis that Kamo`oalewa originated as a debris-fragment from a meteoroidal impact with the lunar surface. As these ejecta escape the Earth-Moon environment, they face a dynamical barrier for entry into Earth's co-orbital space. However, a small fraction of launch conditions yields outcomes that are compatible with Kamo`oalewa's orbit. The most favored conditions are launch velocities slightly above the escape velocity from the trailing lunar hemisphere.

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arXiv2023

The smallest planetary drivers of white dwarf pollution

Many potential mechanisms for delivering planetary debris to within a few Roche radii of white dwarfs rely on gravitational scattering events that feature perturbers which are giant planets or terrestrial planets. However, the population of these planets orbiting white dwarfs is still unknown, and for a substantial fraction of white dwarfs the largest planetary survivors of stellar evolution may be sub-terrestrial mass minor planets. Here, we attempt to identify the smallest mass perturbers that could pollute white dwarfs. Through computationally expensive numerical simulations of both unstable and stable configurations of minor planets, we find that this critical lower bound equals approximately one Luna mass. Further, we find that as this mass limit is approached from above, the typical cooling age at which white dwarf pollution occurs increases. Consequently, there is a two order-of-magnitude range of perturber masses between Earth and its moon that has remained largely unexplored in white dwarf pollution studies, despite the potential formation of thousands of such Luna-sized objects in these systems.

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arXiv2020

Space Occupancy in Low-Earth Orbit

With the upcoming launch of large constellations of satellites in the low-Earth orbit (LEO) region it will become important to organize the physical space occupied by the different operating satellites in order to minimize critical conjunctions and avoid collisions. Here, we introduce the definition of space occupancy as the domain occupied by an individual satellite as it moves along its nominal orbit under the effects of environmental perturbations throughout a given interval of time. After showing that space occupancy for the zonal problem is intimately linked to the concept of frozen orbits and proper eccentricity, we provide frozen-orbit initial conditions in osculating element space and obtain the frozen-orbit polar equation to describe the space occupancy region in closed analytical form. We then analyze the problem of minimizing space occupancy in a realistic model including tesseral harmonics, third-body perturbations, solar radiation pressure, and drag. The corresponding initial conditions, leading to what we call minimum space occupancy (MiSO) orbits, are obtained numerically for a set of representative configurations in LEO. The implications for the use of MiSO orbits to optimize the design of mega-constellations are discussed.

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arXiv2020

Lunar close encounters compete with the circumterrestrial Lidov-Kozai effect

Luna 3 (or Lunik 3 in Russian sources) was the first spacecraft to perform a flyby of the Moon. Launched in October 1959 on a translunar trajectory with large semi-major axis and eccentricity, it collided with the Earth in late March 1960. The short, 6-month dynamical lifetime has often been explained through an increase in eccentricity due to the Lidov-Kozai effect. However, the classical Lidov-Kozai solution is only valid in the limit of small semi-major axis ratio, a condition that is satisfied only for solar (but not for lunar) perturbations. We undertook a study of the dynamics of Luna 3 with the aim of assessing the principal mechanisms affecting its evolution. We analyze the Luna 3 trajectory by generating accurate osculating solutions, and by comparing them to integrations of singly- and doubly-averaged equations of motion in vectorial form. Lunar close encounters, which cannot be reproduced in an averaging approach, decisively affect the trajectory and break the doubly-averaged dynamics. Solar perturbations induce oscillations of intermediate period that affect the geometry of the close encounters and cause the singly-averaged and osculating inclinations to change quadrants (the orbital plane ``flips''). We find that the peculiar evolution of Luna 3 can only be explained by taking into account lunar close encounters and intermediate-period terms; such terms are averaged out in the Lidov-Kozai solution, which is not adequate to describe translunar or cislunar trajectories. Understanding the limits of the Lidov-Kozai solution is of particular significance for the motion of objects in the Earth-Moon environment and of exoplanetary systems.

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arXiv2020

Assessing and Minimizing Collisions in Satellite Mega-Constellations

We aim to provide satellite operators and researchers with an efficient means for evaluating and mitigating collision risk during the design process of mega-constellations. We first establish a baseline for evaluating various techniques for close-encounter prediction and collision-probability calculation (Hoots et al. 1984, Gronchi 2005, JeongAhn and Malhotra 2015) by carrying out brute-force numerical simulations and using a sequence of filters to greatly reduce the computational expense of the algorithm. Next, we estimate conjunction events in the orbital environment following the anticipated deployments of the OneWeb LEO and SpaceX Starlink mega-constellations. As a final step, we investigate Minimum Space Occupancy (MiSO) orbits (Bombardelli et al. 2018), a generalization of the well-known frozen orbits that account for the perturbed-Keplerian dynamics of the Earth-Moon-Sun-satellite system. We evaluate the ability of MiSO configurations of the proposed mega-constellations, as suggested by Bombardelli et al. 2018, to reduce the risk of endogenous (intra-constellation) collisions. The results indicate that the adoption of the MiSO orbital configuration can significantly reduce risk with nearly indistinguishable adjustments to the nominal orbital elements of the constellation satellites.

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arXiv2019

Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods

This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error components. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods to the semi-analytical method implemented in the orbit propagation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy). We show for the first time that efficient implementations of non-averaged regularized formulations of the equations of motion, and especially of non-singular element methods, are attractive candidates for the long-term study of high-altitude and highly elliptical Earth satellite orbits.

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arXiv2019

Dynamical Lifetime Survey of Geostationary Transfer Orbits

In this paper, we study the long-term dynamical evolution of highly-elliptical orbits (HEOs) in the medium-Earth orbit (MEO) region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrations (up to 200 years) within a realistic dynamical model, aimed primarily at recording the dynamical lifetime of such orbits (defined as the time needed for atmospheric reentry) and understanding its dependence on initial conditions and other parameters, such as the area-to-mass ratio (A/m). Our results are presented in the form of 2-D lifetime maps, for different values of inclination, A/m, and drag coefficient. We find that the majority of small debris (> 70%, depending on the inclination) can naturally reenter within 25-90 years, but these numbers are significantly less optimistic for large debris (e.g., upper stages), with the notable exception of those launched from high latitude (Baikonur). We estimate the reentry probability and mean dynamical lifetime for different classes of GTOs and we find that both quantities depend primarily and strongly on initial perigee altitude. Atmospheric drag and higher A/m values extend the reentry zones, especially at low inclinations. For high inclinations, this dependence is weakened, as the primary mechanisms leading to reentry are overlapping lunisolar resonances. This study forms part of the EC-funded (H2020) "ReDSHIFT" project.

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arXiv2019

Dynamical cartography of Earth satellite orbits

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term (120 years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes (400 km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded "ReDSHIFT" project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an "atlas" of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth's oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device.

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arXiv2019

Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable DV cost. We simulated the dynamics over 120-200 years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90deg, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed ~40years, mainly around three specific inclination values: 46deg, 56deg, and 68deg; a result compatible with our understanding of MEO secular dynamics. For DV <= 300 m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with e<0.3), reentry times from GNSS altitudes exceed ~70 years, while low-cost (DV ~= 5-35 m/s) graveyard orbits, stable for at lest 200 years, are found for eccentricities up to e~0.018. This investigation was carried out in the framework of the EC-funded "ReDSHIFT" project.

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arXiv2018

Drift and its mediation in terrestrial orbits

The slow deformation of terrestrial orbits in the medium range, subject to lunisolar resonances, is well approximated by a family of Hamiltonian flow with $2.5$ degree-of-freedom. The action variables of the system may experience chaotic variations and large drift that we may quantify. Using variational chaos indicators, we compute high-resolution portraits of the action space. Such refined meshes allow to reveal the existence of tori and structures filling chaotic regions. Our elaborate computations allow us to isolate precise initial conditions near specific zones of interest and study their asymptotic behaviour in time. Borrowing classical techniques of phase- space visualisation, we highlight how the drift is mediated by the complement of the numerically detected KAM tori.

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