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. We find that this would generally promote the deorbiting process, particularly at the transition region between LEO and MEO. Although direct reentry from very low eccentricities is very unlikely in most cases of interest, we find that a modest ''delta-v" (DV ) budget would be enough for satellites to be steered into a relatively short-lived resonance and achieve reentry into the Earth's atmosphere within reasonable timescales (50 years).

The 2:1 mean-motion resonance with Jupiter harbours two distinct groups of asteroids. The short-lived population is known to be a transient group sustained in steady state by the Yarkovsky semimajor axis drift. The long-lived asteroids, however, can exhibit dynamical lifetimes comparable to 4 Gyr. They reside near two isolated islands of the phase space denoted A and B, with an uneven population ratio B/A ≃ 10. The orbits of A-island asteroids are predominantly highly inclined, compared to island B. The size-frequency distribution is steep but the orbital distribution lacks any evidence of a collisional cluster. These observational constraints are somewhat puzzling and therefore the origin of the long-lived asteroids has not been explained so far.With the aim to provide a viable explanation, we first update the resonant population and revisit its physical properties. Using an N -body model with seven planets and the Yarkovsky effect included, we demonstrate that the dynamical depletion of island A is faster, in comparison with island B. Then we investigate (i) the survivability of primordial resonant asteroids and (ii) capture of the population during planetary migration, following a recently described scenario with an escaping fifth giant planet and a jumping-Jupiter instability. We also model the collisional evolution of the resonant population over past 4 Gyr. Our conclusion is that the long-lived group was created by resonant capture from a narrow part of hypothetical outer main-belt family during planetary migration. Primordial asteroids surviving the migration were probably not numerous enough to substantially contribute to the observed population.

The H2020 ReDSHIFT project aims at finding passive means to mitigate the proliferation of space debris. This goal is pursued by a twofold research activity based on theoretical astrodynamics, computer simulations and the analysis of legal aspects of space debris, coupled with an experimental activity on advanced additive manufacturing (3D printing) applied to the production of a novel small satellite. Several different aspects related to the design and production of a debris compliant spacecraft are treated, including shielding, area augmentation devices for deorbiting (solar and drag sails) and design for demise. A strong testing activity, mainly based on design for demise wind tunnel experiments and hypervelocity impacts is performed as well. The main results obtained so far in the project are outlined.

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.

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 ∆V 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 90 • , 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 ∼ 40 years, mainly around three specific inclination values: 46 • , 56 • , and 68 • ; a result compatible with our understanding of MEO secular dynamics. For ∆V ≤ 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 (∆V 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 * Corresponding author