Search

The impact of formation flying on interferometry is growing over the years for the potential performance it could offer. However, it is still an open field, and many studies are still required. This article presents the basic principles behind interferometry focusing first on a single array and secondly on a formation of satellites. A sensitivity analysis is carried out to evaluate how the performance of the interferometry is affected by an error in the relative position in the formation geometry. This is estimated by computing the loss of the performance in terms of percentage deviation due to a non-nominal relative trajectory, including two-dimensional errors and defining a payload index. The main goal of this study is to estimate whether some errors in the relative state are more impacting than others. The final objective is to compute the link between a position error and a specific loss of performance, to foresee the origin of the the error. Furthermore, a dynamical model is developed to describe the relative motion in the Low Earth Orbit environment, considering both the unperturbed and the J2 and drag contributions. A Proportional, Integral and Derivative controller is implemented for the position control of a multiple satellite formation flying, considering a low thrust control profile. The Formation Flying L-band Aperture Synthesis study is taken as the case scenario, analysing both nominal and non-nominal configurations. This study serves as a starting point for the development of a combined tool to assess the performance of the interferometry and the control on the relative state for future remote sensing studies involving relative motion.

Starting from the Hamiltonian representation of the dynamics in \cite{rosengren2015chaos,colombo2019long}, this work proposes an innovative procedure to design fully-analytical maneuvers for post-mission disposal of HEOs satellites, exploiting the third-body perturbations. The Hamiltonian representation has been selected to include the external perturbing effects and to obtain a phase space representation. Notably, the orbit evolution can be described through the variation of double-averaged orbital elements over the orbital periods of the spacecraft and the perturbing bodies around the central planet. this work conveys a two-dimensional Hamiltonian representation under the third-body perturbations and the central planet's oblateness. The effect of solar radiation pressure has been neglected in this analysis.

Artificial satellites orbiting around the Earth, under certain conditions, result to be visible even to the naked eye. The phenomenon of light pollution jeopardises the researching activities of the astronomical community: traces left by the objects are clear and evident and images for scientific purposes are damaged and deteriorated. The development of a mathematical model able to estimate the satellite's brightness is required and it represents a first step to catch all the aspects of the reflection phenomenon. The brightness model (by Politecnico di Milano) will be exploited to implement a realistic simulation of the apparent magnitude evolution and it could be used to develop an archetype of new-generation spacecraft at low light-pollution impact. Starting from classical photometry theory, which provides the expressions of radiant flux density of natural spherical bodies, the global laws describing flux densities and the associated apparent magnitude are exploited to generalise the analysis. The study is finally focused on three-dimensional objects of whatever shape which can be the best representation of the spacecraft geometry. To obtain representative results of the satellite brightness, a validation process has been carried on. The observation data of OneWeb satellites have been collected by GAL Hassin astronomical observatory, settled in Isnello, near Palermo. The observations were carried out in order to map the satellites brightness at various illumination conditions, also targeting a single satellite across its different positions on the sky (i.e., during its rise, culmination and setting)., Comment: In Press on AISR

Neglecting small fragments in space debris evolutionary models can lead to a significant underestimation of the collision risk for operational satellites. However, when scaling down to the millimeter range, the debris population grows to over one million objects, making deterministic approaches too computationally expensive. On the contrary, probabilistic models provide a more efficient alternative, which however typically work under some simplifying assumptions on the dynamics, limiting their field of applicability. This work proposes an extension of the density-based collision risk models to any orbital dynamics and impact geometry. The impact rate with a target satellite is derived from a multi-dimensional phase space density function in Keplerian elements, which discretely varies over both phase space and time. The assumption of a bin-wise constant cloud density allows for the analytical transformation of the six-dimensional distribution in orbital elements into the three-dimensional spatial density function, guaranteeing an efficient and accurate evaluation of the fragments flux. The proposed method is applied to the assessment of the collision risk posed by real fragmentation clouds in different orbital regions on a high-risk target object. The effect on the impact rate of the additional model features, compared to previous probabilistic formulations, is discussed.

The continuously growing number of objects orbiting around the Earth is expected to be accompanied by an increasing frequency of objects re-entering the Earth's atmosphere. Many of these re-entries will be uncontrolled, making their prediction challenging and subject to several uncertainties. Traditionally, re-entry predictions are based on the propagation of the object's dynamics using state-of-the-art modelling techniques for the forces acting on the object. However, modelling errors, particularly related to the prediction of atmospheric drag may result in poor prediction accuracies. In this context, we explore the possibility to perform a paradigm shift, from a physics-based approach to a data-driven approach. To this aim, we present the development of a deep learning model for the re-entry prediction of uncontrolled objects in Low Earth Orbit (LEO). The model is based on a modified version of the Sequence-to-Sequence architecture and is trained on the average altitude profile as derived from a set of Two-Line Element (TLE) data of over 400 bodies. The novelty of the work consists in introducing in the deep learning model, alongside the average altitude, three new input features: a drag-like coefficient (B*), the average solar index, and the area-to-mass ratio of the object. The developed model is tested on a set of objects studied in the Inter-Agency Space Debris Coordination Committee (IADC) campaigns. The results show that the best performances are obtained on bodies characterised by the same drag-like coefficient and eccentricity distribution as the training set.

This work presents the model of an ejecta cloud distribution to characterise the plume generated by the impact of a projectile onto asteroids surfaces. A continuum distribution based on the combination of probability density functions is developed to describe the size, ejection speed, and ejection angles of the fragments. The ejecta distribution is used to statistically analyse the fate of the ejecta. By combining the ejecta distribution with a space-filling sampling technique, we draw samples from the distribution and assigned them a number of \emph{representative fragments} so that the evolution in time of a single sample is representative of an ensemble of fragments. Using this methodology, we analyse the fate of the ejecta as a function of different modelling techniques and assumptions. We evaluate the effect of different types of distributions, ejection speed models, coefficients, etc. The results show that some modelling assumptions are more influential than others and, in some cases, they influence different aspects of the ejecta evolution such as the share of impacting and escaping fragments or the distribution of impacting fragments on the asteroid surface.

The orbital propagation of large sets of initial conditions under high accuracy requirements is currently a bottleneck in the development of space missions, e.g. for planetary protection compliance analyses. The proposed approach can include any force source in the dynamical model through efficient Picard-Chebyshev (PC) numerical simulations. A two-level augmentation of the integration scheme is proposed, to run an arbitrary number of simulations within the same algorithm call, fully exploiting high performance and GPU (Graphics Processing Units) computing facilities. The performances obtained with implementation in C and NVIDIA CUDA programming languages are shown, on a test case taken from the optimization of a Solar Orbiter-like first resonant phase with Venus.

This work presents a mission concept for in-orbit particle collection for sampling and exploration missions towards Near-Earth asteroids. Ejecta is generated via a small kinetic impactor and two possible collection strategies are investigated: collecting the particle along the anti-solar direction, exploiting the dynamical features of the L$_2$ Lagrangian point or collecting them while the spacecraft orbits the asteroid and before they re-impact onto the asteroid surface. Combining the dynamics of the particles in the Circular Restricted Three-Body Problem perturbed by Solar Radiation Pressure with models for the ejecta generation, we identify possible target asteroids as a function of their physical properties, by evaluating the potential for particle collection.

A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a torsion. When this reduction process is applied to unbounded orbits the solution is made of Keplerian hyperbolae. For this last case, we show that the torsion-based solution provides an effective alternative to the Keplerian approximation customarily used in flyby computations. Also, we check that the extension of the torsion-based solution to higher orders of the oblateness coefficient yields the expected convergence of asymptotic solutions to the true orbit., Comment: 10 pages, 7, figures, submitted to Nonlinear Dynamics

Like any industry, space activities generate pressures on the environment and strives towards more sustainable activities. A consensus among the European industrial stakeholders and national agencies in the Space sector is emerging on the need to address eco-design through the prism of the environmental Life Cycle Assessment (LCA) methodology. While the use of LCA is being implemented within the sector, the current scope disregards the potential environmental impact in term of debris generated by space missions on the orbital environment. The paper highlights the relevance of applying LCA holistically during the design phase of space systems, considering potential impacts occurring in the orbital environment during the utilisation and disposal stages of a space mission. Based on the comparison of two mission designs, the aim is to consider potential emission of space debris into the LCA framework as a way of measuring the resource security for orbits and potential environmental impacts occurring in case of collision.

This paper presents an analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations. Considering the first to be subjected to a continuous tangential acceleration, its spiraling motion would result in a series of close approaches in the proximity of a constellation. The proposed methodology involves the integration of the collision probability density function on the encounter plane, from which two analytical formulas, one for the number of close approaches and one for their respective average collision probability, are obtained. The mathematical description of the crossing dynamics relies on the assumption of circular orbits and independent collision probabilities, but does not require to propagate the satellites' orbit. A comparison with a conventional propagation method has been performed for validation purposes, proving its accuracy also in case of elliptical crossing orbits. The model developed has been used to assess the risk connected to constellation's satellites replacement, once they have reached their programmed End-of-Life. The environmental impact of the full replacement of 12 approved constellations is analysed by means of average collision probability. In particular, it is shown that the key features for space exploitation sustainability are the maximum propulsion available from the thruster, the selection of an optimal crossing orbit and the true anomaly phases between constellations' and crossing satellites. The consequences of an in-orbit collision are also investigated by assessing the collision risk generated by the formation of a debris cloud. The results corroborate the need for international standards for space traffic management as an exponentially increasing satellites population could trigger a chain reaction of collisions, making LEO inaccessible for decades., Comment: 17 pages, 18 figures, Preprint

This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite long-term propagation. The density evolution equation, a pure numerical and pointwise method for the density propagation, is formulated under the influence of solar radiation pressure and Earth's oblateness using semi-analytical methods. Different from the density evolution equation and Monte Carlo techniques, for the Gaussian mixture model, the analytical calculation of the density is accessible from the first two statistical moments (i.e., the mean and the covariance matrix) corresponding to each sub-Gaussian distribution for an initial Gaussian density distribution. An insight is given into the phase space long-term density propagation problem subject to nonlinear dynamics. The efficiency and validity of the density propagation are demonstrated and compared between the density evolution equation and the Gaussian mixture model with respect to standard Monte Carlo techniques.

In recent years, due to the constant increase of the density of satellites in the space environment, several studies have been focused on the development of active and passive strategies to remove and mitigate space debris. This work investigates the feasibility of developing a reliable and fast approach to analyze the re-entry of a satellite. The numerical model interfaces the long-term orbit propagation obtained through semi-analytical methods with the atmospheric destructive re-entry phase exploiting the concept of overshoot boundary, highlighting the effect that an early break-off of the solar panels can have on the re-entry prediction. The re-entry of ESA's INTEGRAL mission is chosen as a test case to demonstrate the efficiency of the model in producing a complete simulation of the re-entry. The simulation of the destructive re-entry phase is produced using an object-oriented approach, paying attention to the demisability process of the most critical components of the space system., Comment: 10 pages, 9 figures, pre-proof of accepted article in Journal of Space Safety Engineering

This paper presents a strategy for optimal manoeuvre design of multi-satellite formation flying in low Earth orbit environment, with the aim of providing a tool for mission operation design. The proposed methodology for formation flying manoeuvres foresees a continuous low-thrust control profile, to enable the operational phases. The design is performed starting from the dynamic representation described in the relative orbital elements, including the main orbital perturbations effects. It also exploits an interface with the classical radial-transversal-normal description to include the maximum delta-v limitation and the safety condition requirements. The methodology is applied to a remote sensing mission study, Formation Flying L-band Aperture Synthesis, for land and ocean application, such as a potential high-resolution Soil Moisture and Ocean Salinity (SMOS) follow-on mission, as part of a European Space Agency mission concept study. Moreover, the results are applicable to a wide range of low Earth orbit missions, exploiting a distributed system, and in particular to Formation Flying L-band Aperture Synthesis (FFLAS) as a follow-on concept to SMOS., Comment: 19 pages

The paper presents a re-entry analysis of Geosynchronous Orbit (GSO) satellites on disposal trajectories that enhance the effects of the Earth oblateness and lunisolar perturbations. These types of trajectories can lead to a natural re-entry of the spacecraft within 20 years. An analysis was performed to characterise the entry conditions for these satellites and the risk they can pose for people on the ground if disposal via re-entry is used. The paper first proposes a methodology to interface the long-term propagation used to study the evolution of the disposal trajectories and the destructive re-entry simulations used to assess the spacecraft casualty risk. This is achieved by revisiting the concept of overshoot boundary. The paper also presents the demisability and casualty risk analysis for a representative spacecraft configuration, showing that the casualty risk is greater than the 10$^{-4}$ threshold and that further actions should be taken to improve the compliance of these satellites in case of disposal via re-entry is used.

Everyday thousands of meteoroids enter the Earth's atmosphere. The vast majority burn up harmlessly during the descent, but the larger objects survive, occasionally experiencing intense fragmentation events, and reach the ground. These events can pose a threat for a village or a small city; therefore, models of asteroid fragmentation, along with accurate post-breakup trajectory and strewn field estimation, are needed to enable a reliable risk assessment. In this work, a methodology to describe meteoroids entry, fragmentation, descent, and strewn field is presented by means of a continuum approach. At breakup, a modified version of the NASA Standard Breakup Model is used to generate the distribution of the fragments in terms of their area-to-mass ratio and ejection velocity. This distribution, combined with the meteoroid state, is directly propagated using the continuity equation coupled with the non-linear entry dynamics. At each time step, the probability density evolution of the fragments is reconstructed using GMM interpolation. Using this information is then possible to estimate the meteoroid's ground impact probability. This approach departs from the current state-of-the-art models: it has the flexibility to include large fragmentation events while maintaining a continuum formulation for a better physical representation of the phenomenon. The methodology is also characterised by a modular structure, so that updated asteroids fragmentation models can be readily integrated into the framework, allowing a continuously improving prediction of re-entry and fragmentation events. The propagation of the fragments' density and its reconstruction, currently considering only one fragmentation point, is first compared against Monte Carlo simulations, and then against real observations. Both deceleration due to atmospheric drag and ablation due to aerothermodynamics effects have been considered., Comment: 29 pages, 26 figures, published in Icarus

This work proposes a continuum-based approach for the propagation of uncertainties in the initial conditions and parameters for the analysis and prediction of spacecraft re-entries. Using the continuity equation together with the re-entry dynamics, the joint probability distribution of the uncertainties is propagated in time for specific sampled points. At each time instant, the joint probability distribution function is then reconstructed from the scattered data using a gradient-enhanced linear interpolation based on a simplicial representation of the state space. Uncertainties in the initial conditions at re-entry and in the ballistic coefficient for three representative test cases are considered: a three-state and a six-state steep Earth re-entry and a six-state unguided lifting entry at Mars. The paper shows the comparison of the proposed method with Monte Carlo based techniques in terms of quality of the obtained marginal distributions and runtime as a function of the number of samples used.

In the past few years, the interest towards the implementation of design-for-demise measures has increased steadily. Most mid-sized satellites currently launched and already in orbit fail to comply with the casualty risk threshold of 0.0001. Therefore, satellites manufacturers and mission operators need to perform a disposal through a controlled re-entry, which has a higher cost and increased complexity. Through the design-for-demise paradigm, this additional cost and complexity can be removed as the spacecraft is directly compliant with the casualty risk regulations. However, building a spacecraft such that most of its parts will demise may lead to designs that are more vulnerable to space debris impacts, thus compromising the reliability of the mission. In fact, the requirements connected to the demisability and the survivability are in general competing. Given this competing nature, trade-off solutions can be found, which favour the implementation of design-for-demise measures while still maintaining the spacecraft resilient to space debris impacts. A multi-objective optimisation framework has been developed by the authors in previous works. The framework's objective is to find preliminary design solutions considering the competing nature of the demisability and the survivability of a spacecraft since the early stages of the mission design. In this way, a more integrated design can be achieved. The present work focuses on the improvement of the multi-objective optimisation framework by including constraints. The paper shows the application of the constrained optimisation to two relevant examples: the optimisation of a tank assembly and the optimisation of a typical satellite configuration., Comment: Pre-print submitted to the Journal of Space Safety Engineering

An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss' planetary equations and relative motion equations are used to map maneuvers at a given time to displacements at the predicted close approach. The model is then extended to map changes in state between two times, allowing one to propagate covariance matrices. The analytical formulation reduces the optimization problem to an eigenproblem, both for maximum deviation and minimum collision probability. Two maximum deviation cases, total deviation and impact parameter, are compared for a large set of spacecraft-debris conjunction geometries derived from European Space Agency's Meteoroid and Space Debris Terrestrial Environment Reference (MASTER-2009) model. Moreover, the maximum impact parameter and minimum collision probability maneuvers are compared assuming covariances known at the maneuver time, to evaluate the net effect of lead time in collision probability. In all cases, solutions are analyzed in the b-plane to leverage its natural separation of phasing and geometry change effects. Both uncertainties and maximum deviation grow along the time axis for long lead times, limiting the reduction in collision probability., Comment: 44 pages, 24 figures. Author's accepted manuscript for a paper published in Journal of Guidance, Control, and Dynamics

The core aspects and latest developments of Manoeuvre Intelligence for Space Safety (MISS), a new software tool for collision avoidance analysis and design, are presented. The tool leverages analytical and semi-analytical methods for the efficient modelling of the orbit modifications due to different control strategies, such as impulsive or low-thrust manoeuvres, and maps them into displacements at the nominal close approach using relative motion equations. B-plane representations are then used to separate the phasing-related and geometry-related components of the displacement. Both maximum miss distance and minimum collision probability collision avoidance manoeuvres are considered. The tool also allows for the computation of state transition matrices and propagation of uncertainties. Several test cases are provided to assess the capabilities and performance of the tool., Comment: 11 pages, 7 figures. Preprint of article published in Journal of Space Safety Engineering

This paper presents a system-level engineering approach for the preliminary coverage performance analysis and the design of a generic Global Navigation Satellite System (GNSS) constellation. This analysis accounts for both the coverage requirements and the robustness to transient or catastrophic failures of the constellation. The European GNSS, Galileo, is used as reference case to prove the effectiveness of the proposed tool. This software suite, named GNSS Coverage Analysis Tool (G-CAT), requires as input the state vector of each satellite of the constellation and provides the performance of the GNSS constellation in terms of coverage. The tool offers an orbit propagator, an attitude propagator, an algorithm to identify the visibility region on the Earth's surface from each satellite, and a counter function to compute how many satellites are in view from given locations on the Earth's surface. Thanks to its low computational burden, the tool can be adopted to compute the optimal number of satellites per each orbital plane by verifying if the coverage and accuracy requirements are fulfilled under the assumption of uniform in-plane angular spacing between coplanar satellites., Comment: 19 pages, 21 figures

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.

The space environment around the Earth is populated by more than 130 million objects of 1 mm in size and larger, and future predictions shows that this amount is destined to increase, even if mitigation measures are implemented at a far better rate than today. These objects can hit and damage a spacecraft or its components. It is thus necessary to assess the risk level for a satellite during its mission lifetime. Few software packages perform this analysis, and most of them employ time-consuming ray-tracing methodology, where particles are randomly sampled from relevant distributions. In addition, they tend not to consider the risk associated with the secondary debris clouds. The paper presents the development of a vulnerability assessment model, which relies on a fully statistical procedure: the debris fluxes are directly used combining them with the concept of the vulnerable zone, avoiding the random sampling the debris fluxes. A novel methodology is presented to predict damage to internal components. It models the interaction between the components and the secondary debris cloud through basic geometric operations, considering mutual shielding and shadowing between internal components. The methodologies are tested against state-of-the-art software for relevant test cases, comparing results on external structures and internal components., Comment: Article accepted for pubblication in Advances in Space Research

Among the mitigation measures introduced to cope with the space debris issue there is the de-orbiting of decommissioned satellites. Guidelines for re-entering objects call for a ground casualty risk no higher than 0.0001. To comply with this requirement, satellites can be designed through a design-for-demise philosophy. Still, a spacecraft designed to demise has to survive the debris-populated space environment for many years. The demisability and the survivability of a satellite can both be influenced by a set of common design choices such as the material selection, the geometry definition, and the position of the components. Within this context, two models have been developed to analyse the demise and the survivability of satellites. Given the competing nature of the demisability and the survivability, a multi-objective optimisation framework was developed, with the aim to identify trade-off solutions for the preliminary design of satellites. As the problem is nonlinear and involves the combination of continuous and discrete variables, classical derivative based approaches are unsuited and a genetic algorithm was selected instead. The genetic algorithm uses the developed demisability and survivability criteria as the fitness functions of the multi-objective algorithm. The paper presents a test case, which considers the preliminary optimisation of tanks in terms of material, geometry, location, and number of tanks for a representative Earth observation mission. The configuration of the external structure of the spacecraft is fixed. Tanks were selected because they are sensitive to both design requirements: they represent critical components in the demise process and impact damage can cause the loss of the mission because of leaking and ruptures. The results present the possible trade off solutions, constituting the Pareto front obtained from the multi-objective optimisation., Comment: Paper accepted for publication in Aerospace Science and Technology

The paper is concerned with examining the effects that design-for-demise solutions can have not only on the demisability of components, but also on their survivability that is their capability to withstand impacts from space debris. First two models are introduced. A demisability model to predict the behaviour of spacecraft components during the atmospheric re-entry and a survivability model to assess the vulnerability of spacecraft structures against space debris impacts. Two indices that evaluate the level of demisability and survivability are also proposed. The two models are then used to study the sensitivity of the demisability and of the survivability indices as a function of typical design-for-demise options. The demisability and the survivability can in fact be influenced by the same design parameters in a competing fashion that is while the demisability is improved, the survivability is worsened and vice versa. The analysis shows how the design-for-demise solutions influence the demisability and the survivability independently. In addition, the effect that a solution has simultaneously on the two criteria is assessed. Results shows which, among the design-for-demise parameters mostly influence the demisability and the survivability. For such design parameters maps are presented, describing their influence on the demisability and survivability indices. These maps represent a useful tool to quickly assess the level of demisability and survivability that can be expected from a component, when specific design parameters are changed., Comment: Accepted for publication in Acta Astronautica

This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the initial uncertainty region in different ways, with the result of either providing a more accurate estimate of the impact probability or reducing the number of required samples during the simulation with respect to standard MC techniques. The two methods are first described and then applied to some test cases, providing evidence of the increased accuracy or the reduced computational burden with respect to a standard MC simulation. Finally, a sensitivity analysis is carried out to show how parameter setting affects the accuracy of the results and the numerical efficiency of the two methods.

In this paper the planar orbit and attitude dynamics of an uncontrolled spacecraft is studied, taking on-board a deorbiting device. Solar and drag sails with the same shape are considered and separately studied. In both cases, these devices are assumed to have a simplified pyramidal shape that endows the spacecraft with helio and drag stable properties. The translational dynamics is assumed to be planar and hence the rotational dynamics occurs only around one of the principal axes of the spacecraft. Stable or slowly-varying attitudes are studied, subject to disturbances due to the Earth oblateness effect and gravity gradient torques, and either solar radiation pressure or atmospheric drag torque and acceleration. The results are analysed with respect to the aperture of the sail and the center of mass - center of pressure offset., Comment: 28 pages, 31 figures

This paper introduces a new analytical method for the determination of the coverage area modeling the Earth as an oblate ellipsoid of rotation. Starting from the knowledge of the satellite's position vector and the direction of the navigation antenna line of sight, the surface generated by the intersection of the oblate ellipsoid and the assumed conical field of view is decomposed in many ellipses, obtained by cutting the Earth's surface with every plane containing the navigation antenna line of sight. The geometrical parameters of each ellipse can be derived analytically together with the points intersection of the conical field of view with the ellipse itself by assuming a proper value of the half-aperture angle or the minimum elevation angle from which the satellite can be considered visible from the Earth's surface. The method can be applied for different types of pointing (geocentric, geodetic and generic) according to the mission requirements. Finally, numerical simulations compare the classical spherical approach with the new ellipsoidal method in the determination of the coverage area, and also show the dependence of the coverage errors on some relevant orbital parameters., Comment: 32 pages, 16 figures, 5 tables, 21 references. Post-print version of the article published on the Journal of Guidance, Control, and Dynamics

Numerical integration of orbit trajectories for a large number of initial conditions and for long time spans is computationally expensive. Semi-analytical methods were developed to reduce the computational burden. An elegant and widely used method of semi-analytically integrating trajectories of objects subject to atmospheric drag was proposed by King-Hele (KH). However, the analytical KH contraction method relies on the assumption that the atmosphere density decays strictly exponentially with altitude. If the actual density profile does not satisfy the assumption of a fixed scale height, as is the case for Earth's atmosphere, the KH method introduces potentially large errors for non-circular orbit configurations. In this work, the KH method is extended to account for such errors by using a newly introduced atmosphere model derivative. By superimposing exponentially decaying partial atmospheres, the superimposed KH method can be applied accurately while considering more complex density profiles. The KH method is further refined by deriving higher order terms during the series expansion. A variable boundary condition to choose the appropriate eccentricity regime, based on the series truncation errors, is introduced. The accuracy of the extended analytical contraction method is shown to be comparable to numerical Gauss-Legendre quadrature. Propagation using the proposed method compares well against non-averaged integration of the dynamics, while the computational load remains very low., Comment: Post-print version of 13 February 2019

In this work the orbital dynamics of Earth satellites about the geosynchronous altitude are explored, with primary goal to assess current mitigation guidelines as well as to discuss the future exploitation of the region. A thorough dynamical mapping was conducted in a high-definition grid of orbital elements, enabled by a fast and accurate semi-analytical propagator, which considers all the relevant perturbations. The results are presented in appropriately selected stability maps to highlight the underlying mechanisms and their interplay, that can lead to stable graveyard orbits or fast re-entry pathways. The natural separation of the long-term evolution between equatorial and inclined satellites is discussed in terms of post-mission disposal strategies. Moreover, we confirm the existence of an effective cleansing mechanism for inclined geosynchronous satellites and discuss its implications in terms of current guidelines as well as alternative mission designs that could lead to a sustainable use of the geosynchronous orbital region., Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronomy