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The primary objective of this paper is to construct an analytical model for determining the total duration of eclipse events of satellites. The approach is based on the assumption that the trace formed in the orbital plane, cutting body's shadow under the classical conical shadow model, can be described as an ellipse. This allows for the derivation of its parameters through the use of classical orbital elements and solar position in the body's centric frame. Consequently, the problem of identifying satellite occultation events is simplified to searching for points of intersection between two ellipses: the satellite orbit and the shadow. The developed model has been demonstrated to be applicable for a wide range of inclinations, with the exception of cases where the orbital plane of the satellite's motion coincides with that of the sun's in the body-centric frame. It is shown that the shadow function constructed under the aforementioned assumptions can be simplified in the cylindrical shadow model. Several simplifications are provided in the research. The paper also considers the extension of the model to account for the non-spherical shape of celestial bodies and presents an algorithm for accounting for changes in eclipse duration caused by the heliocentric motion of celestial bodies. The model has been validated through numerous tests with a numerical algorithm and satellite real data, as well as with other analytical models. • An analytical method for calculating the total duration of satellite eclipses has been developed. • Developed approach can be applied to wide range of satellite orbits either hyperbolical or elliptical ones. • The equations that depend on the satellite's orbital elements and solar longitude to predict satellite eclipses are obtained. • Simplification of the problem in certain scenarios, allowing for rigorous and simple algebraic solutions are provided. [ABSTRACT FROM AUTHOR]

The regional coverage satellite constellations are in demand for fulfilling earth observation needs of specific user regions of interest as opposed to global coverage thus enhancing the revisit period for the area. In this paper, we present a few key mission aspects of the regional coverage constellation designed and operated by the Indian Space Research Organization (ISRO) in low earth orbit. ISRO developed three X-Band Synthetic Aperture Radar (SAR) Earth Observation satellites and placed them in three inclined orbit planes to enhance the Indian region's coverage. This is India's first inclined orbit constellation designed for remote sensing applications in low earth orbit. The satellites were built around a standard bus carrying a Synthetic Aperture Radar payload with a deployable Radial Rib Antenna (RRA). They were designed to achieve a high agility capability. As SAR sensors are capable of all-weather, day, and night imaging; thus, most suitable in inclined orbits where the illumination conditions vary continuously for imaging. Though the inclined orbits provide more revisit opportunities to the region of interest, their characteristics pose challenges in mission design and operations. Though the mission design and planning involved a host of elements, this paper brings out the details of a few key mission analysis elements, planning aspects and operations that were critical in the course of various mission phases. The mission analysis included mission-specific requirements like launch windows selection for the constellation and reference attitude generation specific to inclined orbit geometry. Mission planning had to take care of Radial Rib Antenna (RRA) deployment requirements which were very critical for the mission, apart from taking care of individual subsystem requirements. The SAR payload data product quality and targeting accuracy are very sensitive to the satellite image point range (vis-a-vis SAR operation data window). Extensive post-launch calibration activity was carried out to meet all these mission requirements and data product specifications. The challenge was in fixing the payload beam alignment and fixing the uncertainties in onboard and ground computations. The paper also describes the methods of fixing all possible error sources affecting the high-resolution SAR payload performance. • The regional coverage satellite constellations are in demand for area targets coverage. • Inclined orbit constellations are more suitable for regional coverage using SAR sensors. • Mission operations plans need to consider all the specific requirements of spacecraft systems. • Pre-launch and post -launch calibrations of sensors is mandatory for achieving system performance. [ABSTRACT FROM AUTHOR]

This paper examines the effect of shortening the post-mission disposal (PMD) orbit lifetime (remaining orbit lifetime after PMD) from 25 years to 5 or 1 year. Using NEODEEM, the debris evolutionary model developed by Kyushu University and JAXA, the change in the orbital environment at various altitude bands for long-term stability and short-term safety are discussed. It was confirmed that the PMD compliance rate is more important than shortening the orbit lifetime for improving the long-term stability of the orbital environment. In the short term, the 5- or 1-year rule reduced the collision rate and collision avoidance frequency at an altitude below 700 km, more than the 25-year rule, thus shortening the PMD orbit lifetime improves short-term safety, especially at low altitudes. The paper also evaluates the effect of large constellations (LCs) and it was shown that shortening the PMD orbit lifetime of LCs improves short-term safety, but the long-term impact is dominated by the number of LCs that remain at high operational altitudes due to PMD failure. It shows that the post-mission disposal lifetime and required compliance rate should be set according to the number and size of objects expected to be launched in the future. • The effect of shortening post-mission-disposal lifetime from 25 years are shown. • Short-term safety can be improved by 5-year rule or 1-year rule. • PMD compliance rate is more important for the long-term stability. • Difference between an elliptical and a circular orbit for PMD is shown. • PMD requirement changed according to the characteristics of the large constellation. [ABSTRACT FROM AUTHOR]

Low-thrust trajectory design in the context of the three-body problem, particularly in the vicinity of liberation points, is addressed in this paper with a focus on efficiency and accuracy. The Fourier series, previously successful in approximating near-coplanar low-thrust trajectories within two-body dynamics, is applied to the challenging landscape of the three-body problem, marked by instability and nonlinearity. This paper introduces a novel approach for constructing an initial guess trajectory, that combines coast arcs from periodic orbits and intermediate trajectory arcs from other natural dynamical structures. The resulting initial guess trajectory is instrumental in generating efficient initial estimates for the coefficients of the Fourier series. The study encompasses the analysis of homoclinic and heteroclinic transfers in both two-dimensional and three-dimensional scenarios. The approximated trajectories derived from this methodology serve as invaluable starting points for high-fidelity optimization solvers, offering promise for enhancing the precision and efficiency of low-thrust transfers in cislunar space. • The shape method based on Fourier series is applied to the initial design of the transfer trajectories between periodic orbits in cislunar space. • An innovative approach to construct a continuous initial guess trajectory is introduced to derive initial guess values for the coefficients of Fourier terms. • An accurate approximation of the optimal transfer trajectory can be rapidly obtained. [ABSTRACT FROM AUTHOR]

Comet Interceptor (Comet-I) was selected in June 2019 as the first ESA F-Class mission and aims to explore a pristine comet, which will visit the inner Solar System for the first time. Comet-I will hitch a ride to a Sun-Earth L2 quasi-halo orbit, as a co-passenger in ESA's M4 ARIEL's launch. At the time of writing, this is scheduled for 2029. It will then remain there awaiting the right departure conditions to leave definitively and intercept a newly discovered comet. Comet-I will be the first mission to be designed and launched without an already identified target. Given the latter, the Comet-I Target Identification Working Group is tasked with the continuous follow-up of newly discovered comets, to analyse their characteristics as virtual targets for Comet-I. The goal of the paper is to inform the decision-making process that will eventually be necessary to commit Comet-I spacecraft to its final target. Within this context, this paper presents a trajectory optimization process based on Primer Vector theory that considers intercept trajectories with multiple revolutions and multiple deep space manoeuvres (DSM). The process is applied to 21 long period comets, which were discovered since July 1, 2020 and whose characteristics are of interest for the Comet-I mission. In fact, one of the latest of these recently discovered comets, C/2023H2, is the most accessible virtual target discovered at the time of writing, with delta-V intercept costs well within Comet-I capabilities. A complete launch window analysis is thus presented for C/2023H2, which accounts not only for the most optimal delta-V intercept transfer, but also considers all launch options that satisfy all Comet-I's current boundary conditions and flyby constraints. A systematic launch window analysis is made possible by a grid search approach on which departure and fly-by dates are fixed and the remaining design variables, including the times for manoeuvres and their Δ v impulse vector, are optimized via Primer Vector theory. This allows to understand the latest possible departure date, but also the sensitivity to departure and arrival dates of key encounter characteristics such as relative fly-by speed, the solar aspect angle and the Earth distance. • A Primer Vector Theory-based trajectory optimization tool is shown, tailored for ESA's Comet Interceptor (Comet-I). • The method supports trajectories with multiple revolutions around the Sun and multiple impulses. • The method allows rapid grid search over the search space, finding the lowest cost trajectory and other notable solutions. • A novel analysis of the launch window is presented, contributing to the decision-making process of Comet-I. • A multi-manoeuvre strategy benefits Comet-I's trajectory design, lowering the delta-V cost and improving mission flexibility. [ABSTRACT FROM AUTHOR]

This paper analyzes the change in the heliocentric orbital elements due to the implementation of aerogravity and powered aerogravity assist maneuvers. Three cost functions were selected to maximize the planetocentric latitude, longitude, and velocity at the end of the atmospheric flight. An optimal control problem was solved to guide a spaceplane passing above the three inner planets: Venus, Earth, and Mars. The planets were selected because they have been relevant for gravity assists, and previous studies suggest that taking advantage of their atmospheres could increase the effects of the close approach. The research aims to analyze the variation in the heliocentric orbital elements of the trajectories after performing optimal aerogravity-assists and powered aerogravity-assisted maneuvers at high atmospheric altitudes. The trajectories were calculated via nonlinear programming to find the history of the control variables: angle of attack, bank angle, and thrust. Low-fidelity gravity and atmosphere models were implemented to evaluate this proof of concept. The optimization converged for all cases, and results show that maximization of the longitude increases the duration of the atmospheric flight, increasing the turning angle by almost twice the value of a single gravity assist. Furthermore, it reduces the energy and semimajor axis in half for approach angles between 20 and 90°, saving more than 10 km/s on propulsion. Maximizing the velocity with propulsion increases the semimajor axis by more than 1.1 times the semimajor axis of the respective planet, and the optimal latitude presents a change in inclination of more than 1.0°. This maneuver could be applied to collect atmospheric samples or increase the coverage above the planet of interest. Those kinds of applications are described at the end of this paper, including a brief discussion on the maturity of this technology. • Optimal control in aerogravity assists maneuvers at high atmospheric altitudes. • The maneuvers increase the values of the heliocentric orbital elements. • Multiple advantages over the gravity assist are observed. • Spaceplanes are feasible for performing those maneuvers. • Atmospheric passages at high altitudes reduce the risks associated with low altitudes. [ABSTRACT FROM AUTHOR]

Laser inter-satellite links (LISLs) are crucial for enabling rapid information exchange within low earth orbit (LEO) constellations. Previous research on laser link establishment often relied on the idealized probability density function (PDF) of the pointing uncertainty regions (PURs) when designing scan-and-capture methods, neglecting the impact of various practical uncertainties. To address the above issues, there is an urgent need to analyze the practical uncertainties to enhance the stability and reliability of LISL. This paper first provides a comprehensive introduction to the alignment process in LISL and mathematically formulates typical sources of uncertainty errors. Subsequently, a generalized system model (GSM) for laser link establishment was established at three stages: Orbit, Attitude, and Laser terminal. Finally, we integrate uncertainty models into the GSM and propose a PUR generating method to obtain precise PDFs. The research method proposed in this study can consider the influence of multiple uncertainties and generate the PDF for the PURs. Compared with traditional research, the PDF obtained by fitting the oscillation range considering dynamics is more detailed. By analyzing the PDF generated by typical uncertainty errors, it is observed that the orbit initial uncertainty may be the predominant factor influencing the PUR. • A generalized system model for the laser alignment process is established. • A method to generate the model for the pointing uncertainty region is proposed. • Envelope curve is used to describe the oscillation range for deviation samples. • The impact of different uncertainty errors on the uncertainty region is explored. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimizing minimum-time and minimum-propellant many-revolution low-thrust geocentric orbit-raising maneuvers to an arbitrary target. The proposed direct single-shooting technique utilizes the regularized h , e element set as well as analytical models for ephemeris, shadow geometry, and thrust magnitude for ease of the optimization procedure. Third body and J 2 effects are included for higher fidelity of the computed solution. The gradient information supplied through adjoint sensitivities facilitates the convergence of the numerical optimization scheme. We also propose a new automated, fast and robust initial guess generation methodology by solving a sequence of unconstrained optimization orbit-raising sub-problems. The performance of the developed algorithm is demonstrated for orbit-raising to a variety of targets: the geosynchronous equatorial orbit, the Molniya orbit, and a near-rectilinear halo orbit. • A new low-thrust trajectory algorithm is developed using adjoint sensitivities. • The sequentially generated initial guesses are fast and robust to calculate. • An end-to-end optimization formulation computes minimum-time and minimum-fuel transfers. [ABSTRACT FROM AUTHOR]

Satellite formation plays an important role in space missions such as on-orbit services and distributed space facilities. In these missions, hovering in a bounded range is one of the core tasks, but hovering technologies for the chief satellite in an elliptical orbit have been rarely investigated. Given the boundary constraints of relative motion between the chief and deputy satellites, this paper proposes two models for the design and control of hovering formation near an elliptical reference orbit through impulse: (1) the revisiting hovering formation model, which forces the deputy satellite to revisit the same relative position and maintains the formation via impulses; (2) the sequential-impulse-control hovering formation model, which uses a sequence of impulses to ensure the deputy satellite flies within the given boundary. Unlike the revisiting hovering formation model, this model does not require a fixed revisiting point, so the satellite's trajectory is more flexible. The geometrical properties, formation maintenance strategy, and impulse-control solution for both models are investigated in detail. Finally, numerical simulations are conducted to verify the advantages of the proposed methods over other conventional methods, suggesting their wide applications in practical space missions. • Two impulsive-control models are proposed for bounded hovering formation in elliptical orbit. • The proposed methods support in-plane, out-of-plane, and three-dimension hovering formations. • The in-plane and out-of-plane controls are decoupled to decrease control complexity and difficulty. • Different factors on the fuel cost are analyzed to provide a reference for practical engineering. [ABSTRACT FROM AUTHOR]

Lunisolar resonances shape the dynamics in the MEO region and have the effect of increasing an object's eccentricity possibly up to a value so high that the orbit's perigee reaches the atmosphere and friction determines the re-entry. The focus of this paper is the eccentricity growth phenomenon observed for navigation satellites. In particular, starting from a secular Hamiltonian model, analytical estimates for the maximum eccentricity reachable along an inclination-only dependent lunisolar resonance are derived as a function of the initial inclination. Also, trajectories that minimize an object's lifetime are studied, and analytical estimates for such a minimum lifetime are provided as a function of the initial eccentricity of the object. In addition, lifetime cartography maps are presented in the plane of the argument of perigee and the longitude of the ascending node. • Analytical estimates for the maximum eccentricity along lunisolar resonances. • Analytic formulae of minimum satellite lifetime at GPS and Galileo altitudes. • Litetime maps at GPS and Galileo altitudes in (ω)-(Ω) plane. [ABSTRACT FROM AUTHOR]

This paper presents dynamics and control of orbits around an asteroid that is modelled as a uniformly rotating homogeneous rectangular parallelepiped (HRP). Aside from the non-uniform gravitational field of the asteroid, we include the solar radiation pressure (SRP) as a perturbing force. A simple model based on the polyhedral method is employed for calculating the gravity around the HRP. First, circular periodic orbits are identified both in the presence and absence of solar radiation pressure. Then, families of general non-circular periodic orbits in the presence of SRP are determined and subsequently analysed for stability. Next, for a general orbit in the equatorial plane, its stability against a catastrophic impact of an orbiting spacecraft onto the asteroid's surface is checked in the presence of SRP. Orbits, where the solar radiation pressure is less/more dominant over the central body's gravity, are identified with the aim of finding the best orbits for parking a spacecraft. Then, for long-period orbits, SRP is averaged and the time averaged evolution of the orbital elements is obtained. For a special set of initial condition, a closed form solution for the evolution of the orbital eccentricity is obtained. Using this solution, a lower limit for the life-time of a spacecraft that is left uncontrolled is derived in a closed form. Finally, active control strategies are developed for orbit-keeping ofspacecraft for any choice of orbital parameters. A linear-quadratic regulator (LQR) is designed to track a given Keplerian orbit with minimum fuel expenditure. Fuel expenditure on various orbits are calculated and compared to determine the orbits of cheapest operation. The work presented is applicable to small body (asteroids and comets) exploration missions which require online cancellation of the perturbing forces with minimal knowledge of the accurate shape, size, and composition of the small body prior to the mission. • Radiation perturbed periodic orbits around a parallelepiped-asteroid are obtained. • A boundary for stable non-crossing orbits is also analytically derived. • Closed form solutions for far-range orbits are obtained through Lagrange averaging. • Using the above, an analytical estimate for the lifetime of the orbit is presented. • A linear quadratic regulator (LQR) is employed to obtain ideal parking stations. [ABSTRACT FROM AUTHOR]

Separation and reconfiguration of stacked satellites in orbit is an effective method for constructing large space structures. This paper investigates the dynamics of a stacked satellite system (SSS) during the separation and reconfiguration process. Firstly, the dynamic model of the SSS is established via the natural coordinate formulation (NCF) to conveniently handle the time-varying constraints between satellites. Then, the separation and reconfiguration strategies are proposed for the SSS including the reconstruction step between two configurations. To ensure collision-free satellite assembly, a proportional differential (PD) controller combined with a potential function is introduced. Additionally, a docking mechanism is designed, considering collision force constraints during satellite docking assembly. Finally, several numerical simulations are conducted to demonstrate the effectiveness of the separation and assembly strategies. • An orbital dynamic model of a stacked satellite system (SSS) is established. • A collision detection algorithm for the docking mechanism is introduced. • A PD controller law for the collision-free assembly of satellites is designed. • The dynamics for reconfiguration and assembly of the SSS is studied. [ABSTRACT FROM AUTHOR]

Liquid crystal diffractive sails can generate controllable tangential radiation pressures, which have advantages in the Solar Polar Imager mission (SPI). This paper proposes a composite diffractive sail design consisting of an ideal passive diffraction grating sail and liquid crystal polarization gratings (LCPGs). The main diffractive grating sail generates thrust for orbital transfer with a sun-facing attitude. An optimal 3.8-year transfer trajectory is obtained by an improved direct method. Small-area LCPGs distributed around the edge are used for three-axis attitude control. The LCPGs can continuously modulate the force and torque by controlling the applied voltage based on the electro-optical characteristic of liquid crystal materials. A control strategy, including an adaptive attitude-tracking PD controller and a control allocation method, is designed to track the attitude profile generated by the transfer trajectory. Finally, the attitude-orbit coupling dynamics are used to simulate the whole process, and the results show that orbital insertion errors are minor. • A combined diffractive solar sail model using liquid crystal polarization gratings. • Independent and controllable three-axis attitude control of diffractive solar sails. • Optimizing transfer trajectory for solar polar mission based on the proposed sail. • An adaptive attitude-tracking PD controller and a control allocation method. [ABSTRACT FROM AUTHOR]

Controlled de-orbiting is crucial for a low earth orbiting (LEO) satellite or capsule intending to land in a desired location and to prevent damage to people and property on the ground caused by debris. Drag modulation is one possible mechanism to control de-orbiting, exploiting atmospheric drag variation to reduce the necessary orbital energy from the initial conditions to the re-entry interface. In this context, this paper proposes a novel targeted de-orbiting Artificial Neural Network (ANN) and drag-based guidance algorithm for a LEO artificial satellite. It relies on the combination of empirical and analytical relations with Deep Neural Networks (DNNs) to estimate the main parameters of the optimal control law in real time. The training set is composed of several optimal control solutions generated with a previously developed optimal control algorithm, exploiting the formulation in equinoctial modified orbital parameters to manage the large time scale of the problem and the computational cost. An innovative procedure for the training set generation led to the achievement of general results with a limited number of samples. The successful outcome of the guidance algorithm on over 1000 cases demonstrates its robustness and generalization of results. To conclude, a Linear Quadratic Regulator (LQR) feedback control is applied to one case to deal with a more realistic and uncertain density model. • Analytical optimal guidance for a satellite de-orbiting from Low Earth Orbit. • A novel approach based on Deep Neural Networks. • Prediction of the key parameters of the optimal control law in real time. • A Monte Carlo analysis showed the algorithm's robustness and generalization. • Successful feedback control thanks to a Linear Quadratic Regulator (LQR). [ABSTRACT FROM AUTHOR]

The Korea Pathfinder Lunar Orbiter (KPLO), officially named as Danuri, is the Republic of Korea's first spacecraft to orbit the Moon. The goal of KPLO is to secure core deep space technology for future space exploration in Korea and contribute to lunar science by gathering data from the lunar orbit for one year. This paper presents the results of KPLO's Lunar Orbit Acquisition (LOA) phase in detail, with a particular focus on the operational results of Flight Dynamics (FD). During the LOA phase, the KPLO FD team experienced many expected and unexpected issues. These issues were mitigated by making real-time updates to the LOA phase Design Reference Mission (DRM). The paper also presents the results of the Orbit Determination (OD) and performance of each Lunar Orbit Insertion (LOI) maneuver conducted during the actual flight operation. The importance of considering operational constraints when designing the DRM is emphasized by presenting lessons learned based on actual flight experiences. Unlike the original KPLO LOA phase DRM, KPLO successfully achieved the final mission orbit using only three LOI burns, instead of the planned five LOI burns and an Orbit Trim Maneuver (OTM). Despite the extensive revisions made to the DRM, all mission requirements were still fulfilled during the final lunar orbit insertion, taking into account the significant operational constraints. • Real flight operation results of the Korea Pathfinder Lunar Orbiter's lunar orbit acquisition phase are presented. • Orbit determination and lunar orbit insertion maneuver performance are analyzed based on actual flight data. • Unexpected issues during the actual flight operation were mitigated through real-time updates on the design reference mission. • Considering real-world operational constraints while designing the design reference mission is very critical. [ABSTRACT FROM AUTHOR]

Existing exoatmospheric guidance laws become ineffective when a thrust loss fault (like one or more engines unexpectedly shut down) occurs in a launch vehicle, which makes the nominal orbit unreachable. This paper presents a new abort orbit determination process to determine an abort orbit which the launch vehicle is able to reach. It involves solving at most two optimization problems and the abort orbit may be circular or elliptical. We will present how to transform the nonconvex optimization problems into difference of convex (DC) programming problems which can be solved by existing methods with guaranteed convergence. The main contribution of this paper lies in proposing a relaxation technique to convexify a nonconvex control constraint and the combination of the introduction of new constraints and a relaxation technique to deal with the strict terminal constraints. Validity of the relaxation technique is ensured by theoretical analysis. A unique feature of the transformation process is that the feasible sets defined by both the control constraint and the strict terminal constraints are all enlarged. This brings a critical benefit that the resulting DC programming problems can be very efficiently solved. Thus, an abort orbit determination algorithm, which is based on DC programming, can be designed to very reliably and efficiently determine an abort orbit, which will be demonstrated by numerical examples. • A new concise and practical abort-orbit determination process is proposed. • Relaxation techniques and the introduction of new constraints are properly combined. • Validity of the relaxation techniques are theoretically proved. • An abort orbit can be determined by solving at most two DC programming problems. [ABSTRACT FROM AUTHOR]

Orbiting solar reflectors (OSRs) are flat, thin and lightweight reflective structures that are proposed to enhance terrestrial solar energy generation by illuminating large terrestrial solar power plants locally around dawn/dusk and during night hours. The incorporation of OSRs into terrestrial energy systems may offset the daylight-only limitation of terrestrial solar energy. However, the quantity of solar energy delivered to the Earth's surface remains low due to short duration of orbital passes and the low density of the reflected solar power due to large slant ranges. To compensate for these, this paper proposes a constellation of multiple reflectors in low-Earth orbit for scalable enhancement of the quantity of energy delivered. Circular near-polar orbits of 1000 km altitude in the terminator region are considered in a Walker-type constellation for a preliminary analysis. Starting from a simplified approach, the equations of Walker constellations describing the distribution of the reflectors are first modified by introducing a phasing parameter to ensure repeating pass-geometry over solar power farms. This approach allows for a single groundtrack optimisation to define the constellation, which was carried out by a genetic algorithm for single and two reflectors per orbit with an objective function defined as the total quantity of energy delivered per day, to existing and hypothetical solar power projects around the Earth. When full-scale constellations are considered with a number of reflectors, the quantity of solar energy delivered is substantial in the broader context of global terrestrial solar energy generation. • Terrestrial solar energy enhancement by constellation of orbiting reflectors is proposed. • Scalable, predictable and continuous solar energy from space is aimed. • Walker constellation equations are modified for repeating reflector passes. • Groundtrack optimised by genetic algorithm to maximise daily energy delivery. • Quantity of daily solar energy delivered is considerable in the global context. [ABSTRACT FROM AUTHOR]

Space debris near the synchronous orbit poses significant collision risks to spacecraft in this area. Therefore, it is necessary to analyze the orbital dynamics of space debris in order to predict its orbital evolution and prevent it from colliding with the spacecraft. Due to the combined effect of the dissipative forces and Earth's 1:1 tesseral resonance, the space debris with high area-to-mass ratio near the synchronous orbit exhibits two special dynamical behaviors: resonance capture and resonance jump. By using a simplified model, this paper analyzes in detail the orbital evolution of the debris of the resonance capture and resonance jump, and explores the conditions for their occurrence. It is found that the dynamical behavior of space debris around the resonance capture or resonance jump is highly sensitive to its initial conditions. In addition, the long-term direct numerical integrations with the full dynamical model for the orbital evolution of the debris are performed. The difference between the phase space parameters of the resonance capture and resonance jump for space debris is discussed, and the pendulum-like oscillation of the resonant angle is also studied. • Resonance capture and resonance jump for space debris around the synchronous orbit. • Initial conditions of resonance capture and resonance jump of space debris are found. • Resonance capture and resonance jump of debris are sensitive to initial conditions. • Resonant angle of near-synchronous debris exhibits pendulum-like oscillation. [ABSTRACT FROM AUTHOR]

The rotating detonation rocket engine has certain advantages in propulsion performance and is expected to develop into a new type of attitude/orbit control power device. In this paper, an experimental investigation on the detonation propagation characteristics during the short-time pulse operating process of rotating detonation combustor (RDC) was performed. A 60-mm RDC was employed, and the H 2 and oxygen-rich air were used as the reactant. The results show that the experiment can successfully achieve rotating detonation mode when the RDC is operating with a 10-Hz pulse frequency. With the increase of oxidizer mass flow rate, the velocity and pressure of the detonation wave will increase. The average propagation frequency of the detonation wave shows a trend of first increasing and then slightly decreasing as increasing the equivalence ratio. There is a large velocity fluctuation in the RDC pulse operation, and the stability of the detonation wave is significantly affected by the equivalence ratio. The propagation velocity and stability of the detonation wave can be improved by increasing the supply mass flow rate or equivalence ratio with a certain condition. When the equivalence ratio is larger than 0.7, the establishment time of the detonation wave is less than 1 ms, which can meet the requirement of the fast response when the RDC is applied to attitude control engine. [ABSTRACT FROM AUTHOR]

This study introduces a new method to estimate the orbital parameters (inclination, nodal precession rate, and right ascension of the ascending node) of the broken-up object using in-situ debris measurements. To reduce collision probability with tiny debris generated from breakups of satellites, it is required to identify the origin of breakups and predict the orbit of debris. In general, small debris cannot be tracked from the ground, thus an in-situ measurement is an effective method to detect sub-millimeter-sized debris. Previous studies developed a method to identify the location of breakup origin from an in-situ measurement, however, it can be applied to an ideal situation where the detection occurs at the intersection of the orbit planes. This study introduces a new method to estimate the orbital parameters by fitting the model of geocentric declination to the measurement data. This method can be applied to practical situations that cannot be validated in previous studies. This paper also adopts iteratively reweighted least squares to improve estimation accuracy and mitigate initial value dependencies. [Display omitted] • A New method to estimate the orbital parameters of the broken-up object is derived. • Origin identification of breakup events in practical situations is simulated and validated. • Estimation accuracy is improved by adopting iteratively reweighted least squares. [ABSTRACT FROM AUTHOR]

Pseudo-arclength continuation is a scheme used to generate a set of solutions for nonlinear equations and has been applied in numerous fields. In continuation schemes, solutions are obtained by tracking a parameter associated with the system as it varies, thereby creating a solution path. Pseudo-arclength continuation employs the nullspace vector, which is tangent to the path, as an approximation of the arclength in order to determine the direction of variation at each point on the path. However, the nullspace vector has both positive and negative solutions that are equally valid, leading to uncertainty in the direction of travel along the path at each location. Selecting the wrong nullspace vector can result in returning to a previously located solution instead of continuing the mapping of the solution path. Techniques to ensure consistent path direction have been developed; however, their efficacy does not extend to all scenarios. This paper addresses this gap by introducing a "flipping condition" to track previously determined path directions and ensure continuous following of the same path direction. A clear description of the process used to incorporate the flipping condition into the pseudo-arclength continuation scheme, practical implementation of the scheme, and examples demonstrating its application to the nonlinear circular restricted three-body problem (CR3BP), is provided. The inclusion of the flipping condition ensures a consistent direction of travel along the solution path and allows for families of solutions to be developed. • Pseudo-arclength continuation develops solutions to nonlinear equations along a path. • Uncertainty in path direction comes from equally valid signs of the nullspace. • Previously-located solutions are repeatedly found without a consistent path direction. • Implementation process for pseudo-arclength continuation to track path direction. • Application to periodic orbits families in the circular restricted three-body problem. [ABSTRACT FROM AUTHOR]

The cooperative orbit determination (OD) using inertial inter-spacecraft measurements is of great value for the constellation. Previous studies concluded that the cooperative OD system in the two-body dynamics is observable using the inertial angle measurement. This paper performs an observability analysis for the inertial angle-only cooperative OD system based on the observability matrix (OM), and finds that the previous conclusions do not hold for some special configurations. Eight special configurations are proposed, and for each configuration, the unobservable orbit elements are analytically revealed by analyzing the linear relationship among different columns of the OM. Moreover, a method of improving the observability of the two-spacecraft system is proposed by adding another spacecraft. An extended Kalman filter is employed to numerically illustrate the observability of the proposed special configurations and to show the relationship between the observability and the convergence ratio of estimations. Monte Carlo simulations show that the convergence ratios of the observable orbit elements and state combinations are higher than 97%, while convergence ratios of the unobservable states are lower than 70%. With one non-planar elliptic orbit added, all the elements of the three-spacecraft system are observable, and the estimated errors converge within 6 h. The results found in this paper can provide a reference for the design and management of the constellation. • Observability analysis for the angle-only cooperative OD is performed. • Eight unobservable configurations are revealed using the observability matrix. • A method of improving the observability is proposed by adding another spacecraft. [ABSTRACT FROM AUTHOR]

On-Orbit-Servicing missions aim to improve the operative life of orbiting satellites. Among the studied technologies, the most promising are satellites equipped with one or more robotic arms (space robots). One robotic arm might be employed to establish a rigid connection with the target satellite, while the other performs the servicing operations. Nowadays, the control of the capture tool is managed by the computer of the space robot. However, it is possible to distribute the control tasks between the capture tool and the space robot. For this purpose, this paper presents the development of the SMArt Capture Kit (SMACK). SMACK is a standalone capture system equipped with sensors, actuators, and an integrated computer. In this fashion, the capture tool executes the guidance and navigation algorithms, and the control of the actuators; so that the space robot acts as the "positioning" system for the capture tool. The paper provides a description of all the subsystems of SMACK and their experimental validation. The tests of SMACK at the system level, confirm its capabilities to autonomously perform the capture the target interface. • Smart capture tool. • Autonomous tool with integrated sensors, actuators and computer. • Distributed control. • Use of fuzzy logic to develop the model of a custom sensor. • Use of fuzzy logic to create the approach trajectory. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem and detect possible outliers in the processed measurements. The uncertainty on the initial estimate is propagated forward in time and progressively reduced by exploiting sensor data available in said propagation window. Differential algebra techniques and a novel automatic domain splitting algorithm for second-order Taylor expansions are used to efficiently propagate uncertainties over time. A multifidelity approach is employed to minimize the computational effort while retaining the accuracy of the propagated estimate. At each observation epoch, a polynomial map is obtained by projecting the propagated states onto the observable space. Domains that do no overlap with the actual measurement are pruned thus reducing the uncertainty to be further propagated. Measurement outliers are also detected in this step. The refined estimate and retained observations are then used to improve the robustness of batch orbit determination tools. The effectiveness of the algorithm is demonstrated for a geostationary transfer orbit object using synthetic and real observation data from the TAROT network. • Uncertainty on the initial orbit determination is reduced using other sensor data. • Measurement outliers are detected and isolated. • Multifidelity methods are used for fast and accurate uncertainty propagation. • Robustness of batch orbit determination tools is improved. [ABSTRACT FROM AUTHOR]

In the exploration of celestial bodies, including planets, moons, and asteroids, it is useful to identify stable orbits in which the orbital elements remain, on average, constant (referred to as frozen orbits). This paper aims to investigate the feasibility of frozen orbits for a small body, such as a probe, orbiting a main body under the perturbation due to the gravitational attraction of an inner third-body, on a circular (or slightly eccentric) orbit coplanar with the main body equator, by means of an approach based on mean element theory. The disturbing potential has been developed in Legendre polynomials up to order l = 5 (triakontadipole level of approximation). Thus, the double-averaged potential function and the associated constants of motion have been determined up to the same order. Then, by applying the Lagrange Planetary Equations, the secular and long-term orbital element variations have been obtained. Therefore, frozen orbital solutions have been evaluated, and the effects on them of the addition of main body oblateness perturbation have been considered. Furthermore, the procedure has been repeated, and the frozen solutions are re-evaluated in the case of a disturbing body with small eccentricity up to order l = 4 (hexadecapole level of approximation). These solutions offer significant advantages in exploring bodies subject to a notable perturbation from an inner third-body, such as binary asteroid systems. • Frozen orbits for the inner third-body problem. • Inner circular planar third-body: Double-averaged potential up to triakontadipole. • Inner slightly eccentric planar third-body up to hexadecapole. • Orbital solutions for binary asteroid observation. [ABSTRACT FROM AUTHOR]

Solar sails are an attractive technology for propellant-free propulsion, especially in small satellites with tight power and mass budgets. Several recent missions have shown promising applications of solar sails for nanosatellite orbital control in low Earth orbit (LEO). They enable easier access to and removal from high-altitude orbits. Since solar radiation pressure produces torques in addition to forces, a solar sail can also be used for low-power attitude control. Few missions have exploited this effect. In response, this paper proposes a new nanosatellite mission concept, only achievable by combined orbit-attitude control via solar sail: the sunflower mission, for high-altitude wide-area Earth observation. A realistic sail design meeting the mission requirements is obtained via parametric analysis and comprehensive review of past missions. A pyramid-shaped sail is proposed for the mission, and its advantages and drawbacks are analysed. The dynamics are evaluated using a high-fidelity numerical simulator with all relevant physical perturbations in LEO. The imaging objectives are successfully achieved over a multi-year duration. The sail also provides propellant-free orbit insertion from a low-altitude launch orbit, and fast de-orbit at end-of-life. It uses less power and has a smaller stowed size than several competitor technologies for orbit-attitude control of LEO nanosatellites. [Display omitted] • Sunflower mission proposed for wide-area small satellite Earth observation in LEO. • A pyramid-shaped solar sail provides low-power orbit and attitude control. • Propellant-free orbit raising from a low deployment altitude reduces launch cost. • Passive Sun pointing enables low-power attitude control for remote sensing. • Propellant-free orbit lowering enables quick de-orbit at end-of-life. [ABSTRACT FROM AUTHOR]

The heterogeneity of the small body population complicates the prediction of small body properties before the spacecraft's arrival. In the context of autonomous small body exploration, it is crucial to develop algorithms that estimate the small body characteristics before orbit insertion and close proximity operations. This paper develops a vision-based estimation of the small-body rotational state (i.e., the center of rotation and rotation axis direction) during the approach phase. In this mission phase, the spacecraft observes the rotating celestial body and tracks features in images. As feature tracks are the projection of the landmarks' circular movement, the possible rotation axes are computed. Then, the rotation axis solution is chosen among the possible candidates by exploiting feature motion and a heuristic approach. Finally, the center of rotation is estimated from the center of brightness. The algorithm is tested on more than 800 test cases with two different asteroids (i.e., Bennu and Itokawa), three different lighting conditions, and more than 100 different rotation axis orientations. Each test case is composed of about 250 synthetic images of the asteroid which are used to track features and determine the rotational state. Results show that the error between the true rotation axis and its estimation is below 10 ° for 80% of the considered test cases, implying that the proposed algorithm is a suitable method for autonomous small body characterization. • Small bodies have heterogeneous characteristics complexifying mission design and operations. • The small body properties are hard to predict before the encounter. • Vision-based techniques enables autonomous estimation of the small-body rotational state. • The proposed method estimates the small-body rotational state from images. • The proposed method is tested on numerical simulations with different observational geometries. [ABSTRACT FROM AUTHOR]

This paper examines options for orbit configurations for a space interferometer. In contrast to previously presented concepts for space very long baseline interferometry, we propose a combination of regular and retrograde near-Earth circular orbits in order to achieve a faster filling of (u , v) coverage. With the rapid relative motion of the telescopes, it will be possible to quickly obtain high quality images of supermassive black holes. As a result of such an approach, it will be possible for the first time to conduct high quality studies of the supermassive black hole close surroundings in dynamics. • A new configuration for the space interferometer is proposed. • This configuration uses near-Earth regular and retrograde orbits. • Calculated orbits are stable more than 10 years. • The supermassive black hole can be imaged within 20 h. • Synthetic simulations show observations of black holes are possible in dynamics. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for a satellite mission with the goal to perform Lunar Occultations within the context of the circular restricted three-body problem (CR3BP) of the Earth-Moon system. This is achieved by exploiting the geometrical relationships between the Earth, Moon, and a spacecraft orbiting around L 4. Additionally, it examines the viability of a linear state-feedback control policy to stabilize short-period orbits under the presence of the gravitational effect of the Sun, Solar radiation pressure, and the Lunar orbital eccentricity, which is not accounted for in the CR3BP dynamics. Given the unprecedented NUV angular resolution achieved by a spacecraft at L 4 , this research proposes a framework for a remote sensing observatory for Solar activity, thereby enabling the monitoring of the entire hemisphere of Solar radiation, and to study different astrophysical issues via Lunar Occultations. • Lunar Occultations are studied by leveraging short-period orbits about L 4. • Short-period orbits (SPO) are selected to increase observation time of the Solar corona. • A linear controller is used to account for unmodeled orbital perturbations. • SPO with lower angular velocity is preferred to observe LO and Kordylewski clouds. • LO from L 4 offer unprecedented NUV angular resolution. [ABSTRACT FROM AUTHOR]

In this paper, Particle Swarm Optimization with energy-to-fuel continuation is proposed for initializing the co-state variables for low-thrust minimum-fuel trajectory optimization problems in the circular restricted three-body problem. Particle Swarm Optimization performs a search of the solution space by minimizing the weighted sum of squares of the two-point boundary-value problem final boundary condition residuals for the minimum-energy problem. Next, an energy-to-fuel homotopy is employed to transition the minimum-energy trajectory to a minimum-fuel trajectory, starting from the generated guess. The proposed methodology is applied to two low-thrust transfer problems in the Earth–Moon system: a transfer from a geostationary transfer orbit to an L1 halo orbit, and a transfer from an L2 halo orbit to an L1 halo orbit. The resulting minimum-fuel trajectories are validated with the literature. It is demonstrated that the methodology can successfully generate guesses for the initial co-state variables which converge to a solution for both scenarios. A strategically chosen particle swarm size is shown to improve the efficiency of the methodology. The proposed approach is of simple implementation, can be easily extended to other trajectory optimization problems, facilitates the discovery of multiple candidate trajectories, and does not require a user-provided guess, all of which are advantageous features for the preliminary phase of mission design. • Particle Swarm Optimization is proposed to guess the Lagrange co-states variables. • PSO initialization is paired with homotopy continuation for trajectory optimization. • The proposed algorithm facilitates discovery of multiple unique optimal trajectories. • Two minimum-fuel trajectory optimization problems are solved. • The effect of the particle swarm size on successful convergence is analyzed. [ABSTRACT FROM AUTHOR]

This paper presents the methodologies to design the transfer trajectories from Earth nearby to heliocentric orbits. For multiple spacecraft with the same initial condition but aiming to different phases in the heliocentric orbit, several lunar gravity assists are used to divert them into different interplanetary orbits. Firstly, based on the patched-conic approximation, a complete design process for deep-space transfer orbits was proposed for multiple spacecraft performing lunar gravity assist maneuvers. In this design process, it was assumed that each spacecraft had the same initial conditions. The periodic matching method was introduced to design the interplanetary transfer orbit, satisfying the initial and terminal constraints. An iterative method was proposed to search lunar gravity assist parameters that satisfied the hyperbolic excess velocity condition for the escape trajectories. Furthermore, a semi-analytical correction method was proposed to further approximate the precise transfer trajectory. This correction method was found to have a reduced time cost and a better error convergence compared with conventional correction methods. • Design of deep-space transfer trajectories for multiple spacecraft with identical initial conditions. • Periodic matching analysis of heliocentric orbit design. • Iterative method for searching lunar gravity assist parameters for spacecraft. • High performance recorded for the proposed semi-analytical correction method. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of constructing a flight scheme to Venus, in which a spacecraft flying to the planet after a gravity assist maneuver and transition to a resonant orbit in order to re-encounter with Venus, makes a passage of a minor celestial body. The 117 candidate asteroids from the NASA JPL catalogue, whose diameter exceeds 1 km, were selected. The flight trajectories which meet the criteria of impulse-free both flyby Venus and asteroid, and the subsequent landing on the surface of Venus were found within the interval of launch dates from 2029 to 2050. The trajectory of the spacecraft flight from the Earth to Venus including flyby of Venus and asteroids with a subsequent landing on the surface of Venus was analyzed. • Found 53 possible scenarios for a flight to Venus with free-impulse flyby of an asteroid for the launch dates from 2029 to 2050. • In the framework of the developed schemes it is possible to perform the free-impulse encounter with comet 2P/Encke for launch in 2032 and 2044. • The impulse-free flyby of Venus and the asteroid occurs when the spacecraft transfers to resonant 1:1 orbit after Venus flyby. • The link between attainable landing points and conditions of the free impulse flyby of an asteroid was established. [ABSTRACT FROM AUTHOR]

In terms of cataloged debris produced, the anti-satellite test carried out by Russia, in November 2021, at an altitude of about 480 km, leading to the destruction of the old satellite Cosmos 1408, was the second worst to date and represented the third worst fragmentation in orbit. It generated more than 1/4 of the cataloged debris produced over 55 years by all such tests and almost twice as many as were produced by all previous Soviet tests. After placing this event in its historical context, this paper analyzes in detail how the evolution of the Cosmos 1408 debris cloud affected the environment below 600 km in the first seven months, focusing on the two operational space stations and the Starlink large constellation of satellites. During the first six months following the test, the Cosmos 1408 cloud of fragments nearly doubled the average flux of cataloged objects on the International Space Station and increased by about 3/4 that on China's Tiangong. In the same period, the Starlink large constellation saw an average increase in the flux of cataloged objects of about 20%. Some orbital planes, the "counter-rotating" ones with respect to the Cosmos 1408 debris cloud, were more affected than others, and the affected planes gradually changed over time, due to the differential precession of cloud and constellation nodes. However, being the Starlink constellation 70 km higher up, the flux of Cosmos 1408 cataloged debris steadily decreased over the period analyzed, due to the cloud orbital decay, reducing to just over a quarter of its extrapolated initial value after seven months. • A review of ASAT tests as a source of orbital debris was presented. • The impact of the Cosmos 1408 destruction was put into context. • The cataloged debris flux increase on space stations was computed and discussed. • The debris flux increase and evolution on Starlink orbit planes was analyzed. • A moratorium on this type of ASAT tests was recommended, including low LEO. [ABSTRACT FROM AUTHOR]

On-orbit Servicing in the form of space-manufacturing, refuelling, assembly and robotic manipulation are deemed to become a fundamental part of the space market in the short-to-middle term. One of the key aspects to reach extensive use of OOS operations is having a standardized, reliable, and cost-effective interface that embeds as much functionality as possible to simplify operations. In this context, SENER Aeroespacial has developed SIROM (Standard Interface for Robotic Manipulation), which provides mechanical coupling, electric interface, thermal and data transfer in a single compact solution. In this paper, the current design for SIROM is presented, with a focus on the electronics subsystem and the integration of the electromechanical design. A functional breakdown of the electronic boards is presented after a review of the current state of the art. For the validation, a TRL6 Test Campaign that was successfully passed in early 2021, including vibration, temperature, vacuum and life tests. Its results are presented here, along with the details of the functional validation on the context of the EROSS project in May/June 2021. To conclude the paper, on-going projects involving the SIROM interface are reviewed, finishing with future lines of development on the SIROM roadmap. • On Orbit Servicing is becoming a fundamental part of the space market. • SENER designed the SIROM interface for this purpose, developing a fully integrated model in 2021. • SIROM has passed a qualification campaign for Technology Readiness Level 6. • SIROM has been validated in the H2020 project EROSS in an On Orbit Servicing scenario. • SIROM is developing to reach TRL 8 as part of European projects (MIRROR, PERIOD). [ABSTRACT FROM AUTHOR]

Over the past few decades, a considerable increase in the number of space debris has become a serious threat to the safety of the operating satellites. So, collision avoidance maneuvers have become indispensable in providing immediate and cost-effective solutions. The unavoidable presence of uncertainty associated with any physical system adds to the challenge. In this paper, a method is presented to determine the fuel-optimal collision avoidance trajectory using a convex optimization technique while incorporating the evolution of uncertainty associated with the space objects. The safety of the satellite is ensured by the collision avoidance constraints which involve calculating the instantaneous collision probability and using the Mahalanobis distance. An avoidance region is also demarcated around a space object with uncertain states to prevent any collision. Posing the problem as a convex optimization problem helps to eliminate the problem caused by dependency of the optimization variables on the initial guesses used. However, convexification of this problem with evolving uncertainty and collision probability calculation presents a set of challenges. The evolution of the positional error covariance ellipsoid leads to a feasible non-convex space surrounding the avoidance region. Moreover, implementation of a convex optimization formulation here requires convexification of the expression for collision probability, which is originally not purely convex in nature when a Gaussian probability density function is involved. This paper presents an approach to tackle the above-mentioned challenges. The satellite is returned to its nominal orbit in a timely manner, as time spent off the nominal trajectory can often lead to disruption of the space mission. The effects of various parameters on the required Δv are also explored. • Collision avoidance maneuver is formulated as a convex optimization problem. • Collision probability calculation and nonconvex feasible region are convexified. • The optimization includes evolution of uncertainty in the states of space objects. • An approximated Mahalanobis distance leads to a more conservative approach. • The effects of orbital, control and uncertainty parameters are explored. [ABSTRACT FROM AUTHOR]

L 4 and L 5 axial orbits provide special locations to monitor and search for near Earth objects (NEOs) due to their offset locations. In this paper, we propose a detection system of NEOs on the axial orbit in the Sun–Earth circular restricted three-body problem. Taking the Sun exclusion zone into consideration, we design an observation strategy for space-based telescopes on axial orbits. Then, an observation accessibility measure for the motionless point is presented to evaluate the performances of the different axial orbits and formations. In addition, the detection performance of axial orbits is compared with the distant retrograde orbits (DROs) and Earth-displaced heliocentric orbits (EDHOs). Numerical simulations indicate that the detection performance of axial orbits for the motionless point is better than that of DROs but is inferior to EDHOs. On the other hand, the axial orbit is dynamical stable, but EDHOs are unstable and their fuel costs for maintenance cannot be ignored with the increase of service time. Furthermore, the detection system on axial orbits is applied to moving objects. For example, the detection system of the EDHOs cannot predict the Chelyabinsk asteroid impact, but it is possible for the DRO and axial orbits. Numerical simulations for 4000 virtual NEOs indicate that due to a better observation geometry, the detection system of axial orbits can find more NEOs than those of the DRO and EDHOs. • We propose a detection system of near Earth objects (NEOs) on the axial orbit. • We design an observation strategy for space-based telescopes. • An observation accessibility measure is presented to evaluate the performances. • The detection system is applied to the Chelyabinsk asteroid impact and virtual NEOs. [ABSTRACT FROM AUTHOR]

This paper presents an optimal control design method for multi-satellite assembly in an elliptic orbit in close proximity operations considering input saturation constraints. Tschauner–Hempel (T–H) equations are utilized to model the relative motion dynamics of the satellites in the Local Vertical Local Horizontal (LVLH) frame of the target satellite, where every satellite in the assembly is modeled as a point mass. The communication topology between the satellites in the assembly is modeled using graph theory, where the graph has several nodes representing the satellites and several edges representing the data exchange direction. It is assumed that every satellite exchanges its states with a few neighbors in the team, where the neighbors of every satellite are prespecified and do not change during the mission. This graph is utilized to construct the global dynamic model of the assembly, in which every node is represented by the dynamic model of a single satellite. The local control law, which is applied to every satellite in the assembly, consists of a state feedback gain and a coupling gain. The state feedback gain is designed using the discrete-time periodic Riccati equation to guarantee the local stability of every satellite separately, while the coupling gain is selected to satisfy the Lyapunov condition to guarantee the global stability of the assembly. The invariant-set method is utilized to prove the stability of the global dynamic system that is subjected to symmetric input saturation. The precision and optimality of the proposed control law are successfully demonstrated by numerical nonlinear simulations in a MATLAB environment for a cubic formation satellite assembly. • Assembling multiple satellites into an elliptic orbit in a cubic configuration. • Controlling a discrete-time periodic multi-agent system. • Designing an optimal control system using the discrete-time periodic Riccati equation. • Analyzing the stability of a discrete-time periodic multi-agent system under input saturation. [ABSTRACT FROM AUTHOR]

This paper proposes a method of using multiple spacecraft flying in formation in an artificially reduced halo orbit around the 2nd Lagrange point in the Sun–Earth system (SEL2) to make interferometric observations. One of the requirements for interferometric observations is to collect baseline vectors between telescopes or antennas. A shape-based approach is introduced to design a formation flight orbit that spirally spreads to satisfy this requirement. In this approach, orbits are designed on the basis of a linear theory. However, the formation orbits based on the linear theory quickly diverge because of the unstable dynamics around the SEL2. Therefore, the state-dependent Riccati equation, which allows for nonlinear control, is applied to orbit maintenance. The control system consists of two components: one for maintaining the reference orbit around the SEL2 and the other for controlling the relative position between the multiple spacecraft. The performance of the developed formation flight system is verified through a numerical simulation, confirming that the position accuracy requirement of the infrared interferometer is satisfied. It is also shown that both controls can be achieved with a low-thrust magnitude by using an electric propulsion system. • Formation flights around the Lagrange points are useful for interferometer. • An artificial halo orbit is designed with a reduced radius and a fixed shape. • Spacecraft formations are designed to collect more baseline vectors. • A nonlinear control is designed using the state-dependent Riccati equation. [ABSTRACT FROM AUTHOR]

This research looks towards improving the accuracy and efficiency of orbit transfer speed increment estimation and task assignment for space patrol missions involving multiple platforms. First, we set up a quick prediction model for the increment in orbit transfer velocity. Then, a two-layered hybrid optimization framework is developed, with a deep neural network sub-model as the inner layer to find the optimal speed increase and the consensus-based bundle algorithm as the outer layer to solve the multi-task patrol sequence problem. Finally, the simulation and analysis of the patrol task assignment problem are conducted under two types of scenarios. The results show that the hierarchical optimization method proposed in this paper is three orders of magnitude faster than the traditional optimization method. In addition, the suggested hierarchical optimization method has significant promise in practical applications, where it can produce solutions more quickly to adapt to more complex patrol scenarios. • A multi-layered framework is established to handle the optimization of space patrol task assignment. • The deep neural network-based orbit-transfer speed increment calculator is proposed. • The consensus-based bundle algorithm-based task allocator achieves efficient assignments. • Calculating performance of the proposed method is evaluated. [ABSTRACT FROM AUTHOR]

The global space sector has to increasingly consider sustainability concerns in the orbit, given the rising challenge of space debris. In which direction the management of space debris will develop in terms of technological solutions, policies, and actor strategies remains still unclear. This paper applies the concept of 'global socio-technical regimes' to better understand how actors in the global space sector frame, conceive, and legitimize the space debris problem. More specifically, we apply a discourse network analysis method – sociotechnical configuration analysis – to identify and map different value orientations by core actors over the last fifteen years. This analysis reveals three development stages in the discourse: a problem identification period (2007–2011), followed by the rise of national interests amidst increasing promises of space-based infrastructures (2012–2015), and finally, the emergence of a global socio-technical regime that increasingly connects space sustainability with Earth-bound sustainability (2016–2019). Based on our analysis, we expect that ensuring future earth-space sustainability will include a broader mix of challenges. Future approaches to space debris management will have to consider a broader and clearer problem framing to help inform effective policy making. • We mapped the institutional structures that shape global space debris management. • We analyzed value considerations of actors by means of socio-technical configuration analysis. • We observed a broader sustainability framing concerning space over time. • There is a growing consensus on Earth-bound and space-based interdependencies. • Future policies to address space debris require an integrative approach. [ABSTRACT FROM AUTHOR]

This paper investigates the numerical computation of minimum-fuel low-thrust trajectories subject to bound constraints on the duration of thrust and coast arcs. First, an optimal control problem is formulated. The constraints on thrust and coast periods are written as a single discontinuous bound constraint on the control norm depending on time and on a set of free parameters considered as additional state variables. Then, the constraint is regularized and the problem is converted into an equivalent one where the norm of the control is simply upper-bounded by one. Finally, the latter problem is solved efficiently through an indirect single shooting algorithm. The great advantage of this approach is that it does not require knowing beforehand the control switching profile. Moreover, it has the ability to generate multiple suboptimal solutions in addition to the optimal one, thus offering more options for mission design. Numerical results are provided to illustrate the interest and effectiveness of the method. An electric small satellite rendezvous problem in circular orbit is considered. The fuel-optimal control of the constrained problem as well as several suboptimal controls are computed and analyzed, each of which showing a different number of thrust and coast arcs. • A set of parameters, considered as additional state variables, is introduced. • Thrust and coast times constraints are written as a constraint on the control norm. • A regularization method is used to make the constraint continuously differentiable. • The approach converges to the optimal solution of the constrained problem. • No prior information on the structure of the control law is required. [ABSTRACT FROM AUTHOR]

The future of deep space communications encompasses a challenging situation where the current facilities used to communicate with different spacecraft may become saturated as a result of an increasing number of missions and their complexity. From this forecast, the present study intends to provide a solution to saturation problems through strategically-located upgradable relays for Earth–Mars communications. The foremost goal of this paper is to quantitatively uncover the potential enhancements coming from relay placement in strategic orbits between Earth and Mars. Herein, two relay configurations – a.k.a. network topologies – are analyzed: the Lagrange-relays network topology and a circular, homogeneously-distributed satellite constellation, acknowledged here as pearl constellation. The first uses the Earth–Sun system Lagrange points L 3 , L 4 and L 5 as potential locations for the relays, whilst the second defines an optimized orbit between Earth and Mars with 3 or 4 relay satellites. To aid in the analysis, the authors developed an open-sourced piece of software that obtains the link availability as well as the data rate at which two nodes may communicate, taking as a reference the Deep Space Network (DSN) for Earth, and the Mars Reconnaissance Orbiter for Mars. For complex topologies with more than two communicating nodes, the software outputs the end-to-end bit rate and optimal communication route at each time step. Moreover, this product is extensible to analyze and optimize any network topology and could be adapted to be used for contact management and mission planning in the future. The results show that the network-topology proposals are an advantageous option to significantly increase the link availability of Earth–Mars communications. Nevertheless, the Direct-To-Earth (DTE) link always outperforms the multi-hop path due to the limited telecommunication system's capabilities of both the spacecraft and the relays. As a result of this, the study includes an analysis on the requirements of the relay's design in order to make the constellation a beneficial and comparable alternative to the DTE link. This way, the proposed network topologies become a suitable option whom to share with the DSN communications workload, providing enhanced bit rates and data volumes as well as higher availability of the communication. [Display omitted] • Deep space relays in strategic orbits help to improve Earth–Mars communications. • Solar conjunctions may be successfully avoided through relays. • Communication availability is significantly improved; up to continuous visibility. • Reasonable gain enhancements could lead to bit rates comparable to the current ones. • Total downlink data volume could be tripled. [ABSTRACT FROM AUTHOR]

In recent years, in parallel to Earth Observation (EO) consolidating its role in space applications, spacecraft miniaturisation has been gaining increasing popularity. Smaller satellites represent the ideal platform for cost-effective and relatively quicker technology demonstrations. Furthermore, the perspective of high-volume production would simplify the design of constellations made of identical spacecraft in order to improve the revisit time. Optical payloads could be enhanced by using deployable systems based on carbon fibre-reinforced polymer (CFRP) tape-springs, which are very compact before deployment and highly stable in their extended configuration. In a previous work by the authors, an engineering model of a telescope intended for CubeSats was fabricated and tested. In this paper, the coefficients of thermal expansion (CTE) found experimentally by the authors were implemented in the Finite Element (FE) model via the mathematical framework of the Classical Laminated Plate Theory (CLPT). Thermally-induced distortions of the deployed telescope were analysed numerically for different illumination conditions in low-Earth orbits. The orientation of the assembly with respect to the radiation was found particularly critical. An uncertainty analysis that took into account composite material properties errors was carried out. The results indicated that the predicted response lies in a wide range of uncertainty, which can be detrimental regarding the fulfilment o mission requirements. The impact of different thermal control finishes was evaluated, and the overall response over the spacecraft lifetime was heavily affected by absorptivity degradation. Alternative cross-sections rather than semi-circular tape-springs were implemented in the model, although the increased bending stiffness mainly affected the temperature distribution and showed only a minor impact on the deformations. • Novel design for a deployable space telescope based on CFRP tape springs. • Numerical thermo-structural analysis in LEO thermal environment. • Implementation of CTE found experimentally into FE model. • Uncertainty analysis of the thermally-induced deformations. • Analysis of the impact of different coating and cross-sections. [ABSTRACT FROM AUTHOR]

Space debris detection and characterisation is an important and pressing field, as the amount of space debris is growing due to the increase in spacecraft launches and increasing interests for space uses. Space agencies like NASA and ESA keep track of over 5,000 spacecraft and 20,000 spacecraft-related debris objects currently orbiting the Earth. An active spacecraft may undergo trajectory changes through an impulsive maneuver, or an inactive spacecraft may change its trajectory because of uncontrolled explosions due to residual fuel without warning. These pose risks to operational satellites. In addition, measurement data from tracking and detection consists of uncertainties, causing maneuver detection and characterisation methods to become computationally expensive. Thus, the goal of this work was to develop a quick, reliable, computationally inexpensive method for spacecraft maneuver detection and characterisation to be used by satellite operators and assist in collision avoidance measures. This paper presents such a technique, which is applied to simulated measurement data of an orbiting spacecraft taken from one ground site. With these objectives, a method using a modified Extended Kalman Filter (EKF) with covariance inflation from previous studies was explored and simplified. A new parameter definition is presented for maneuver detection and characterisation, named the Kaderali-parameter, or K , with focus on transverse apogee and perigee maneuvers. A relationship was then found between the parameter and the magnitude of the impulsive artificial maneuver. The method was tested in several different scenarios, varying Δ v magnitude and scale, Δ v direction, maneuver orbital location, orbit geometry, noise covariance, detection parameter threshold, state covariance inflation threshold, and maneuver duration. In general, it was found that as the Δ v magnitude increases, the magnitude of the detection parameter also increases. This relationship was found to be a nonlinear logarithmic relationship through best fit curve testing. Possible extensions of this work in the future include: testing multi-maneuver scenarios, multi-sensor data collection and fusion, break-up or berthing events, rendezvous or mating events, and matlab EKF protocol implementation. • Unknown spacecraft maneuvers pose collision risks, leading to a Kessler Syndrome. • A computationally inexpensive one-parameter Kalman Filtering solution is utilised. • New parameter, K , is created to clearly detect and characterise impulsive maneuvers. • An analytical relationship between K and the maneuvering speed is established. • The relationship describes a nonlinear direct relationship to be used by operators. [ABSTRACT FROM AUTHOR]

Space debris creates a serious problem for Space flights safety in Low Earth Orbits. In this paper, the results of high velocity Space debris fragment interaction with thin metallic shields are presented. The formulas for determining critical thickness of the target preventing from penetration being functions of impactor mass, speed and material properties of both impactor and target are developed. The developed simplified models are supported by results of physical and numerical experiments. • Formula for calculating ballistic limit thickness of the shield is obtained. • Formula for calculating ballistic limit velocity is presented. • New criterion for different scenarios of the high-speed collision is introduced. • For low density impactors the ballistic limit curve is practically monotonous. [ABSTRACT FROM AUTHOR]

This paper presents a machine learning (ML) approach that can improve orbit prediction precision and reduce uncertainties with a properly designed fusion strategy. The ML models are trained based on historical TLE sets and then ML-modifications are generated for the future states and uncertainty predictions. The ML-modification is first interpreted as a pseudo-measurement of the true orbit prediction error and then fused with the conventional orbital state and uncertainty propagation result. The regularized particle filter (PF) with progressive correction and systematic sampling is adopted for uncertainty propagation while using the Simplified General Perturbations #4 (SGP4) model. Comprehensive experiments are conducted and analyzed on over 100 resident space objects (RSOs) in different orbit types. The results demonstrate that the fusion strategy enables the ML approach to work with the advanced PF prediction method. The prediction precision can be significantly improved for the majority of the cases. The prediction accuracy is observed to be improved in some cases but without a clear pattern. The results and analysis also suggest that future studies of a monitoring system facilitating the fusion process would be helpful in practical applications. • Machine learning (ML) learns from data to improve orbit prediction accuracy. • ML reduces prediction uncertainty of Resident Space Objects (RSOs) in TLE catalog. • A medium-scale ML study over 100 RSOs in the TLE catalog was carried out. • RSOs in SSO, LEO, MEO, GEO can all be improved. • RSOs classified as debris, rocket bodies, or normal satellites can all be improved. [ABSTRACT FROM AUTHOR]

Coverage analysis is an essential process when designing a satellite constellation, and the variations of global revisit characteristics are usually elusive in discontinuous coverage problems. In dealing with this, a general method for analyzing the global revisit characteristics of constellations with repeating ground track orbits is proposed in this paper. Firstly, a two-dimensional map based analytical model for the point coverage of constellations is introduced. Then, the variations of revisit characteristics along both the parallel and meridian are analyzed based on the presented analytical model. Finally, numerical examples are carried out. On the one hand, the proposed analytical model for point coverage is demonstrated to be of high precision. On the other hand, all possible positions where the discontinuous changes of revisit characteristics occur can be analytically obtained, which can reveal the discontinuous variations of revisit characteristics along both the parallel and meridian, and can also ensure that all possible global or regional revisit characteristics are counted for a given constellation. The proposed method can contribute to constellation design and coverage performance analysis. • An analytical model for the coverage calculation of satellite constellations is developed. • Conditions for the appearance of the discontinuous changes of global revisit characteristics are deduced analytically. • Variations of the revisit characteristics of satellite constellations along both the parallel and meridian are revealed. [ABSTRACT FROM AUTHOR]

Proliferated low Earth orbit constellations are becoming more common both in reality and in planning. The resilience of these constellations to the radiation effects of adverse solar weather is of interest given that some of them pass over polar regions. This paper stochastically simulates solar weather events over the course of solar cycle 25 in order to quantify radiation effects on a model of Planet Lab's Flock constellation under various design and programmatic decisions. The Flock constellation is a highly proliferated, commercial, and polar low Earth orbit earth observation architecture. Lifecycle and radiation failures are simulated along with a reconstitution system in order to quantify architectural performance as a function of constellation population. This time-based measure of performance is then used to quantify the constellation resilience and allow for programmatic and design variables to be altered in order to observe the effects on the resilience of proliferated constellations against adverse solar weather radiation effects. A sensitivity analysis is performed in order to assess which decisions most improve or degrade resilience. Broadly, the results show that commercial off the shelf components and programmatic decisions such as launch and manufacturing schedules may improve constellation resilience against adverse solar weather effects. More specifically, the results also show that commercial off the shelf components with even basic shielding levels provide high resilience to cumulative total ionizing dose effects and single event upset radiation effects. However, any further reductions to shielding would have significant impacts on single event upset rates whereas total ionizing dose would remain negligible. Furthermore, manufacturing time for Flock satellites is sufficient to maintain a resilient reconstitution strategy. Finally, results show that in order to improve the resilience afforded by a reconstitution strategy, improvements to manufacturing and launch times should be made in parallel, rather than one or the other in isolation. • COTS and programmatics may improve LEO constellation resilience to solar weather. • LEO constellations are highly resilient to even extreme solar weather radiation. • Shielding and launch times are significant for resilience to LEO solar radiation. • Manufacture and launch times should improve parallelly for constellation resilience. • Cumulative radiation in LEO is negligible, primary concern is single event effects. [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear dynamics and control problem of deorbiting an electrodynamic tethered satellite system in an inclined elliptical orbit. Considering the perturbing Lorenz forces, a set of modified equinoctial elements is employed to describe the slow-varying orbital dynamics. In addition, the fast-varying attitude dynamics of the system is incorporated into dynamic modeling by adopting an assumption of a dumbbell model. To circumvent the difficulties in computation of a real-time optimal control law for a long-term deorbiting process, a compound control scheme is proposed. A time-scale separation method is adopted to facilitate the controller design. In the scheme, a nonlinear optimal control law accounting for system constraints and nonlinear dynamics is first proposed to find an initial nominal periodic orbit without considering the variations of orbital elements. Subsequently, a closed-loop feedback control law based on energy rate is presented to track the periodic solutions for several orbits by considering the overall dynamics. Notably, the periodic solution will be re-computed after each tracking procedure to account for the slow variation in orbital elements. Comparative studies are presented to demonstrate the advantages of the proposed control law in reducing computational costs. • Orbital motion and attitude dynamics are distinguished by time-scale separation. • Nonlinear dynamics and inherent constraints of the system are accounted for. • A low-cost compound control law is proposed for long-term deorbiting maneuver. [ABSTRACT FROM AUTHOR]

Hydroterra was selected in September 2018 as one of the three candidates for the ESA's Earth Explorer-10 mission. Hydroterra aims at observing and improving the understanding of fundamental processes of daily water cycle, enhancing prediction capability of extreme rainfall and related flooding. To achieve this goal, the mission concept envisages placing a satellite embarking a synthetic aperture radar instrument in geosynchronous orbit. The satellite is designed to be launched with VEGA-C into low Earth orbit and to be transferred to the operational orbit by means of electric propulsion. In this paper, the multidisciplinary optimization process carried out to obtain the baseline electric orbit raising transfer for Hydroterra will be presented. The computed trajectory will meet the mission requirements, including targeting to the operational orbit, the launcher performance model, and the target on-station mass. Additionally, system-level constraints related to the satellite design that have an influence on the ideally optimized trajectory will be derived and considered in the optimization. In particular, the impact of the solar cell degradation on the thrust and specific impulse levels of the thruster due to the passage through the Van-Allen belts, the need to re-charge the batteries before entering the next eclipse, and the agility requirements will be accounted for. The obtained results show that a feasible electric orbit raising trajectory can be successfully obtained for the Hydroterra mission. • The Hydroterra electric orbit raising and satellite are concurrently optimized. • Solar cells damage, power, agility, launcher and on-station mass requirements apply. • Four thruster operational points switching criteria are defined to streamline the optimization problem. • A feasible baseline transfer minimizing the time in the Van-Allen belts is found. [ABSTRACT FROM AUTHOR]