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Given the growing threat of an impending space debris crisis, nations worldwide have intensified their research efforts in satellite deorbiting technologies. Electrodynamic tether and braking sails stand out as popular methods for spacecraft deorbiting that do away with the necessity for propellant. However, these methods possess their own set of limitations. This paper presents a holistic dynamical model for a fusion of electrodynamic tether and braking sails. The aim is to avoid the complex nonlinear dynamics during the deployment, retrieval, and dwell time of electrodynamic tether, while compensating for the insufficient trust generated by braking sails in high orbital environments. The objective is to enable satellite to deorbit swiftly and stably under a broader range of conditions. Specifically accomplishing the following three aspects: conceptualizing the design of an ideal equipment, implementing simulated deorbiting process, and conducting an efficiency comparative analysis with prevalent current deorbiting methods. Through numerical simulations, the effectiveness and feasibility of this proposed design have been validated. • Electrodynamic tethers attachment arrangement to avoid complex dynamics control. • Combined de-orbiting strategy is practical and more efficient. • Accurate environmental modelling considering size effects. [ABSTRACT FROM AUTHOR]

A simulator and a hardware-in-the-loop (HIL) setup for the study of the electric system made by a short electrodynamic tether (EDT), an Electric Power Module (EPM) and a heaterless Hollow Cathode (HC) are presented. In the simulator, the EDT is modeled by the current–voltage (IV) characteristic of a bare EDT, the EPM involves a power supply and a variable resistor, and the IV curves of the emitter and the keeper of the HC are given by the linear fittings of the experimental curves obtained in the laboratory. The simulator was used to study an important problem for short EDT: the minimum power required by the power supply to reach an electric current at the cathode above the critical threshold to keep the plasma discharge as a function of ambient variables (the motional electric field and plasma density). Regarding the HIL, it emulates the EDT with a programmable power supply and a resistor, the EPM with a power supply and a set of resistors, and the HC by a set of Zener diodes. Additionally, the emulator has a computer and a microcontroller that allow to measure key electrical variables and command in real time and in closed-loop the programmable power supply to ensure that the EDT emulator satisfy the bare EDT IV curve. The three elements of the HIL were tested and compared with the theoretical model to validate its correct implementation and operation. Finally, the HIL was used to test and verify the electronic boards of the device of the E.T.PACK-F project. • A simulator and a hardware-in-the-loop (HIL) setup of the electric elements of an EDT system were developed. • Both of them consider the tether, the electric power module and a hollow cathode. • The simulator allowed to find the power requirements to keep the plasma discharge in the cathode. • The HIL setup was validated by comparing experimental result with the theoretical simulator. • The HIL was used to test the electronic boards of power module of the E.T.PACK's deorbit device. [ABSTRACT FROM AUTHOR]

A bare-photovoltaic tether (BPT) is a long conductive tape in orbit that provides propellant-less propulsion and power harvesting. An electric model for a BPT operating in the passive mode and composed of a bare segment and a bare-photovoltaic (bare-pv) segment coated with thin-film solar cells on one side is presented. The pv cells, which are electrically insulated from the conductive substrate, are connected to two electric busbars that also serve as electrical contacts to the spacecraft. The power harvested by the cells can be used by the spacecraft or, as considered in this work, to boost tether performance. The electric model takes into account that, depending on the number and location of zero-bias points, four regimes of operation exist for this type of BPT. Current and voltage profiles solutions that are not possible for standard bare tethers are presented. A parametric analysis of the operation regimes varying the tether length, the length of the pv segment, and the power was carried out. Two complementary methods to find the optimum length of the bare-pv segment for a given total tether length and mission are presented. The first method is based on the optimization of the normalized average current, which controls the strength of the Lorentz force and measures tether efficiency and the second method uses as figure of merit the deorbit time in postmission disposal scenarios. For both of them it is shown that an optimum exists for the length of the pv segment. An enhancement in performance above 30% as compared with standard bare tethers was found for the considered scenario. • A model for the current and voltage profiles of Bare-pv Tethers (BPTs) is presented. • New profiles that are not possible for standard bare tethers are shown. • Based on the number of zero-bias points, four operation regimes are identified. • Optimization of the efficiency and the deorbit time are used to design the pv segment. • Adding the thin film solar cells increases significantly tether performances. [ABSTRACT FROM AUTHOR]

Consumable-free electron emitters are presently not feasible for autonomous tether-based deorbit devices such as E.T.PACK due to their power requirement. The bare-photovoltaic-tether (BPT) concept combines the bare tether electron collection with a tether segment, coated with thin film Copper Indium Gallium Selenide solar cells to harvest additional power for the cathodic contact, potentially enabling propellant-less operation. This thesis presents the first prototype of the photovoltaic tether segment, its architecture, its electrical characteristics, major challenges of the system and possible solutions. Photovoltaic tether segments of up to 3 m in length were manufactured, consisting of parallelized submodules of 25 cm in length. Due to space limitations, only the I-V-characteristics of these submodules were measured under a self-built Class BCA LED Solar-Simulator inside a vacuum chamber and at varying temperatures between −100 °C and 100 °C. In addition, the suitability of the concept for a low Earth orbit environment was assessed by performing atomic oxygen exposure tests using a microwave-based low pressure plasma atomic oxygen source. Based on the experimental data, a model is provided for predicting the performance of the photovoltaic segment in orbit, highlighting the main problems of the BPT: temperature, orientation and partial shading. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear dynamics and deorbiting control of an electrodynamic tether (EDT) system in elliptical orbits. The orbital dynamics of the system under Lorentz forces is modelled using a set of modified equinoctial elements, whereas the attitude dynamics of the system is modelled based on the dumbbell assumption. A deep learning scheme of nonlinear model predictive control (NMPC) schemes is proposed for deorbiting control of the EDT system. To facilitate controller design, a time-scale separation method is utilized to simplify the attitude dynamics of the EDT system. A deep learning-based NMPC control law is developed with two stages. In the first stage, a large amount of data is generated using a conventional NMPC law to construct a dataset for training a deep neural network (DNN). In the second stage, the trained DNN is used to realize the real-time mapping from the system state to the system control, and thereby the feedback control of the system deorbit is achieved with extremely low computational cost. Finally, the efficacy and performance of the proposed deep learning-based NMPC control law are demonstrated via numerical case studies. • Nonlinear dynamics and inherent constraints of the system are accounted for. • Dataset is obtained by nonlinear model predictive control method. • Extremely low computational cost of feedback control is achieved by deep learning. [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]

The electrodynamic tether (EDT) system is used as one of the end-of-life disposal technologies to deorbit defunct satellites with the benefit of Earth's magnetic field and plasma environment. However, due to the flexibility of the conductive tether, the orbit-attitude coupling effects as well as the influence of Multiphysics fields, this system suffers from time-consuming computations using complicated mathematical model in long-term simulations. Therefore, this paper proposes a high-fidelity high-efficiency dynamics model for the EDT system, in which the tether libration and transverse motions are described by the articulated model, and the system equations are formulated using recursive dynamics algorithm. Computational cost of the recursive method is compared with a nonrecursive method, and the result shows that with the number of tether elements larger than 15, the recursive method would show better computational efficiency. Since the conductive tether tends to be kilometers long in application, this new model would definitely contribute to the numerical efficiency. In addition, simulations are conducted with 2 and 16 tether elements solutions. By comparing the obtained results, it is found that the two cases show large differences over time. For a long tether, it is reasonable to use a larger number of elements in the dynamics analysis. Besides, in order to suppress the libration motion and avoid unstable states in the EDT system, a current control strategy is proposed and verified by a deorbit simulation in low Earth orbit. • A high-fidelity high-efficiency model is proposed for the electrodynamic tether system. • The recursive method shows better efficiency with the number of elements larger than 15. • Different tether elements would result in large differences in simulation. • A current control strategy is proposed to stabilize the libration motion. [ABSTRACT FROM AUTHOR]

The main novelties and capabilities of the second version of the Bare Electrodynamic Tether Mission Analysis Software (BETsMA v2.0) are presented. Recent advances on Orbital-Motion-Theory have been incorporated to the electric model of Low-Work-function Tethers (LWTs). An electric model that considers a switch to embed a power supply or a resistor between a Bare Electrodynamic Tether (BET) and an electron emitter is also introduced. For both types of tethers (LWT and BET) and modes of operations (active and passive), robust and efficient numerical algorithms to compute the current and voltage profiles were constructed based on a change of variable proposed in a previous work. The capabilities of the code are illustrated by considering two relevant scenarios. For a BET in the passive mode, it was shown that onboard power can enhance tether performance and reduce significantly the deorbit time. For a BET in the active mode, a performance map varying the orbit inclination, the length of the insulated tether segment, and the power was constructed. For both cases, the code was used to investigate through simulations the conditions to keep constant the electric current at the electron emitter. • The second version of the tether software BETsMA v2.0 is presented. • Electric models for bare and low-W tethers in active and passive modes are given. • Tether performances in the active and the passive modes are shown. • The impact of a power supply on tether performances in the passive mode is shown. [ABSTRACT FROM AUTHOR]

Electrodynamic tethers can be employed as an immensely promising propulsion system for boosting the altitude of spacecraft, cite instance space stations, satellites, and the like, which ameliorates the expenditure of fuel and minimizes detrimental spacecraft impacts. This paper analyzes the libration dynamics and stability of reboost spacecraft with insulation electrodynamic tethers. A key aspect of spacecraft reboost with an electrodynamic tether is how to keep the tether aligned with the local vertical and stabilized in the context of external disturbances. It has been shown in the current research that the librational instability results in the tether slackness and swings in long-term motion without effective control. Moreover, electrodynamic force (Ampere force) is regarded as a distributed load acting on the tether causing tether deformations which may be detrimental if severe. Aiming at the problem, an optimal control method and PID are given to stabilize the libration motion by modulating the tether current. The dynamical model of the electrodynamic tether system is established using Lagrange equations of the second kind under considering tether deformation and control laws are proposed based on the model. The effectiveness of libration stability control is validated through numerical results in which a current regulation law with appropriate control parameters is used for the libration motion of electrodynamic tether system.

Consumable-free electron emitters are presently not feasible for autonomous tether-based deorbit devices such as E.T.PACK due to their power requirement. The bare-photovoltaic-tether (BPT) concept combines the bare tether electron collection with a tether segment, coated with thin film Copper Indium Gallium Selenide solar cells to harvest additional power for the cathodic contact, potentially enabling propellant-less operation. This thesis presents the first prototype of the photovoltaic tether segment, its architecture, its electrical characteristics, major challenges of the system and possible solutions. Photovoltaic tether segments of up to 3 m in length were manufactured, consisting of parallelized submodules of 25 cm in length. Due to space limitations, only the I-V-characteristics of these submodules were measured under a self-built Class BCA LED Solar-Simulator inside a vacuum chamber and at varying temperatures between −100 °C and 100 °C. In addition, the suitability of the concept for a low Earth orbit environment was assessed by performing atomic oxygen exposure tests using a microwave-based low pressure plasma atomic oxygen source. Based on the experimental data, a model is provided for predicting the performance of the photovoltaic segment in orbit, highlighting the main problems of the BPT: temperature, orientation and partial shading.

This paper focuses on the nonlinear dynamics and control for the spin-up maneuver of an electrodynamic tethered satellite system in an inclined elliptical orbit. A nonsingular formulation is established by using a unit vector along the tether to define the tether orientation and avoid the Euler angle singularity, and is adopted to describe the attitude dynamics of the system and to facilitate the controller design. The spin-up problem of concern is to accelerate the electrodynamic tether system into the prescribed spinning motions and maintain the expected angular velocity. A nonlinear model predictive control law accounting for nonlinear dynamics and system constraints is proposed to achieve this control goal by actively regulating the changing rate of the bounded tether current. Finally, numerical simulations are performed to validate the effectiveness of the proposed control law for the spin-up maneuver and evaluate the control performance. Meanwhile, comparative studies are presented to demonstrate the advantages of the proposed control law in stabilizing the out-of-plane libration motions of the system in inclined orbits. • A nonsingular formulation is developed for an EDT system in elliptical orbits. • Nonlinear dynamics and inherent constraints of the system are accounted for. • Model predictive control law is proposed for spin-up maneuver of the system. [ABSTRACT FROM AUTHOR]

Space missions in the environments of the outer planets require a large amount of propellant or assistant flybys. Moreover, the quadratic decrease of the radiation intensity with the distance from the sun makes solar panels less convenient as power source. Electrodynamic tether (EDT) technology is receiving increasing attention since it allows for obtaining both power and propulsion profiting from the high magnetic field and plasma density in the proximity of the giant planets. In particular, it has been shown that a self-propelled vehicle with a single EDT could be captured by Jupiter, were it not for the relativistic effects in the electron collection and the overheating of the tether due to the interaction with the environment. Here, we show that a multi EDT (MEDT) propulsion system can be used to circumvent these limitations. The suitable number, shape, and length of the tethers, depending on the size of the vehicle, are selected by structural and thermal analysis. A possible MEDT-propelled mission to Jupiter is described, including the design of the interplanetary trajectory, the orbital insertion, and the subsequent orbits around the planet. The results obtained demonstrate that such a bare MEDT system is a feasible option to provide propulsion and power in outer planets environments. • Electrodynamic tethers are studied for propellant-less Jovian capture of a spacecraft. • An analysis of the structural, thermal, and relativistic constraints is performed. • A multi tether configuration is shown to be required and is used for the design. • An optimal solution to Lambert's problem is selected for the interplanetary transfer. • The tether system can be switched to power generation mode after the capture. [ABSTRACT FROM AUTHOR]

State-of-the-art electrodynamic tethers reach a steady electric current by using a bare segment to capture electrons passively from the ambient plasma (anodic contact) and an active electron emitter or a tether segment coated with a low-work-function material (cathodic contact) to emit electrons back and close the electrical circuit. This work proposes to take advantage of recent developments on thin-film solar cells and insert a photovoltaic (pv) tether segment in between the anodic and the cathodic contacts. Since thin-film solar cells can be folded and manufactured with any desired length and the same cross-section dimensions as the bare segment, i.e. width and thickness around few centimeters and tens of microns, the resulting device is compact and preserves bare tether simplicity. Detailed analysis of the current and voltage profiles throughout the tether shows that the electrical power introduced by the pv-segment into the tether-plasma circuit improves the performance and makes them less dependent on ambient conditions. The pv-segment decreases considerably the tether-to-plasma bias at the cathodic contact, thus opening the possibility to emit substantial current while using consumable-less electron emitters like thermionic and electron field emitters. The pv-segment also favors the current collection by increasing the tether-to-plasma bias at the bare segment. Propulsion and power generation applications and alternative architectures of bare-pv tethers are briefly discussed. • Novel tether concept that combines a bare segment with thin-film photovoltaic cells. • Increased power generation enables consumable-less electrodynamic tether with high currents. • Attractive de-orbit technology which is less dependent on ambient conditions. [ABSTRACT FROM AUTHOR]

The growing amount of orbital debris is becoming a serious concern for space development activities. To remedy the situation, it is necessary to prevent new debris generation through highly probable post-mission disposal operations and remove existing large debris objects from crowded orbits. An electrodynamic tether (EDT) is a promising deorbit propulsion device for both purposes, as it is propellant-less in principle and thus simple and cost effective. An on-orbit EDT experiment called the Kounotori Integrated Tether Experiment (KITE) was conducted in early 2017 on the sixth H-II Transfer Vehicle (HTV-6) for demonstrating and raising the maturity of the core EDT technologies. In the KITE mission, EDT operation was planned using the combination of a bare tether (720 m long) and a field emission cathode (FEC). Although tether deployment was unsuccessful due to a mechanical malfunction of the holding & releasing mechanism of the end-mass, the FEC operated successfully throughout the mission period and demonstrated its capabilities in low Earth orbit (LEO). Another KITE device – an electrical potential monitor called LP-POM – also operated successfully from HTV launch to re-entry, obtaining engineering and scientific results. In addition to these experimental results, the lessons learned during the development process are meaningful for future EDT research and development. • An on-orbit experiment of an electrodynamic tether (called KITE) was conducted. • KITE features the combination of a net-like bare tether and a field emission cathode. • End-mass was not released by a mechanical trouble, so the tether was not deployed. • The field emission cathode operated successfully and showed its capabilities in space. [ABSTRACT FROM AUTHOR]

A deorbit device is required for some microsatellites to meet space debris mitigation guidelines, although very challenging in terms of limited resources and reliability. Many groups are conducting research on post-mission disposal (PMD) devices using an electrodynamic tether (EDT) due to its high efficiency and simplicity. Since an EDT for microsatellites must be lightweight, with some strength, high conductivity, high survivability, and meet other requirements, such new materials as carbon nanotube yarn, metal-plated fiber, and metal-deposited thin film are assumed for a tape type tether. In order to determine the appropriate EDT dimensions such as tether width and length, the deorbit capabilities must be evaluated by numerical simulations in advance, as the thrust obtained varies depending on the EDT dimensions, orbital parameters, and other factors. The required resources of the EDT system such as mass and electric power can then be obtained for each orbit, satellite, and deorbit time. Thus, several prototypes of tape type tethers were made and evaluated in various tests. • Deorbit device for microsatellites using electrodynamic tether(EDT) was investigated. • Our concept features the use of a folded tape type bare tether made from new materials. • The results of numerical simulations on EDT performance under various conditions were shown. • Several prototypes of tape type tethers were made and evaluated in various tests. [ABSTRACT FROM AUTHOR]

Electrodynamic tethers are proposed as propulsion and energy harvesters for space probes orbiting planets with a magnetic field and ionosphere, however there are no descriptions in the technical literature of the design of an electrical power system for such an application at subsystem and circuit detail. This paper presents a proposal for such a power system that extracts energy from the kinetic energy of a spacecraft using a bare electrodynamic tether, i.e. an unsheathed conductive wire or band, in low-Earth orbit. The application of the system is the powering of the spacecraft while in its final de-orbiting maneuvers at end-of-life with no reliance on the main spacecraft bus. • Energy harvesting power system for tether-based LEO satellite de-orbit operations. • System through circuit description of the tether energy harvesting power system. • Use of concepts and state of the art with space heritage to support the validity. • De-orbit power flow control scheme based on space proved three domain control. • Isolation scheme proposal for operation with independence to the main power bus. [ABSTRACT FROM AUTHOR]

Graphene-oxide-semiconductor (GOS) planar-type electron sources—which consist of a graphene electrode layer, a thin SiO 2 insulator, and a Si substrate—can be driven by applying gate biases of 5–15 V to produce high emission current densities of 10–100 mA/cm2. In this study, propellantless cathodes using GOS electron sources are developed for aerospace applications. Because a single emission site usually has an area smaller than 100 μm × 100 μm, its maximum emission current is below 10 μA. To increase the emission current to several milliamperes or more, the total emission area must be expanded. However, it is difficult to increase the emission current by merely enlarging a single emission area because the graphene layer acts not only as the gate electrode but also as a series resistor, which means that the emission current density decreases as the effective gate bias decreases. Thus, the optimum relationship between the area of a single emission site and the emission current of the site array is investigated, showing a result that an electron source with hundreds of 100 μm × 100 μm sites on a 3 mm × 3 mm wafer produces an emission current of 6.0 mA at a gate bias of 11.1 V. • The cathode can be driven at ~15 V with emission current densities of ~100 mA/cm2. • A relationship between a single emission area and the array pattern is optimized. • The array cathode on a 3 × 3 mm2 wafer produces an emission current of 6.0 mA. [ABSTRACT FROM AUTHOR]

This paper investigates spacecraft orbital boost maneuver by a fully insulated electrodynamic tether using a coupled multiphysics dynamic model that considers electric-magnetic-dynamic energy coupling. The current-potential characteristics of the electrodynamic tether is described by a simplified analytical model, where revised Parker-Murphy model is employed to evaluate electric current generation at plasma contactors together with libration dynamics of tether. The 13th-order Earth's magnetic field model is used to account influence of inhomogeneity of Earth's magnetic field on orbital parameters of electrodynamic tether system, especially in inclined orbits. Parametric analysis has been conducted for orbital boost maneuver from 400 km to 1,200 km at four different orbital inclinations. The results show that (i) the orbit of electrodynamic tether system will change from circular to elliptical orbits, especially in inclined orbits, (ii) the voltage of onboard power supply at the anode affect electric current generation, (iii) the coupled multiphysics model is necessary to characterize the interaction of electrodynamic tether with the surrounding space environment and the controllability of electric current in electrodynamic tether, (iv) the motion of orbital boost maneuver by electrodynamic tether is stable, which is different from the deorbit by electrodynamic tether. • Developed coupled multiphysics model for orbit boost by electrodynamic tether. • Derived close-loop current-potential relation of electrodynamic tether. • Demonstrated orbital boost efficiency by dynamic simulation. [ABSTRACT FROM AUTHOR]

It is well known that the libration motion of the electrodynamic tether is unstable. Libration control of the electrodynamic tether system using the Lorentz force produced by current in the tether is studied. In the libration dynamic equation, the Lorentz force is virtually divided into two parts. One part takes the role of keeping the essential function of the electrodynamic tether system. The other part takes the role of controlling the libration motion. The control scheme of the Lorentz force is based on the extended time-delay autosynchronization method. In this scheme, the control current which is the control parameter is determined by real-time states of libration and angular velocities for delay time of previous periods. The validity of the control scheme proposed in this study is confirmed by numerical simulations in the case of circular orbit, elliptical orbit, orbit in the equatorial plane and noises existing in measuring the states of libration. The results show that the perturbed libration motions converge to the periodic solution with time growing in examples of circular orbit, elliptical orbit, and noises existing. The perturbed libration motion converges to an approximate periodic orbit in the example of equatorial orbit. The control current is in a reasonable range during the process of control, and converges to zero in the end. The curve of the current in the tether is continuous and smooth which can be easily achieved in an actual system. • The current in the tether is taken as the control parameter. • The Lorentz force is virtually divided into two parts. • The control scheme is based on the extended time delay autosynchronization method. • The perturbed libration motion successfully converges to the periodic libration. • The control current is small and gradually converges to zero. [ABSTRACT FROM AUTHOR]

Abstract The libration dynamics of the electrodynamic tether system is studied for 13° International Geomagnetic Reference Field. Using the International Geomagnetic Reference Field including up to 13 t h order and 13° terms to describe the geomagnetic field, the attitude dynamic equations of the system in the elliptical orbits are built. The generalized forces produced by this magnetic model are derived. The generalized forces related to the in-plane and out-of-plane angles are sum of generalized forces for nontilted dipole model and generalized forces for higher order geomagnetic model terms. In the analysis of the libration dynamic characteristics, the generalized forces for higher order geomagnetic model terms are regarded as perturbations to the dynamic equations for the nontilted dipole model. The simulation results show that differences of components of these two geomagnetic model and differences of generalized forces related to them are all small. Failure time of the libration motion is defined to measure the influence of the perturbation to the system. Examples for different electrodynamic parameters and orbital parameters are simulated. The results show that the perturbations have obvious effects on the attitude dynamics. The influences of perturbations caused by higher order terms of 13° International Geomagnetic Reference Field for different parameters are all obtained. Highlights • The generalized forces for higher order IGRF terms are regarded as perturbations. • Increasing ε enhance the instability of the attitude libration. • Parameter e has no concern with the attitude libration. • Increasing h weaken the instability of the attitude libration. • The instability of the EDT first increases and then decreases with increasing i. [ABSTRACT FROM AUTHOR]

A comprehensive tour of the complex outer planet systems is a central goal in space science. However, orbiting multiple moons of the same planet would be extremely prohibitive using traditional propulsion and power technologies. In this paper, a new mission concept, named Magnetour, is presented to facilitate the exploration of outer planet systems and address both power and propulsion challenges. This approach would enable a single spacecraft to orbit and travel between multiple moons of an outer planet, without significant propellant or onboard power source. To achieve this free-lunch ‘Grand Tour’, Magnetour exploits the unexplored combination of magnetic and multi-body gravitational fields of planetary systems, with a unique focus on using a bare electrodynamic tether for power and propulsion. Preliminary results indicate that the Magnetour concept is sound and is potentially highly promising at Jupiter. [ABSTRACT FROM AUTHOR]

This paper developed a new multiphysics finite element method for the elastodynamic analysis of space debris deorbit by a bare flexible electrodynamic tether. Orbital motion limited theory and dynamics of flexible electrodynamic tethers are discretized by the finite element method, where the motional electric field is variant along the tether and coupled with tether deflection and motion. Accordingly, the electrical current and potential bias profiles of tether are solved together with the tether dynamics by the nodal position finite element method. The newly proposed multiphysics finite element method is applied to analyze the deorbit dynamics of space debris by electrodynamic tethers with a two-stage energy control strategy to ensure an efficient and stable deorbit process. Numerical simulations are conducted to study the coupled effect between the motional electric field and the tether dynamics. The results reveal that the coupling effect has a significant influence on the tether stability and the deorbit performance. It cannot be ignored when the libration and deflection of the tether are significant. [ABSTRACT FROM AUTHOR]

The ever increasing population of space debris poses a great threat to the sustainable development of space industry. Electrodynamic tether has been recognized as a promising technology for the active removal of space debris from overpopulated orbital regions. A typical electrodynamic tether system consists of two end-bodies connected by a conductive tether in space. The electric current flowing in the tether will interact with the magnetic field of the Earth to generate the Lorentz force, by which the system can be deorbited almost without expending propellant. The dynamics and control of any electrodynamic tether system is highly nonlinear by nature and have two critical aspects for practical application: the deployment of electrodynamic tether and the attitude stability during the deorbiting process. This paper summarizes some recent efforts made to address these two issues by the authors' research team in Nanjing University of Aeronautics and Astronautics. Moreover, some open problems deserving future investigation are discussed. [ABSTRACT FROM AUTHOR]

It has recently been shown that a thin-tape tether, as opposite to a round one, has a high probability of survival to single impacts by space debris, under a broad range of de-orbit operation conditions. The purpose of the present work is to extend that analysis to survival to multiple impacts by smaller, but more abundant, debris. The method used here consist, essentially, in separating the particles into “large” and “small” ones. The large ones are so rare that the probability of them concurring on the same spot can be neglected. The small ones are a sort of background, and it is shown that the probability of them impinging close enough to a large particle crater to cause malfunction of the tape is negligible. A particular mission is considered, de-orbiting a 3000 kg spacecraft from 800 km altitude at 90 ° inclination by means of an aluminium tape of dimensions 10,000 m × 0.06 m × (5 × 10 −5 ) m. It is shown that the probability that this mission survives to multiple impacts is at least 0.978. The application of this method to missions of different parameters is also discussed. [ABSTRACT FROM AUTHOR]

This paper developed a high-fidelity dynamic model of flexible space tether systems by considering the elastic, thermal, and electrical coupling effects on the dynamics and stability of bare electrodynamic tether systems. A simple and effective control strategy based on the libration energy of the flexible tether is derived and applied in the deorbit process. Numerical results show that the newly proposed energy control strategy is effective in controlling the libration and transverse elastic motion of the electrodynamic tether. In addition, the effect of the mass of sub-satellite on the system dynamics and stability is investigated. It is found that the libration and transverse motion of the electrodynamic tether can be stabilized by the proposed control strategy even without the sub-satellite when the electrodynamic force is dominant. This new finding shows the satellite deorbit with the electrodynamic tethers is advantageous in term of mass saving. [ABSTRACT FROM AUTHOR]

Highlights: [•] The paper presents an analytical model for tape-tethers probability of survival against debris in LEO orbit. [•] The model quite accurately follows full numerical results using NASA and ESA debris flux data. [•] It keeps the complex dependency on tape cross-section dimensions and orbit altitude/inclination. [Copyright &y& Elsevier]

Abstract: It is well known that libration motion of electrodynamic tethers operating in inclined orbits is affected by dynamic instability due to the electromagnetic interaction between the tether and the geomagnetic field. We study the application of two feedback control methods in order to stabilize the periodic attitude motions of electrodynamic tethers in elliptic inclined orbits. Both control schemes are based on the time-delayed autosynchronization of the system. Numerical simulations of the controlled libration motion show that both control techniques are able to transform the uncontrolled unstable periodic motions into asymptotically stable ones. Such stabilized periodic attitude motions can be taken as starting points for the operation of the tether. The control domains of both methods have been computed for different values of the system parameters, as functions of the two control parameters shared by both control schemes. The relative effectiveness of the two techniques in the stabilization of the periodic attitude motion has also been studied. [Copyright &y& Elsevier]