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Minimum-Time Trajectories of Electric Sail with Advanced Thrust Model
Abstract
The Electric Solar Wind Sail is an advanced propulsion system concept that, similar to the more conventional solar sail, is able to generate a propulsive thrust without any propellant. The main performances of such a propulsion system have been studied in different mission scenarios and are reported in the literature. However, the analyses available so far are based on a simplified thrust model that neglects the effect of the spacecraft attitude on both the thrust modulus and its direction. The recent availability of a refined thrust model requires a critical reappraisal of the simulation results and a new analysis of the optimal trajectories of a spacecraft equipped with such a propulsion system. The aim of this paper is to review the different thrust models used over the last years for mission analysis purposes, and to illustrate the optimal control law and the corresponding minimum-time trajectories that can be obtained with the new, refined, thrust model. The study highlights new analytical relations for the propulsive thrust as a function of the spacecraft attitude, whereas simple and accurate closed-form equations are also proposed for the study of a classical circle-to-circle coplanar heliocentric orbit transfer.
... In particular, α n is defined as the angle between the directions ofr andn, the latter being a unit vector normal to the sail nominal plane in the direction opposite to the Sun (i.e.,r ·n > 0); see Fig. 15. Finally, a constraint on the maximum thrust angle α max , on the order of 30-35 deg (i.e., α n ∈ [0, [60][61][62][63][64][65][66][67][68][69][70] deg) is necessary to prevent the E-sail from possible mechanical instabilities. In other words, according to the thrust model discussed in Ref. [56], the E-sail propulsive acceleration vector a is constrained to lie within a conical region as described in Fig. 15, while the value of a does not depend on the thrust angle α. râr n conical region max a Sun a n a Figure 15: E-sail thrust vector constraint described in Ref. [56]. ...
... where, again, α = arccos (â ·r) α n /2 is the thrust angle, with α n ∈ [0, [60][61][62][63][64][65][66][67][68][69][70] deg. Further investigations [60] highlighted a more complex relationship between α and α n and, in addition, reported a variation (i.e., a decrease) in the thrust magnitude F with the sail pitch angle α n . ...
... In particular, γ {1, 0.7, 0.5} when α n = {0, 55, 90} deg, respectively. Starting from the results of Ref. [60], Quarta and Mengali [62] have proposed an analytical approximation of Eqs. (5)-(6) with the aim of investigating minimum-time trajectories using an indirect approach. ...
The Electric Solar Wind Sail (E-sail) is an innovative propellantless propulsion system conceived by Pekka Janhunen in 2004 for use in interplanetary space. An E-sail consists of a network of electrically charged tethers maintained at a high voltage level by an electron emitter. The electrostatic field surrounding the E-sail extracts momentum from the incoming solar wind ions, thus giving rise to the generation of a continuous thrust. In a geocentric context, the same physical principle is also exploited by the plasma brake, a promising option for reducing the decay time of satellites in low Earth orbits after the end of their operational life. This paper discusses the scientific advances of both E-sail and plasma brake concepts from their first design to the current state of the art. A general description of the E-sail architecture is first presented with particular emphasis on the proposed tether deployment mechanisms and thermo-structural analyses that have been carried out over the recent years. The working principle of an E-sail is then illustrated and the evolution of the thrust and torque vector models is retraced to emphasize the subsequent refinements that these models have encountered. The dynamic behavior of an E-sail is also analyzed by illustrating the mathematical tools that have been proposed and developed for both orbital dynamics and attitude control. A particular effort is devoted to reviewing the numerous mission scenarios that have been studied to date. In fact, the extensive literature about E-sail-based mission scenarios demonstrates the versatility of such an innovative propulsion system in an interplanetary framework. Credit is given to the very recent studies on environmental uncertainties, which highlight the importance of using suitable control strategies for the compensation of solar wind fluctuations. Finally, the applications of the plasma brake are thoroughly reviewed.
... In recent years, much effort has been devoted to the study of an Electric Solar Wind Sail (E-sail), which is able to generate a continuous low-thrust by momentum exchange with the incoming ions from the solar wind, without the need of any reaction mass nor any propellant consumption [1]. The peculiarity of such an advanced propulsive concept promotes the feasibility of complex space missions [2][3][4][5][6], especially when a spacecraft is to be placed for a long time in the nearby of collinear libration points in the Sun-Earth system [7]. In fact, the instability of the resulting orbits requires suitable station keeping maneuvers to be implemented [8,9]. ...
... For illustrative purposes, two different artificial potential functions, V (1) ij and V (2) ij , are now illustrated. Their derivatives are given by ...
... ij if ρ i (0) − ρ j (0) ≥ δ max and with V (2) ij otherwise, as is suggested in Ref. [23]. An example of the artificial potential functions V (1) ij and V (2) ij is shown in Fig. 3, in which the desired spacecraft relative distance is δ ij = 80 km, the maximum sensing radius is δ max = 100 km, and the minimum safe distance is δ min = 50 km. ...
... Because the E-sail thrust is inversely proportional to the Sun-spacecraft distance r, that is, decreases with the distance at a slower rate than that of a photonic solar sail (which instead scales as 1/r 2 ) [15], an E-sail becomes a superior alternative in a number of mission scenarios, especially for those interplanetary transfers formulated within a time-optimal framework [16]. Most of the previous work about E-sail focused on its thrust model, with a continuous improvement in the accuracy and complexity of the mathematical models. ...
... The mathematical thrust model of the electric solar wind sail underwent important revisions in last few years for obtaining a more accurate calculation of the propulsive acceleration vector [15][16][17][18]27]. In this context, the latest Esail thrust analytical model proposed in Ref. [18] is adopted in this paper. ...
... Introducing the vector [ ] T X = r r , the controlled linearized equation of the system becomes 1 X = MX + u (17) where M is given by Eq. (16), and u 1 is the active control due to the grid voltage modulation (which is assumed to be sufficiently small) in the form ...
This paper discusses the linearized relative motion and control of Electric Solar Wind Sails (E-sails) operating in formation flight around a heliocentric displaced orbit. An E-sail is constituted by thin and centrifugally stretched tethers, and generates a propulsion by momentum interaction with the charged particles from the solar wind. Feasible regions and linear stability of circular displaced non-Keplerian orbits generated by E-sails are investigated using the latest thrust model. The linearized relative motion of E-sails in a formation flight is developed in the chief's orbital frame, and a linear stability analysis of the relative motion is carried out with eigenvalue decomposition. Relative trajectories are classified into three categories, according to whether the relative orbit is stable, fully unstable or locally unstable, the latter corresponding to an instability in the along-track direction. Two control strategies are proposed for stabilization, the first one is an active control aiming to change the topology of the relative motion to eliminate the instability caused by positive real eigenvalues, and the other is a closed-loop feedback control to maintain stability in the along-track direction. Numerical simulations indicate a high accuracy of the linearized relative dynamical model and a good performance of the control strategies.
... In this advanced thrust model, the thrust modulus and thrust cone angle were described as polynomial functions of the pitch angle based on numerical and experimental data. Using the polynomial fitting model proposed by Yamaguchi and Yamakawa, Mengali and Quarta [13] obtained a series of minimum-time trajectories of the electric sail for a classical circle-to-circle coplanar heliocentric orbit transfer to review the different thrust models. Furthermore, an advanced thrust model of the electric sail in analytical form was introduced in [14]. ...
... In the preliminary mission analysis of the electric sail, the vector of thrust acceleration is usually described by the pitch angle n and clock angle [13]. As shown in Fig ...
... which can be adjusted by an electron gun. [12][13], which is used to characterize the effect of sail attitude on the modulus of thrust acceleration. ...
The electric sail is an innovative concept for spacecraft propulsion, which can generate continuous thrust without propellant by reflecting solar wind ions. In previous studies, the thrust of an electric sail is described by a classical model that neglects the effects of the electric sail attitude on the propulsive thrust modulus and direction. This study reappraised the performance of the electric sail in the Vesta and Ceres exploration mission with an advanced thrust model that considers the effect of the spacecraft attitude on both the thrust modulus and direction. By using a hybrid optimization method, the trajectory optimization of the electric-sail-based spacecraft from Earth to Vesta and Ceres is implemented in an optimization framework. Numerical results show that the minimal flight time with the advanced thrust model is longer than that with the classical model. The difference in performance between the classical and advanced models is attributable to over-estimation of the maximum thrust cone angle and the thrust modulus by the classical model.
... The interaction of the artificial electric field generated by the tethers with the solar wind deflects the proton flow and generates a propulsive thrust. In the last years, much efforts have been dedicated to estimate the E-sail propulsive acceleration for mission analysis purposes, as is thoroughly discussed in Ref. [1]. ...
... The correctness of the last relation is confirmed by a plot of the polynomial function γ = γ(αn) given by Eq. (37), which overlaps to the upper curve drawn in Fig. 5. Starting from the model by Yamaguchi and Yamakawa [4,10], Ref. [1] discusses the optimal control law using both an analytical and a graphical approach. In the latter case, the curve ar = ar( at) calculated with Eqs. ...
... (19) and (38) when ρ = R = 1/4 and d = 3/4, see Fig. 6. Moreover, the results obtained in Ref. [1] show that the optimal pitch angle is about one half of αp, as is stated by Eq. (30), and the optimal switching parameter is zero when αp is greater than a critical value of about 110 deg. In fact, according to Fig. 7 and Eq. ...
... It is a propellantless propulsion system (such as solar sail) and consists of a spinning grid of tethers that are kept at a high potential by an onboard electron gun. When the grid is immersed in the solar wind, the charged tethers interact with the incoming ions, and the momentum exchange generates a continuous propulsive acceleration whose modulus varies with the spacecraft attitude [6,7,8], and, unlike the solar sail case, it scales with the inverse heliocentric distance [9]. ...
... The latter, see Fig. 1, is defined as the angle between the Sun-spacecraft line and the unit vector normal to the E-sail nominal plane in the direction opposite to the Sun. An useful approximation of R = R(α n ) and T = T (α n ) is given in Ref. [8] ...
... Therefore, according to Eqs. (8) and (12), the variation of q with the angular coordinate θ is given by the following (approximate) equation ...
This work analyzes an approximate solution of the equations of motion for a spacecraft propelled by an Electric Solar Wind Sail with a fixed attitude. The peculiarity of such a propulsion system is that its thrust scales as the inverse heliocentric distance. This represents a substantial difference from a classical solar sail, whose propelling force is known to be proportional to inverse square distance from the Sun. Assuming a heliocentric, two-dimensional mission scenario, the polar form of the spacecraft trajectory equation is obtained for a closed parking orbit of given characteristics by means of an asymptotic expansion procedure. The proposed approach significantly improves the existing results as presented in the literature. A suitable choice of propulsion system parameters and parking orbit characteristics provides interesting similarities with recent solutions obtained for a solar sail-based spacecraft in a heliocentric, two-dimensional, mission scenario.
... The aim of this paper is to study, for the first time, the formation flight of E-sail based spacecraft in elliptic displaced orbits. The analysis uses the recent E-sail thrust model (Yamaguchi and Yamakawa, 2013;Quarta and Mengali, 2016), in which the propulsive acceleration modulus and the cone angle are both parameterized with numerical fitting polynomial equations as functions of the pitch angle. The relative motion of the spacecraft is addressed in the configuration space using suitable coordinate transformations that incorporate a set of displaced orbital elements. ...
... Each spacecraft is assumed to be equipped with an Esail, whose thrust model is taken from Yamaguchi and Yamakawa (2013) and thoroughly discussed in Quarta and Mengali (2016). In particular, Yamaguchi and Yamakawa (2013) represent the more recent evolution of the E-sail model used for mission analysis purposes, whose first appearance is in the works of Janhunen and Sandroos (2007). ...
... Since a belongs to the plane ðn;rÞ, the propulsive acceleration can be conveniently written as a function of the radial and normal unit vectors as (Quarta and Mengali, 2016) a ¼ a È rÈ r À Á j sin anÀa ð Þ sin anr þ sin a sin ann h i if a n 2 0; p=2 ð a È rÈ r À Ár if a n ¼ 0 ...
We present a geometrical methodology for analyzing the formation flying of electric solar wind sail based spacecraft that operate in heliocentric, elliptic, displaced orbits. The spacecraft orbit is maintained by adjusting its propulsive acceleration modulus, whose value is estimated using a thrust model that takes into account a variation of the propulsive performance with the sail attitude. The properties of the relative motion of the spacecraft are studied in detail and a geometrical solution is obtained in terms of relative displaced orbital elements, assumed to be small quantities. In particular, for the small eccentricity case (i.e. for a near-circular displaced orbit), the bounds characterized by the extreme values of relative distances are analytically calculated, thus providing an useful mathematical tool for preliminary design of the spacecraft formation structure.
... Accordingly, this paper assumes that the spacecraft is equipped with an E-sail whose more recent thrust model has been introduced by Yamaguchi and Yamakawa [14] and thoroughly analyzed, for a minimumtime heliocentric-transfer mission scenario, in a recent paper by Quarta and Mengali [18]. To summarize the advanced thrust model [14] conveniently, letn be the unit vector normal to the nominal plane containing the E-sail tethers, in the direction opposite to the Sun. ...
... According to Refs. [14,18], the E-sail propulsive acceleration vector a is a suitable function of both the Sun-spacecraft distance r, and the sail pitch angle α n ∈ [0, 90] deg, defined as the angle between the direction ofn and the direction of the spacecraft position unit vectorr (i.e. the direction of the spacecraft position vector measured from O), viz. ...
... For an in depth analysis of the thrust mathematical model for mission analysis purposes, the interested reader is referred to Refs. [15,18]. ...
This paper analyzes the performance of an Electric Solar Wind Sail for generating and maintaining an elliptic, heliocentric, displaced non-Keplerian orbit. In this sense, this paper extends and completes recent studies regarding the performances of an Electric Solar Wind Sail that covers a circular, heliocentric, displaced orbit of given characteristics. The paper presents the general equations that describe the elliptic orbit maintenance in terms of both spacecraft attitude and performance requirements, when a refined thrust model (recently proposed for the preliminary mission design) is taken into account. In particular, the paper also discusses some practical applications on particular mission scenarios in which an analytic solution of the governing equations has been found.
... The origin C of T coincides with the center of mass of the spacecraft and the x-axis is aligned with the conducting tether. Plane (î,ĵ), which is perpendicular to the spin-unit vectork, coincides with the E-sail nominal plane [20] According to Ref. [19], the propulsive acceleration vector a given by a single-tether E-sail can be analytically described as Eq. (1): ...
... A comparison of Eqs. (11) and (20) indicates that the optimal control law is equivalent to Eq. (12) by simply substituting α d with α λ , that is ...
This study analyzes the optimal transfer trajectory of a spacecraft propelled by a spin-stabilized electric solar wind sail (E-sail) with a single conducting tether and a spin axis with a fixed direction in an inertial (heliocentric) reference frame. The approach proposed in this study is useful for rapidly analyzing the optimal transfer trajectories of the current generation of small spacecraft designed to obtain in-situ evidence of the E-sail propulsion concept. In this context, starting with the recently proposed thrust model for a single-tether E-sail, this study discusses the optimal control law and performance in a typical two-dimensional interplanetary transfer by considering the (binary) state of the onboard electron emitter as the single control parameter. The resulting spacecraft heliocentric trajectory is a succession of Keplerian arcs alternated with propelled arcs, that is, the phases in which the electron emitter is switched on. In particular, numerical simulations demonstrated that a single-tether E-sail with an inertially fixed spin axis can perform a classical mission scenario as a circle-to-circle two-dimensional transfer by suitably varying a single control parameter.
... which is illustrated in Fig. 1.7(a). The latter highlights that the maximum thrust angle is about 20 deg and, as such, an E-sail has a limited capability of generating a transverse thrust component (Quarta et al., 2016). Moreover, similarly to the solar sail case, the same value of φ can be obtained with two different values of α. ...
... Unlike the circular DNKO case, a switching parameter τ ∈ [0, 1] has been inserted in the equations because the spacecraft thrust must now be modulated for orbital maintenance. In the solar sail case, such a thrust modulation may be achieved by means of electrochromic control devices (Aliasi et al., 2013b;Funase et al., 2011;Lücking et al., 2012;Mengali et al., 2016), which change their optical properties when a voltage is applied (Monk et al., 2007). On the other hand, for an E-sail the thrust modulation can be obtained by adjusting the grid voltage (Toivanen et al., 2013(Toivanen et al., , 2017, which is directly proportional to the propulsive acceleration magnitude (Huo et al., 2018). ...
A displaced non-Keplerian orbit is a trajectory whose orbital plane does not contain the center of mass of the primary body, so that its orbital maintenance requires the application of a suitable continuous thrust. Although the latter could be provided, in principle, by a low-thrust electric propulsion system, innovative propellantless propulsive technologies are well suited to such a mission scenario, due to their ability to generate thrust without requiring any propellant, thus significantly extending mission lifetime. This chapter focuses on the possibility of maintaining a displaced non-Keplerian orbit by means of both solar sails and electric solar wind sails (or E-sails). In fact, these advanced propulsion systems are both capable of generating a propulsive acceleration without consuming any propellant, by exploiting the solar radiation pressure (in case of solar sails) or the solar wind dynamic pressure (E-sails). This analysis uses recent models to provide a mathematical description of the propulsive acceleration generated by both propulsion systems, and different scenarios involving non-Keplerian orbits are analyzed. Particular focus is given to Type II displaced orbits, non-Keplerian orbits lying on the ecliptic plane, and heliostationary positions. Performance and attitude requirements are provided for each scenario. A linear stability analysis is also performed, in order to identify the combination of orbital parameters that characterize stable non-Keplerian orbits. The results suggest the feasibility of the mission scenarios discussed, but for most of them performance requirements are very demanding. A possible exception is non-Keplerian orbits lying on the ecliptic, which represent a very promising near-term scenario.
... Currently, NASA's Advanced Composition Explorer (ACE) is monitoring the solar activity while tracking a Lissajous orbit around the Sun-Earth L 1 point, which guarantees an early warning time of about 1 hour [9]. In principle, such a warning time could be further increased by means of propellantless propulsion systems such as solar sails or electric solar wind sails [10,11,12], which are able to artificially displace the collinear point towards the Sun by exploiting a continuous (outward) radial thrust. In this regard, the Authors [13] have recently analyzed the impact of solar wind fluctuations [14] on the dynamics of an electric solar wind sail orbiting around the Sun-Earth L 1 point. ...
... The (linearized) spacecraft dynamics around the design L 1 -type AEP is obtained by substituting Eq. (24) into Eq. (1), subtracting the equilibrium condition (10), and neglecting the second order terms. The resulting dynamical equations in the vicinity of an L 1 -type point are in the forṁ ...
A solar sail generates thrust without consuming any propellant, so it constitutes a promising option for mission scenarios requiring a continuous propulsive acceleration, such as the maintenance of a (collinear) L1-type artificial equilibrium point in the Sun-[Earth+Moon] circular restricted three-body problem. The usefulness of a spacecraft placed at such an artificial equilibrium point is in its capabilities of solar observation, as it guarantees a continuous monitoring of solar activity and is able to give an early warning in case of catastrophic solar flares. Because those vantage points are known to be intrinsically unstable, a suitable control system is necessary for station keeping purposes. This work discusses on how to stabilize an L1-type artificial equilibrium point with a solar sail by suitably adjusting its lightness number and thrust vector orientation. A full-state feedback control law is assumed, where the control gains are chosen with a linear-quadratic regulator approach. In particular, the numerical simulation results show that an L1-type artificial equilibrium point can be maintained with small required control torques, by using a set of reflectivity control devices.
... An advanced solar wind force model in which the thrust angle and magnitude were expressed as a form of the polynomial function of the sail inclination was proposed [19]. Even assuming this advanced force model, the E-sail still can conduct missions such as accelerating an impactor [17] and minimum-time circle-to-circle transfers [19,20]. In Ref. [21], the E-sail force model was refined with an analytical/geometrical approach. ...
... Weight coefficients w 1 , w 2 , and w 3 are also introduced. The spacecraft transverse velocity and sun-spacecraft distance at the terminal = t t F were used as the final boundary condition for circle-to-circle rendezvous missions [12,19,20]. When the eccentricity of the target orbit is zero, the boundary condition enables us to leave the spacecraft angular position and velocity free. ...
The electric solar wind sail is a propulsion system that extracts the solar wind momentum for the thrust force of a spacecraft by using an interaction between solar wind protons and the electric potential structure around charged long thin conducting tethers. The system enables a spacecraft to generate a thrust force without consuming
reaction mass. This paper investigates the capability of the electric solar wind sail as a propulsion system for deep space exploration missions. The shape of the conducting tether that is determined by the equilibrium of the solar wind force and centrifugal force is numerically calculated for formulating an advanced solar wind force
model. The conducting tethers deviate from the ideal sail spin plane, and the maximum value of the thrust direction varies from 13∘ to 19∘. To estimate the spacecraft thrust vector, which is calculated as the sum of solar wind force vectors exerted on each tether, best-fit polynomial equations are proposed. We performed numerical simulations for a two-dimensional orbital transfer mission to investigate the capability of the electric solar wind sail. Results of numerical simulations show that the electric solar wind sail enables spacecraft to perform Earth-Venus, Earth-Mars, and Earth-Itokawa transfer missions. Additionally, this paper performs three-dimensional
simulations for an Earth–Ryugu transfer mission. The electric solar wind sail achieves a more complicated orbital transfer in a reasonable mission time.
... The results associated to locally-optimal trajectories can be used as a starting guess for a succeeding analysis of globally optimal trajectories, in which, for example, an approach based on the classical calculus of variations 5 or on direct optimization algorithms 6 is used to find the minimum flight time. Unlike most of the existing results on E-sail mission design, which are obtained with a simplified thrust model 5,7 , this paper uses the most recent E-sail thrust mathematical model 8,9,10 that accounts for a dependence of both the modulus and direction of the thrust vector on the spacecraft attitude. ...
... the latter being the angle betweenê r andn. The value of the maximum pitch angle is taken equal to α nmax π/3 rad, in order to prevent the E-sail from possible mechanical instabilities10 . Accordingly, the three spacecraft scalar control variables are {α n , δ, τ }. ...
This paper analyzes the locally-optimal heliocentric transfer of a spacecraft propelled by an electric solar wind sail, an innovative propellantless propulsion system that generates a propulsive acceleration exploiting the momentum of solar wind particles. The potentialities of such an advanced thruster are investigated in terms of flight times required to achieve a given heliocentric orbit. The problem is addressed using a locally-optimal formulation, by minimizing a scalar performance index that depends on the time derivatives of the osculating orbital elements. The proposed algorithm gives an estimate of the globally-optimal flight time with reduced computational efforts compared to a traditional optimization approach. Also, when the performance index involves a single orbital parameter and the transfer trajectory is two-dimensional, the proposed approach provides an analytical solution to the locally-optimal control problem. The procedure discussed in the paper is used to quantify the near-optimal performance of an electric solar wind sail in some advanced mission scenarios, such as the design of a heliocentric non-Keplerian orbit for solar activity monitoring, the exploration of the Solar System boundaries, and the rendezvous with comets 1P Halley and 67P/Churyumov-Gerasimenko.
... In the recent literature several interplanetary mission analyses have been conducted using an E-sail as primary propulsion system [11,12,13]. Usually, the E-sail is described in a simplified way assuming that the tether arrangement looks like a rigid disc [14,15]. In such an ideal configuration, the propulsive acceleration may be analytically modeled using the recent results by Huo et al. [16]. ...
The Electric Solar Wind Sail is an innovative propulsion system that gains thrust from the interaction of the incoming ions from the solar wind with an artificial electric field produced by means of long charged tethers, which are deployed and maintained stretched by rotating the spacecraft around a spin axis. Under the combined interaction between solar wind dynamic pressure and centrifugal force, the tethers reach an equilibrium configuration whose spatial shape must be known for obtaining a reasonable estimate of the propulsive acceleration, a fundamental information for preliminary mission analysis purposes. This problem has been addressed in recent papers, which deal with the analytical expressions of thrust and torque vectors of a spinning and axially-symmetric Electric Solar Wind Sail. The torque acting on the sail induces a perturbation on the orientation of the thrust vector, which is here studied by analyzing the attitude dynamics. Numerical simulations show that the spacecraft motion is characterized by an undamped precession combined with a nutation motion. The effect due to the torque acting on the spacecraft is to align the thrust direction along the Sun-sail line, thus reducing the maneuvering capabilities. This paper proposes an effective control law which is able to remove the torque by suitably adjusting the tether electric voltage. It is shown that the proposed solution maintains the nominal thrust magnitude, and requires a small electric voltage modulation.
... In this work, the heliocentric phasing maneuvers are therefore analyzed within an optimal framework, by minimizing the required flight time [30] and considering the nonlinear equations of motion of the E-sail-based spacecraft. In particular, the optimal control law of the E-sail attitude and the corresponding minimum maneuver time are obtained by means of an indirect approach. ...
The aim of this work is to investigate heliocentric phasing maneuvers performed by a spacecraft propelled by an Electric Solar Wind Sail, that is, an innovative propellantless propulsion system that consists of a spinning grid of charged tethers that uses solar wind momentum to produce thrust. It is assumed that the Electric Solar Wind Sail may be controlled by varying its attitude with respect to a classical orbital reference frame, and by switching the tether grid off to obtain Keplerian arcs along its phasing trajectory. The analysis is conducted within an optimal framework, the aim of which is to find both the optimal control law and the minimum-time phasing trajectory for a given angular drift along the (assigned) working orbit. A typical phasing scenario is analyzed, by considering either a drift ahead or a drift behind maneuver on a circular, heliocentric orbit of given radius. The paper also investigates the possibility of using an Electric Solar Wind Sail-based deployer to place a constellation of satellites on the same working orbit. In that case, the optimal flight time is obtained in a compact, semianalytical form as a function of both the propulsion system performance and the number of the sail-deployed satellites.
... An Electric Solar Wind Sail (E-sail) is a propellantless propulsion system [1,2] that gains thrust from the interaction of solar wind particles with a grid of long and charged tethers, which are kept at a high voltage level by means of an electron emitter [3]. The tethers are deployed and maintained stretched by spinning the spacecraft about its symmetry axis [4,5,6], so that the E-sail ideally takes the shape of a spoked wheel [7]; see Fig. 1. The propulsive acceleration vector may be described with the analytical model by Huo et al. [8], which incidentally shows that an E-sail does not generate any torque as long as its electrical voltage is uniform. ...
An Electric Solar Wind Sail is a propellantless propulsion system that gains thrust from the interaction of solar wind particles with a grid of long and charged tethers, which are deployed by spinning the spacecraft about its symmetry axis. In an ideal arrangement, the tethers are all stretched out and the sail takes the shape of a spoked wheel. Actually, the solar wind dynamic pressure warps the tethers and, therefore, the expressions of thrust and torque vectors are difficult to predict in analytical form. Recent works have shown that the bending of the tethers induces a disturbance torque, which can be counterbalanced through a modulation of the tether electrical voltage. Under the assumption that the Electric Solar Wind Sail behaves like an axially-symmetric rigid body, this paper proves that a modulation of the tether electrical voltage is also a feasible option for actively controlling and maintaining the spacecraft attitude. The proposed control law, which is analytically derived as a function of time and spacecraft attitude, is validated through numerical simulations.
... An E-sail heliocentric trajectory is often analyzed in an optimal framework, by looking for the optimal control law that minimizes the total time of flight required to reach a target celestial body [4,5]. In a preliminary mission analysis phase, the E-sail thrust vector is usually modelled by considering the sail as an ideally flat and axially-symmetric body, and assuming average values of the solar wind characteristics. ...
An Electric Solar Wind Sail (E-sail) is an innovative propellantless propulsion system that generates a propulsive acceleration by exchanging momentum with the solar wind charged particles. Optimal E-sail trajectories are usually investigated by assuming an average value of the solar wind characteristics, thus obtaining a deterministic reference trajectory. However, recent analyses have shown that the solar wind dynamic pressure should be modeled as a random variable and an E-sail-based spacecraft may hardly be steered toward a target celestial body in an uncertain environment with just an open-loop control law. Therefore, this paper proposes to solve such a problem with a combined control strategy that suitably adjusts the grid electric voltage in response to the measured value of the dynamic pressure, and counteracts the effects of the solar wind uncertainties by rectifying the nominal trajectory at suitably chosen points. The effectiveness of such an approach is verified by simulation using two-dimensional transfer scenarios.
... Owing to the potential of the E-sail in deep-space exploration, it has received increased interest in the past years [7], [8]. In particular, much effort has been devoted to the trajectory optimization and mission analysis of an E-sailbased spacecraft. ...
Electric solar wind sail (E-sail) is an innovative propulsion system, which can generate low and continuous thrust without any propellant by reflecting ions from the solar wind. Because the propulsive acceleration of E-sail is low and continuous, its trajectory is usually characterized by long flight time. In order to explore more flight plans, rapid trajectory design is useful for preliminary mission analysis and design. This paper presents a method for rapid generation of minimum-time, three-dimensional trajectories for an E-sail using the finite Fourier series shapebased method. Unlike the more conventional electric thruster, the thrust vector of an E-sail is constrained. In order to consider the characteristics of the E-sail thrust, inequality constraints of thrust acceleration are investigated based on a recent thrust model. The numerical simulation results show that the proposed method is useful to quickly design the flight trajectory of the E-sail by considering the actual characteristics of the thrust vector
... The latter is a propellantless and continuous-thrust propulsion concept [14,15,16], which essentially consists of a spinning grid of tethers, kept at a high positive potential by a power source and maintained stretched by the centrifugal force effect; see Fig. 1. In the proposed approach, The other (unknown) coefficients are instead obtained by minimizing the total flight time and by taking into account the constraints on the E-sail thrust vector magnitude and direction [17,18,19,20]. In particular, it is shown how those constraints may be fitted into the trajectory optimization algorithm by means of a compact, geometrical approach. ...
The aim of this paper is to propose a shape-based method in which the concept of Bezier curve is used to efficiently design the three-dimensional interplanetary trajectory of a spacecraft whose primary propulsion system is an Electric Solar Wind Sail. The latter is a propellantless propulsion concept that consists of a spinning grid of tethers, kept at a high positive potential by a power source and maintained stretched by the centrifugal force. The proposed approach approximates the time variation of the components of the spacecraft position vector using a Bezier curve function, whose geometric coefficients are calculated by optimizing the total flight time with standard numerical methods and enforcing the boundary conditions of a typical interplanetary rendezvous mission. The paper also discusses a geometrical approach to include, in the optimization process, the propulsive acceleration vector constraints obtained with the latest Electric Solar Wind Sail thrust model.
... The typical E-sail performance parameter in the preliminary mission phase is the spacecraft characteristic acceleration a c . Its value is usually assumed to remain constant along the whole spacecraft trajectory [27,28,29], and is written as [12] ...
The Electric Solar Wind Sail (E-sail) is a propellantless propulsion system that generates thrust by exploiting the interaction between a grid of tethers, kept at a high electric potential, and the charged particles of the solar wind. Such an advanced propulsion system allows innovative and exotic mission scenarios to be envisaged, including non-Keplerian orbits, artificial Lagrange point maintenance, and heliostationary condition attainment. In the preliminary mission analysis of an E-sail-based spacecraft, the local physical properties of the solar wind are usually specified and kept constant, while the E-sail propulsive acceleration is assumed to vary with the heliocentric distance, the sail attitude, and the grid electric voltage. However, the solar wind physical properties are known to be characterized by a marked variability, which implies a non-negligible uncertainty as to whether or not the solutions obtained with a deterministic approach are representative of the actual E-sail trajectory. The aim of this paper is to propose an effective method to evaluate the impact of solar wind variability on the E-Sail trajectory design, by considering the solar wind dynamic pressure as a random variable with a gamma distribution. In particular, the effects of plasma property fluctuations on E-sail trajectory are calculated with an uncertainty quantification procedure based on the generalized polynomial chaos method. The paper also proposes a possible control strategy that uses suitable adjustments of grid electric voltage. Numerical simulations demonstrate the importance of such a control system for missions that require a precise modulation of the propulsive acceleration magnitude.
... Assuming a two-dimensional mission scenario, introduce a heliocentric polar reference frame T (O; r, θ), where r is the Sun-spacecraft distance (with r ⊕ 1 au), and θ is the polar angle measured counterclockwise from the apse line of the parking orbit, see Fig. 2. Letî r (orî θ ) be the radial (or transverse) unit vector of the polar reference frame T . The E-sail propulsive acceleration vector a depends on the Sun-spacecraft distance r and the E-sail attitude through the pitch angle α n ∈ [−π/2, π/2] rad, defined as the angle between the Sun-spacecraft line and the normal to the E-sail nominal plane in the direction opposite to the Sun [14,15,17,18], see Fig. 2. In this two-dimensional scenario, the pitch angle is the only control variable. Starting from the geometrical analysis by [16], the propulsive acceleration vector a may be written in a compact form as ...
Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.
... Moreover, it is known that the actual geometric characteristics of the sail shape may significantly affect the performance of an E-sail-based spacecraft. Nevertheless, in a preliminary phase of mission design the mathematical model adopted to describe the sail shape must be simple enough to be successfully implemented within a simulation code, especially when optimal trajectories are investigated [14,15]. Indeed, in the latter case, a number of transfer trajectories need to be simulated to minimize a scalar performance index, such as the flight time [16,17,18,19]. ...
The Electric Solar Wind Sail is an innovative propulsion system concept that gains propulsive acceleration from the interaction with charged particles released by the Sun. The aim of this paper is to obtain analytical expressions for the thrust and torque vectors of a spinning sail of given shape. Under the only assumption that each tether belongs to a plane containing the spacecraft spin axis, a general analytical relation is found for the thrust and torque vectors as a function of the spacecraft attitude relative to an orbital reference frame. The results are then applied to the noteworthy situation of a Sun-facing sail, that is, when the spacecraft spin axis is aligned with the Sun-spacecraft line, which approximatively coincides with the solar wind direction. In that case, the paper discusses the equilibrium shape of the generic conducting tether as a function of the sail geometry and the spin rate, using both a numerical and an analytical (approximate) approach. As a result, the structural characteristics of the conducting tether are related to the spacecraft geometric parameters.
In this paper, the two-dimensional trajectory of a solar sail with fixed pitch angle from a heliocentric elliptical orbit is analytically approximated using the linear perturbation theory. The lightness number is defined as the perturbation coefficient and the analytical solution is expressed as a function of the propulsive acceleration and the orbital elements. Different from the assumption of small eccentricity in some other methods, the proposed method is applicable to solar sails flying away from a general heliocentric elliptical orbit. Additionally, in the long-period mission scenario, in order to reduce the approximation error caused by the change of the osculating orbit elements, rectification steps for all relevant elements are added to the trajectory approximation process. The trajectory obtained by numerical integration is used to compare the approximate accuracy of the analytical trajectory and the modified analytical approximations. Moreover, the comparative analytical trajectory derived by referring to another method is used to verify the superiority of the proposed analytical trajectories. For the propelled trajectory of 20 revolutions corresponding to solar sail with characteristic acceleration of 0.01 mm/s2, the relative error of the modified analytical trajectory compared with the numerically integrated trajectory can be as low as 10-6. The analytical solution and its rectification proposed in this paper can be used for the preliminary design and mission evaluation of interplanetary exploration missions, especially for long-term mission scenarios.
The Electric Solar Wind Sail (or E-sail) is a propellantless propulsion system conceived by Dr. Janhunen in 2004. An E-sail extracts momentum from the charged particles constituting the solar wind by means of long and electrically charged tethers, which are deployed and kept stretched by spinning the spacecraft about a symmetry axis. Trajectory analysis of an E-sail-based spacecraft is usually performed assuming that the tether arrangement resembles that of a rigid disc. However, this assumption may be inaccurate since the actual shape of each tether is affected by the chaotic interaction between the solar wind dynamic pressure and the centrifugal force due to the spacecraft spin. The first goal of this chapter is therefore to describe the thrust and torque vectors of a non-flat E-sail. Then, the orbital and the attitude dynamics of a spinning E-sail are analyzed separately due to the marked separation between their characteristic timescales, showing that the torque acting on the E-sail induces a perturbation on the orientation of the thrust vector. Accordingly, the modulation of the tether electrical voltage is proposed and investigated as a possible attitude control strategy. An effective control law is first obtained as a function of spacecraft attitude and time, and then validated through numerical simulations. Finally, two heliocentric mission scenarios (useful, for example, for the monitoring of near-Earth objects or the surveillance of solar activity) are analyzed, where the thrust vectoring of the E-sail is exploited for the generation of Earth-following orbits or the maintenance of a heliostationary equilibrium point.
Electric sail-based propulsion is an innovative propellant-less propulsion technology that generates continuous thrust through the interaction between an artificial electric field and the solar wind. In an electric sail, the propulsive acceleration is adjusted by controlling the attitude of its normal plane and the coefficient determining the maximum thrust. However, the attitude adjustment speed of the electric sail is relatively small and the direction of the normal vector is constrained. Consequently, the electric sail is required to maintain a continuous propulsive acceleration vector when flying by the intermediate targets in multitarget interplanetary exploration. Therefore, an indirect optimization of three-dimensional optimal continuous interplanetary trajectory for electric sails with refined thrust model is investigated in this article. First, the optimal propulsive angles and thrust adjustment coefficient of electric sails with a refined thrust model are derived using Pontryagin's minimum principle. Second, a homotopy function is introduced in the process of trajectory optimization with an indirect method to approximate the step of the thrust adjustment coefficient to improve the accuracy of numerical integration. Additionally, the initial costates of the electric sail are transformed from the numerical simulation results of the Bezier shaping approach (BSA) and integrative BSA (IBSA) using the Karush–Kuhn–Tucker condition. The numerical simulation results for the Earth–Mars rendezvous mission and the multitarget flyby mission reveal that the initial values of the costates are effective to implement an indirect optimization process of the optimal continuous trajectory for the rapid convergence of the electric sail. According to the numerical simulation results for multitarget mission, the indirect method is on average 2.5% better than the Gauss pseudospectral method (GPM) in overall index, and the calculation time is only 1.06% of GPM.
As an innovative spacecraft propellantless propulsion technology, the electric sail can generate electric fields that interact with the solar wind, generating continuous propulsive thrust. However, unlike conventional electric thrusters, the thrust vector of the electric sail is constrained, and the attitude cannot be adjusted quickly. Consequently, the position and velocity of each flight trajectory at the connecting node and the direction of propulsion acceleration must be continuous. In this study, the continuous trajectory optimization of the electric sail–based probe in multi-target exploration is investigated. An integrative Bezier shaping approach (IBSA) is proposed to realize the rapid optimization of a multi-target exploration trajectory with continuous acceleration. The relationship between boundary constraints, intermediate constraints, and Bezier basis function coefficients is derived, transforming the original continuous optimal control problem of multiple stages into a problem of nonlinear programming that naturally satisfies the boundary and intermediate constraints. Numerical simulation results demonstrate that the IBSA can obtain a better interplanetary trajectory with a shorter calculation time than that obtained with the traditional Bezier shaping approach using piecewise optimization. Furthermore, the simulation results are successfully applied to the initial value estimation of the Gauss pseudospectral method (GPM). Compared with the GPM, the proposed shaping approach differs from the objective function by approximately 2%–6%, but requires approximately 1.5% of the computational time. During the preliminary mission design stage, the IBSA can be used for rapid feasibility assessments of different electric sail–based probe mission profiles.
Book of Abstracts of the Sixth International Conference on Tethers in Space. Madrid, 12-14 June 2019, Edited by G. Sánchez-Arriaga, S. Naghdi, and S. Shahsavani.
A survey of highly non-Keplerian orbits with low-thrust propulsion is presented. Keplerian orbits neglect atmospheric drag, solar radiation pressure, nonspherical central bodies, and other perturbations. The term non-Keplerian has been used in reference to orbits where a perturbing or propulsive acceleration acts in addition to that of the effects of gravity. Highly-non-Keplerian orbits can be obtained by considering the dynamics of a low-thrust spacecraft in a rotating frame of reference, where the angular velocity of rotation of the frame of reference is used as a free parameter of the problem. Stationary solutions to the equations of motion can then be sought in this rotating frame of reference, which correspond to periodic, displaced orbits when viewed from an inertial frame of reference. The more thrust that an ion engine can generate, the greater the gravity gradient that can be compensated for and hence the more opportunities there are for applying non-Keplerian orbits.
http://www.sciencedirect.com/science/article/pii/S0094576515001290
The novel propellantless electric solar wind sail (E-sail) concept promises
efficient low thrust transportation in the solar system outside Earth's
magnetosphere. Combined with asteroid mining to provide water and synthetic
cryogenic rocket fuel in orbits of Earth and Mars, possibilities for affordable
continuous manned presence on Mars open up. Orbital fuel and water eliminate
the exponential nature of the rocket equation and also enable reusable
bidirectional Earth-Mars vehicles for continuous manned presence on Mars. Water
can also be used as radiation shielding of the manned compartment, thus
reducing the launch mass further. In addition, the presence of fuel in Mars
orbit provides the option for an all-propulsive landing, thus potentially
eliminating issues of heavy heat shields and augmenting the capability of
pinpoint landing. With this E-sail enabled scheme, the recurrent cost of
continuous bidirectional traffic between Earth and Mars might ultimately
approach the recurrent cost of running the International Space Station, ISS.
The existence and stability of artificial equilibrium points (AEPs) for an electric solar wind sail (ESWS)-based spacecraft was investigated within an elliptical restricted three-body problem under the assumption of constant orientation of the ESWS nominal plane. The equilibrium points belong to the plane on which the two primaries move and consist of segments along which the spacecraft oscillates back and forth synchronously to the motion of the planet. The linear stability analysis for the sun [Earth+moon] system has shown the existence of stable regions of AEPs close to the classical equilibrium Lagrange points L1 and L4. The propulsive acceleration required to generate AEPs in the neighborhood of the L1 point in the sun [Earth+moon] system is compatible with the capabilities of a first-order generation ESWS propulsion system.
An electric sail uses the solar wind dynamic pressure to produce a small but continuous thrust by interacting with an electric field generated around a number of charged tethers. Because of the weakness of the solar wind dynamic pressure, quantifiable in about 2 nPa at Earth's distance from the sun, the required tether length is of the order of some kilometers. Equipping a 100-kg spacecraft with 100 of such tethers, each one being of 10-km lengths, is sufficient to obtain a spacecraft acceleration of about 1 mm/s(2). These values render the electric sail a potentially competitive propulsion means for future mission applications. The aim of this paper is to provide a preliminary analysis of the electric sail performance and to investigate the capabilities of this propulsion system in performing interplanetary missions. To this end, the minimum-time rendezvous/transfer problem between circular and coplanar orbits is considered, and an optimal steering law is found using an indirect approach. The main differences between electric sail and solar sail performances are also emphasized.
Solar Sail propulsion has been validated in space (IKAROS, 2010) and soon several more solar-sail propelled spacecraft will be flown. Using sunlight for spacecraft propulsion is not a new idea. First proposed by Frederick Tsander and Konstantin Tsiolkovsky in the 1920's, NASA's Echo 1 balloon, launched in 1960, was the first spacecraft for which the effects of solar photon pressure were measured. Solar sails reflect sunlight to achieve thrust, thus eliminating the need for costly and often very-heavy fuel. Such "propellantless" propulsion will enable whole new classes of space science and exploration missions previously not considered possible due to the propulsive-intense maneuvers and operations required.
A simplified mathematical model has been developed to define the main spacecraft parameters, including the sail dimension and the total spacecraft mass, as a function of the desired artificial equilibrium point position. Finally, a simple steering logic, in the form of a proportional-integral-derivative control system, has been introduced for stabilizing the spacecraft about an Lagrange type point. A feasible solution is offered by a proportional-derivative (PD) control logic, which has been shown to guarantee an asymptotical stability, in the (x, y) plane, for the spacecraft trajectory. APD control logic, however, could produce unacceptable errors in the final spacecraft position when an uncertainty in the actual sail lightness number occurs. To get over this problem, a classical proportional-integral-derivative (PID) control law is used. Each reflective surface contributes to the total spacecraft acceleration by converting, with different efficiencies, the solar radiation pressure into propulsive thrust.
An analytical expression for the heliocentric trajectory of a spacecraft propelled by a low-performance electric sail is studied. Assuming that the sail pitch angle is maintained constant along the whole heliocentric trajectory, equation states that the angular momentum increases linearly with time according to the relationship. Under the assumption of constant sail pitch angle, the spacecraft trajectory can be found in a parametric manner, and the main characteristics of the osculating orbit can be obtained as a function of the flight time. The numerical simulations confirm the accuracy of the analytical solution even on timescales of several years. A constant pitch angle essentially corresponds to a constant angle between the electric sail nominal plane and the incoming solar wind flux. On the other hand, an approximate analytical expression for the spacecraft trajectory can be found if the initial parking orbit is circular.
The electric solar wind sail (E-sail) is a new type of propellantless
propulsion system for Solar System transportation, which uses the
natural solar wind for producing spacecraft propulsion. This paper
discusses a mass breakdown and a performance model for an E-sail
spacecraft that hosts a scientific payload of prescribed mass. In
particular, the model is able to estimate the total spacecraft mass and
its propulsive acceleration as a function of various design parameters
such as the tethers number and their length. A number of subsystem
masses are calculated assuming existing or near-term E-sail technology.
In light of the obtained performance estimates, an E-sail represents a
promising propulsion system for a variety of transportation needs in the
Solar System.
Mini-Magnetospheric Plasma Propulsion is a potentially revolutionary plasma propulsion concept that could enable spacecraft to travel out of the solar system at unprecedented speeds of 50 to 80 km s-1 or could enable travel between the planets for low power requirements of ~1 kW per 100 kg of payload and ~0.5 kg fuel consumption per day for acceleration periods of several days to a few weeks. The high efficiency and specific impulse attained by the system are due to its utilization of ambient energy, in this case the energy of the solar wind, to provide the enhanced thrust. Coupling to the solar wind is produced through a large-scale magnetic bubble or mini-magnetosphere generated by the injection of plasma into the magnetic field supported by solenoid coils on the spacecraft. This inflation is driven by electromagnetic processes, so that the material and deployment problems associated with mechanical sails are eliminated.
The investigation of the problem of outer planet missions based on minimagnetospheric plasma propulsion is presented. The concept of minimagnetospheric plasma propulsion is the creation of a large magnetic bubble around the spacecraft and to use the intersection between the artificial magnetic field and the solar wind. The thrust vector is constrained to remain inside a cone whose half-opening angle is equal to the tilted angle Αmax. The problem can be mathematically translated into an optimal formulation by finding the time histories of the control variables. A set of canonical units have been used in the integration of the differential equations to reduce their numerical sensitivity. The effectiveness of the control law has been demonstrated by simulating interplanetary rendezvous missions to the Jupiter. The simulations reveal significant differences with respect to the results achieved by a two dimensional trajectory model.
Electric sail for extracting momentum from the solar wind was described. Another way to use the solar wind momentum is to use a magnetic sail, which requires a superconducting one-dimensional loop wire of length smaller than the linear extent of the electric wire mesh. It was found that the electric sail does not need any magnetic fields or superconductors and its power requirements are modest. Accurate maneuvering is difficult but the method is expected to be well suited for missions whose purpose is just to travel fast out of the solar system across the heliosphere to interstellar space.
A semi-analytical model for the description of a missions with minimagnetospheric plasma propulsion (M2P2) system, is presented. This model considers both the radial thrust variations due to the presence of an azimuthal thrust component and the corresponding increase in propelling consumption. Numerical simulation revealed that a pure radial thrust provides better performance in mission time in case of small spacecrafts. The analytical results show that M2P2 could be a good option for new interplanetary missions.
A new concept, the magnetic sail, or 'magsail' is proposed which propels spacecraft by using the magnetic field generated by a loop of superconducting cable to deflect interplanetary or interstellar plasma winds. The performance of such a device is evaluated using both a plasma particle model and a fluid model, and the results of a series of investigations are presented. It is found that a magsail sailing on the solar wind at a radius of one astronautical unit can attain accelerations on the order of 0.01 m/sec squared, much greater than that available from a conventional solar lightsail, and also greater than the acceleration due to the sun's gravitational attraction. A net tangential force, or 'lift' can also be generated. Lift to drag ratios of about 0.3 appear attainable. Equations are derived whereby orbital transfers using magsail propulsion can be calculated analytically.
This work presents the outline and so far completed design of the Aalto-1 science mission. Aalto-1 is a multi-payload remote-sensing nanosatellite, built almost entirely by students. The satellite aims for a 500–900 km sun-synchronous orbit and includes an accurate attitude dynamics and control unit, a UHF/VHF housekeeping and S-band data links, and a GPS unit for positioning (radio positioning and NORAD TLE's are planned to be used as backup). It has three specific payloads: a spectral imager based on piezo-actuated Fabry–Perot interferometry, designed and built by The Technical Research Centre of Finland (VTT); a miniaturised radiation monitor (RADMON) jointly designed and built by Universities of Helsinki and Turku; and an electrostatic plasma brake designed and built by the Finnish Meteorological Institute (FMI), derived from the concept of the e-sail, also originating from FMI. Two phases are important for the payloads, the technology demonstration and the science phase. The emphasis is placed on technological demonstration of the spectral imager and RADMON, and suitable targets have already been chosen to be completed during that phase, while the plasma brake will start operation in the latter part of the science phase. The technology demonstration will be over in a relatively short time, while the science phase is planned to last two years. The science phase is divided into two smaller phases: the science observations phase, during which only the spectral imager and RADMON will be operated for 6–12 months and the plasma brake demonstration phase, which is dedicated to the plasma brake experiment for at least a year. These smaller phases are necessary due to the drastically different power, communication and attitude requirements of the payloads. The spectral imager will be by far the most demanding instrument on board, as it requires most of the downlink bandwidth, has a high peak power and attitude performance. It will acquire images in a series up to at least 20 spectral bands within the 500–900 nm spectral range, forming the desired spectral data cube product. Shortly before an image is acquired, the parallel visual spectrum camera will take a broader picture for comparison. Also stereoscopic imaging is planned. The amount of data collected by the spectral imager is adjustable, and ranges anywhere from 10 to 500 MB. The RADMON will be on 80% of an orbit period on average and together with housekeeping data will gather around 2 MB of data in 24 h. An operational limitation is formed due to the S-band downlink capability of 29–49 MB per 24 h for a 500 900 km orbit altitude, as only one ground station is planned to be available for the satellite. This will limit both type and quantity of spectral imager images taken during the science phase. The plasma brake will in turn be within an angle of 20° over the poles for efficient use of the Earth's magnetic field and ionosphere during its spin-up and operation.
Missions towards the boundaries of the Solar System require long transfer times and advanced propulsion systems. An interesting option is offered by electric sails, a new propulsion concept that uses the solar wind dynamic pressure for generating a continuous thrust without the need for reaction mass. The aim of this paper is to investigate the performance of such a propulsion system for obtaining escape conditions from the Solar System and planning a mission to reach the heliosphere boundaries. The problem is studied in an optimal framework, by minimizing the time to reach a given solar distance or a given hyperbolic excess speed. Depending on the value of the sail characteristic acceleration, it is possible that, in an initial mission phase, the sailcraft may approach the Sun to exploit the increased available thrust due to the growing solar wind electron density. The corresponding optimal trajectory is constrained to not pass inside a heliocentric sphere whose admissible radius is established by thermal constraints. Once the escape condition is met, the sail is jettisoned and the payload alone continues its journey without any propulsion system. A medium performance electric sail is shown to have the potentialities to reach the heliosheath, at a distance of 100 AU, in about fifteen years. Finally, the Interstellar Heliopause Probe mission is used as a reference mission to further quantify the electric sail capabilities for an optimal transfer towards the heliopause nose (200 AU).
An electric sail is capable of guaranteeing the fulfilment of a class of trajectories that would be otherwise unfeasible through
conventional propulsion systems. In particular, the aim of this paper is to analyze the electric sail capabilities of generating
a class of displaced non-Keplerian orbits, useful for the observation of the Sun’s polar regions. These orbits are characterized
through their physical parameters (orbital period and solar distance) and the spacecraft propulsion capabilities. A comparison
with a solar sail is made to highlight which of the two systems is more convenient for a given mission scenario. The optimal
(minimum time) transfer trajectories towards the displaced orbits are found with an indirect approach.
The electric solar wind sail (E-sail) is a space propulsion concept that uses the natural solar wind dynamic pressure for producing spacecraft thrust. In its baseline form, the E-sail consists of a number of long, thin, conducting, and centrifugally stretched tethers, which are kept in a high positive potential by an onboard electron gun. The concept gains its efficiency from the fact that the effective sail area, i.e., the potential structure of the tethers, can be millions of times larger than the physical area of the thin tethers wires, which offsets the fact that the dynamic pressure of the solar wind is very weak. Indeed, according to the most recent published estimates, an E-sail of 1 N thrust and 100 kg mass could be built in the rather near future, providing a revolutionary level of propulsive performance (specific acceleration) for travel in the solar system. Here we give a review of the ongoing technical development work of the E-sail, covering tether construction, overall mechanical design alternatives, guidance and navigation strategies, and dynamical and orbital simulations.
An electric solar wind sail is a recently introduced propellantless space propulsion method whose technical development has also started. The electric sail consists of a set of long, thin, centrifugally stretched and conducting tethers which are charged positively and kept in a high positive potential of order 20 kV by an onboard electron gun. The positively charged tethers deflect solar wind protons, thus tapping momentum from the solar wind stream and producing thrust. The amount of obtained propulsive thrust depends on how many electrons are trapped by the potential structures of the tethers, because the trapped electrons tend to shield the charged tether and reduce its effect on the solar wind. Here we present physical arguments and test particle calculations indicating that in a realistic three-dimensional electric sail spacecraft there exist a natural mechanism which tends to remove the trapped electrons by chaotising their orbits and causing them to eventually collide with the conducting tethers. We present calculations which indicate that if these mechanisms were able to remove trapped electrons nearly completely, the electric sail performance could be about five times higher than previously estimated, about 500 nN/m, corresponding to 1 N thrust for a baseline construction with 2000 km total tether length.
One possibility for propellantless propulsion in space is to use the momentum flux of the solar wind. A way to set up a solar wind sail is to have a set of thin long wires which are kept at high positive potential by an onboard electron gun so that the wires repel and deflect incident solar wind protons. The efficiency of this so-called electric sail depends on how large force a given solar wind exerts on a wire segment and how large electron current the wire segment draws from the solar wind plasma when kept at a given potential. We use 1-D and 2-D electrostatic plasma simulations to calculate the force and present a semitheoretical formula which captures the simulation results. We find that under average solar wind conditions at 1 AU the force per unit length is (5±1×10?8 N/m for 15 kV potential and that the electron current is accurately given by the well-known orbital motion limited (OML) theory cylindrical Langmuir probe formula. Although the force may appear small, an analysis shows that because of the very low weight of a thin wire per unit length, quite high final speeds (over 50 km/s) could be achieved by an electric sailing spacecraft using today's flight-proved components. It is possible that artificial electron heating of the plasma in the interaction region could increase the propulsive effect even further.
The electric solar wind sail (E-sail) is a space propulsion concept that uses the natural solar wind dynamic pressure for producing spacecraft thrust. In its baseline form, the E-sail consists of a number of long, thin, conducting, and centrifugally stretched tethers, which are kept in a high positive potential by an onboard electron gun. The concept gains its efficiency from the fact that the effective sail area, i.e., the potential structure of the tethers, can be millions of times larger than the physical area of the thin tethers wires, which offsets the fact that the dynamic pressure of the solar wind is very weak. Indeed, according to the most recent published estimates, an E-sail of 1 N thrust and 100 kg mass could be built in the rather near future, providing a revolutionary level of propulsive performance (specific acceleration) for travel in the solar system. Here we give a review of the ongoing technical development work of the E-sail, covering tether construction, overall mechanical design alternatives, guidance and navigation strategies, and dynamical and orbital simulations.
A hybrid optimization algorithm based on genetic algorithm and Gauss pseudospectral method is proposed for an electric sail to generate the optimal trajectory to explore Ceres. Plenty of simulations are carried out to verify the effectiveness of the proposed algorithm. Effects of mission starting date and characteristic acceleration of the electric sail on the exploration mission are also studied. Results show that the optimal transfer time varies periodically with the starting time. The period is close to the synodic period of Ceres. The optimal transfer time decreases with the characteristic acceleration. An acceptable transfer time can be achieved by an electric sail with a medium characteristic acceleration. Simulations illustrate the effectiveness of the proposed hybrid optimization algorithm, which is capable to obtain the optimal trajectory without any initial value guess.
An electric solar wind sail uses the natural solar wind stream to produce low but continuous thrust by interacting with a number of long thin charged tethers. It allows a spacecraft to generate a thrust without consuming any reaction mass. The aim of this paper is to investigate the use of a spacecraft with such a propulsion system to deflect an asteroid with a high relative velocity away from an Earth collision trajectory. To this end, we formulate a simulation model for the electric solar wind sail. By summing thrust vectors exerted on each tether, a dynamic model which gives the relation between the thrust and sail attitude is proposed. Orbital maneuvering by fixing the sail’s attitude and changing tether voltage is considered. A detailed study of the deflection of fictional asteroids, which are assumed to be identified 15 years before Earth impact, is also presented. Assuming a spacecraft characteristic acceleration of 0.5 mm/s 2, and a projectile mass of 1,000 kg, we show that the trajectory of asteroids with one million tons can be changed enough to avoid a collision with the Earth. Finally, the effectiveness of using this method of propulsion in an asteroid deflection mission is evaluated in comparison with using flat photonic solar sails.
An electric solar sail (E-sail) is a recent propellantless propulsion concept for a direct exploration of the solar system. An E-sail consists of an array of bare, conductive tethers at very high positive/negative bias, prone to extract solar-wind momentum by Coulomb deflection of protons. This paper focuses on the positive-bias case with a thick sheath that must be correctly modeled. Ion scattering within the sheath and the resulting thrust are determined. Use of E-sail for outer planet missions would reduce the time of flight; a 2-ton spacecraft might reach Jupiter in less than two years.
The aim of this paper is to quantify the performance of an Electric Solar Wind Sail for accomplishing flyby missions toward one of the two orbital nodes of a near-Earth asteroid. Assuming a simplified, two-dimensional mission scenario, a preliminary mission analysis has been conducted involving the whole known population of those asteroids at the beginning of the 2013 year. The analysis of each mission scenario has been performed within an optimal framework, by calculating the minimum-time trajectory required to reach each orbital node of the target asteroid. A considerable amount of simulation data have been collected, using the spacecraft characteristic acceleration as a parameter to quantify the Electric Solar Wind Sail propulsive performance. The minimum time trajectory exhibits a different structure, which may or may not include a solar wind assist maneuver, depending both on the Sun-node distance and the value of the spacecraft characteristic acceleration. Simulations show that over 60% of near-Earth asteroids can be reached with a total mission time less than 100 days, whereas the entire population can be reached in less than 10 months with a spacecraft characteristic acceleration of 1 mm/s(2).
An electric sail is a new propulsion system uses the solar wind dynamic pressure as a thrust force. We analyzed the probability of the orbital control not changing sail plane angle but switching an electron gun connected with tethers. First, locally optimal switching laws are derived from Lagrange variational equations analytically. By theoretical calculations and numerical simulations, these switching laws are effective for changing some orbital elements. Moreover, mission applicability is studied. Assuming minimum time transfer problem between circular and coplanar orbits, optimal control laws are studied with direct approach. We conclude that the switching orbital control method is effective for exploration of other planets.
This paper presents an overview and the current status of hosting the electrostatic plasma brake (EPB) experiment on-board the Finnish Aalto-1 satellite. The goal of the experiment is to demonstrate the use of an electrostatically charged tether for satellite attitude and orbital maneuvers. The plasma brake device is based on electrostatic solar sail concept, invented in Finnish Meteorological Institute (FMI). The electrostatic solar sail is designed to utilize the solar wind charged particles to propel the spacecraft by using long conductive tethers, surrounded by electrostatic field. Similar phenomenon can be used in low Earth orbit
plasma environment, where the relative motion between the electrostatically charged tether and the ionospheric plasma can produce a significant amount of drag. This drag can be utilized for deorbiting the satellite. The Aalto-1, a multi-payload CubeSat, will carry, among others, the plasma brake payload. Plasma brake payload consists of a 100 m long conductive tether, a reel mechanism for tether storage, a high voltage source, and electron guns to maintain the tether charge. The experiment will be performed in positive
and negative tether charge modes and includes a long term passive deorbiting mode. The experiment hardware, the satellite mission and different phases of the experiment are presented.
A charged tether or wire experiences Coulomb drag when inserted into flowing
plasma. In the solar wind the Coulomb drag can be utilised as efficient
propellantless interplanetary propulsion as the electric solar wind sail
(electric sail, E-sail). In low Earth orbit (LEO) the same plasma physical
effect can be utilised for efficient low-thrust deorbiting of space debris
objects (the plasma brake). The E-sail is rotationally stabilised while the
deorbiting Coulomb drag devices
According to numerical estimates, Coulomb drag devices have very promising
performance figures, both for interplanetary propulsion and for deorbiting in
LEO. Much of the technology is common to both applications. E-sail technology
development was carried out in ESAIL FP7 project (2011-2013) which achieved TRL
4-5 for key hardware components that can enable 1 N class interplanetary E-sail
weighing less than 200 kg. The thrust of the E-sail scales as inverse solar
distance and its power consumption (nominally 700 W/N at 1 au) scales as the
inverse distance squared. As part of the ESAIL project, a continuous 1 km
sample of E-sail tether was produced by an automatic and scalable "tether
factory". The manufacturing method uses ultrasonic wire to wire bonding which
was developed from ordinary wire to plate bonding for the E-sail purpose. Also
a "Remote Unit" device which takes care of deployment and spin rate control was
prototyped and successfully environmentally tested. Our Remote Unit prototype
is operable in the solar distance range of 0.9-4 au.
The 1-U CubeSat ESTCube-1 was launched in May 2013 and it will try to measure
the Coulomb drag acting on a 10 m long tether in LEO when charged to 500 V
positive or negative. A more advanced version of the experiment with 100 m
tether is under preparation and will be launched in 2015 with the Aalto-1 3-U
CubeSat to polar LEO.
BETs is a three-year project financed by the Space Program of the European Commission, aimed at developing an efficient deorbit system that could be carried on board any future satellite launched into Low Earth Orbit (LEO). The operational system involves a conductive tape-tether left bare to establish anodic contact with the ambient plasma as a giant Langmuir probe. As a part of this project, we are carrying out both numerical and experimental approaches to estimate the collected current by the positive part of the tether. This paper deals with experimental measurements performed in the IONospheric Atmosphere Simulator (JONAS) plasma chamber of the Onera-Space Environment Department. The JONAS facility is a 9- vacuum chamber equipped with a plasma source providing drifting plasma simulating LEO conditions in terms of density and temperature. A thin metallic cylinder, simulating the tether, is set inside the chamber and polarized up to 1000 V. The Earth's magnetic field is neutralized inside the chamber. In a first time, tether collected current versus tether polarization is measured for different plasma source energies and densities. In complement, several types of Langmuir probes are used at the same location to allow the extraction of both ion densities and electron parameters by computer modeling (classical Langmuir probe characteristics are not accurate enough in the present situation). These two measurements permit estimation of the discrepancies between the theoretical collection laws, orbital motion limited law in particular, and the experimental data in LEO-like conditions without magnetic fields. In a second time, the spatial variations and the time evolutions of the plasma properties around the tether are investigated. Spherical and emissive Langmuir probes are also used for a more extensive characterization of the plasma in space and time dependent analysis. Results show the- ion depletion because of the wake effect and the accumulation of ions upstream of the tether. In some regimes (at large positive potential), oscillations are observed on the tether collected current and on Langmuir probe collected current in specific sites.
JAXA launched the world's first deep space solar sail demonstration spacecraft “IKAROS” on May 21, 2010. IKAROS was injected to an Earth–Venus trajectory to demonstrate several key technologies for solar sail utilizing the deep space flight environment. IKAROS succeeded in deploying a 20m-span solar sail on June 9, and is now flying towards the Venus with the assist of solar photon acceleration. This paper describes the mission design, system design, solar sail deployment operation and current flight status of IKAROS.
In the early 2000s, NASA made substantial progress in the development of solar sail propulsion systems for use in robotic science and exploration of the solar system. Two different 20-m solar sail systems were produced. NASA has successfully completed functional vacuum testing in their Glenn Research Center’s Space Power Facility at Plum Brook Station, Ohio. The sails were designed and developed by Alliant Techsystems Space Systems and L’Garde, respectively. The sail systems consist of a central structure with four deployable booms that support each sail. These sail designs are robust enough for deployment in a one-atmosphere, one-gravity environment and are scalable to much larger solar sails – perhaps as large as 150 m on a side. Computation modeling and analytical simulations were performed in order to assess the scalability of the technology to the larger sizes that are required to implement the first generation of missions using solar sails. Furthermore, life and space environmental effects testing of sail and component materials was also conducted.NASA terminated funding for solar sails and other advanced space propulsion technologies shortly after these ground demonstrations were completed. In order to capitalize on the $30 M investment made in solar sail technology to that point, NASA Marshall Space Flight Center funded the NanoSail-D, a subscale solar sail system designed for possible small spacecraft applications. The NanoSail-D mission flew on board a Falcon-1 rocket, launched August 2, 2008. As a result of the failure of that rocket, the NanoSail-D was never successfully given the opportunity to achieve orbit. The NanoSail-D flight spare was flown in the Fall of 2010. This review paper summarizes NASA’s investment in solar sail technology to date and discusses future opportunities.
The aim of this paper is to study, from a mission analysis point of view, the performance of a hybrid propulsion concept for a two-dimensional transfer towards a planet of the Solar System. The propulsion system is obtained by combining a chemical thruster, used for the phases of Earth escape and/or target planet capture, with an electric sail, which provides a continuous thrust during the heliocentric transfer. Two possible mission scenarios are investigated: in the first case the sailcraft reaches the target planet with zero hyperbolic excess velocity, thus performing a classical rendezvous mission in a heliocentric framework. In the second mission scenario, a given final hyperbolic excess velocity relative to the planet is tolerated in order to decrease the mission flight time. The amount of final hyperbolic excess velocity is used as a simulation parameter for a tradeoff study in which the minimum flight time is related to the total velocity variation required by the chemical thruster to accomplish the mission, that is, for Earth escape and planetary capture.
In the early to mid-2000s, NASA made substantial progress in the development of solar sail propulsion systems. Solar sail propulsion uses the solar radiation pressure exerted by the momentum transfer of reflected photons to generate a net force on a spacecraft. To date, solar sail propulsion systems were designed for large robotic spacecraft. Recently, however, NASA has been investigating the application of solar sails for small satellite propulsion. The NanoSail-D is a subscale solar sail system designed for possible small spacecraft applications. The NanoSail-D mission flew on board the ill-fated Falcon Rocket launched August 2, 2008, and due to the failure of that rocket, never achieved orbit. The NanoSail-D flight spare is ready for flight and a suitable launch arrangement is being actively pursued. This paper will present an introduction solar sail propulsion systems and an overview of the NanoSail-D spacecraft.
- L Friedman
L. Friedman, Starsailing: Solar Sails and Interstellar Travel, 1st edition, Science
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Achievement of IKAROS -Japanese deep space solar sail demonstration mission
- Y Tsuda
- O Mori
- R Funase
- S Hirotaka
- T Yamamoto
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- H Hoshino
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Y. Tsuda, O. Mori, R. Funase, S. Hirotaka, T. Yamamoto, T. Saiki, T. Endo, K.
Yonekura, H. Hoshino, J. Kawaguchi, Achievement of IKAROS -Japanese deep
space solar sail demonstration mission, in: G. Genta (Ed.), Missions to the Outer
Solar System and Beyond, Seventh IAA Symposium on Realistic Near-Term Advanced Scientific Space Missions, Aosta, Italy, 2011.
Attitude control of IKAROS solar sail spacecraft and its flight results
- O Mori
- Y Tsuda
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- T Saiki
- Y Mimasu
- J Kawaguchi
O. Mori, Y. Tsuda, Y. Shirasawa, T. Saiki, Y. Mimasu, J. Kawaguchi, Attitude control of IKAROS solar sail spacecraft and its flight results, in: 61st International
Astronautical Congress, Prague, Czech Republic, 2010, paper IAC-10.C1.4.3.
Solar sails: technology and demonstration status
- L Johnson
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- L Friedman
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- C R Mcinnes
L. Johnson, R. Young, N. Barnes, L. Friedman, V. Lappas, C.R. McInnes, Solar
sails: technology and demonstration status, Int. J. Aeronaut. Space Sci. 13 (4)
(2012) 421-427, http://dx.doi.org/10.5139/IJASS.2012.13.4.421.
Status of solar sail technology within NASA
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L. Johnson, R. Young, E. Montgomery, D. Alhorn, Status of solar sail technology within NASA, Adv. Space Res. 48 (11) (2011) 1687-1694, http://dx.doi.org/
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Survey of highly-non-Keplerian orbits with low-thrust propulsion
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- M Macdonald
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R.J. McKay, M. Macdonald, J.D. Biggs, C.R. McInnes, Survey of highly-non-Keplerian orbits with low-thrust propulsion, J. Guid. Control Dyn. 34 (3) (2011)
645-666, http://dx.doi.org/10.2514/1.52133.
Use of magnetic sails for mars exploration missions
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- R M Zubrin
D.G. Andrews, R.M. Zubrin, Use of magnetic sails for mars exploration missions, in: AIAA/ASME/SAE/ASEE 25th Joint Propulsion Conference, Monterey
(CA), 1989, paper AIAA 89-2861.
The use of magnetic sails to escape from low earth orbit
- R M Zubrin
R.M. Zubrin, The use of magnetic sails to escape from low earth orbit, in:
AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, Sacramento (CA), 1991,
paper AIAA 91-3352.
Electric sail performance analysis
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- P Janhunen
G. Mengali, A.A. Quarta, P. Janhunen, Electric sail performance analysis, J.
Spacecr. Rockets 45 (1) (2008) 122-129, http://dx.doi.org/10.2514/1.31769.
Drifting plasma collection by a positive biased tether wire in LEO-like plasma conditions: current measurement and plasma diagnostics
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- P Sarrailh
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J. Siguier, P. Sarrailh, J. Roussel, V. Inguimbert, G. Murat, J. SanMartin, Drifting
plasma collection by a positive biased tether wire in LEO-like plasma conditions: current measurement and plasma diagnostics, IEEE Trans. Plasma Sci.
41 (12) (2013) 3380-3386, http://dx.doi.org/10.1109/TPS.2013.2257871.
Accommodating the plasma brake experiment on-board the Aalto-1 satellite
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- J Praks
- M Hallikainen
O. Khurshid, T. Tikka, J. Praks, M. Hallikainen, Accommodating the plasma
brake experiment on-board the Aalto-1 satellite, Proc. Est. Acad. Sci. 63 (2S)
(2014) 258-266, http://dx.doi.org/10.3176/proc.2014.2S.07.
EMMI -electric solar wind sail facilitated manned Mars initiative
- P Janhunen
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- M Paton
P. Janhunen, S. Merikallio, M. Paton, EMMI -electric solar wind sail facilitated
manned Mars initiative, Acta Astronaut. 113 (2015) 22-28, http://dx.doi.org/
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A graphical approach to electric sail mission design with radial thrust
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- A A Quarta
- G Aliasi
G. Mengali, A.A. Quarta, G. Aliasi, A graphical approach to electric sail mission design with radial thrust, Acta Astronaut. 82 (2) (2013) 197-208, http://
dx.doi.org/10.1016/j.actaastro.2012.03.022.
Electric solar wind sail kinetic energy impactor for near earth asteroid deflection mission
- K Yamaguchi
- H Yamakawa
K. Yamaguchi, H. Yamakawa, Electric solar wind sail kinetic energy impactor
for near earth asteroid deflection mission, J. Astronaut. Sci. 63 (1) (1 March
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European Planetology Network and the European Geosciences Union
- P Janhunen
P. Janhunen, The electric solar wind sail status report, in: European Planetary
Science Congress 2010, vol. 5, European Planetology Network and the European
Geosciences Union, 2010, paper EPSC 2010-297.