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07:30-08:00Morning Coffee
08:15-09:00 Session 9: Keynote


Achieving Science with CubeSats: Thinking Inside the Box

ABSTRACT. We present the results of a study conducted by the National Academies of Sciences, Engineering, and Medicine. The study focused on the scientific potential and technological promise of CubeSats. We will first review the growth of the CubeSat platform from an education-focused technology toward a platform of importance for technology development, science, and commercial use, both in the United States and internationally. The use has especially exploded in recent years. For example, of the over 400 CubeSats launched since 2000, more than 80% of all science-focused ones have been launched just in the past four years. Similarly, more than 80% of peer-reviewed papers describing new science based on CubeSat data have been published in the past five years.

We will then assess the technological and science promise of CubeSats across space science disciplines, and discuss a subset of priority science goals that can be achieved given the current state of CubeSat capabilities. Many of these goals address targeted science, often in coordination with other spacecraft, or by using sacrificial or high-risk orbits that lead to the demise of the satellite after critical data have been collected. Other goals relate to the use of CubeSats as constellations or swarms, deploying tens to hundreds of CubeSats that function as one distributed array of measurements.

Finally, we will summarize our conclusions and recommendations from this study; especially those focused on near-term investment that could improve the capabilities of CubeSats toward increased science and technological return and enable the science communities’ use of CubeSats.

09:00-10:20 Session 10: Subsystem Technologies to Enable Space Tether Missions
Examination of Deployment Performance of Super-Tether in Inverse-Origami Method (Invited)

ABSTRACT. The super tape is a bare electrodynamic tape tether which has superior properties than thin tether as Hoyt tether in anti debris feature and high electron collection characteristics. The super tether is thus expected to play important roles in space debris mitigation and space elevator construction. .A spaceflight validation of bare electrodynamic tape tether technology was conducted on a S520-25 sounding rocket launched successfully on August 2010 and successfully deployed 132.6m of tape tether over 120 seconds in a ballistic flight. The results of flight experiment are examined as the premier report of the international cooperation between Japan, Europe, USA and Australia. This talk reports a variety of experimental studies of the pre- and post flight examinations of the folded tape deployment in the inverse-Origami method, including more than dozen methods of examination, vertical ejection, horizontal ejection, inclined ejection, vertical and horizontal extraction, in the environments of rotational, micro-gravity, vacuum and their combinations, numerical studies, and on launch condition. The report is expected to serve as the useful employment of the super tether for such future space development as debris mitigation and also space elevator system.

Past Results and Future Plans for Tether Technology Demonstration in STARS Project

ABSTRACT. STARS (Space Tethered Autonomous Robotic Satellite) project purposes to evaluate and to verify a space mechanical control system by a university satellite, whose characteristics are: it consists of a mother and a daughter (and grandchildren in future) satellites; it becomes a large scale space system using tether; and also robotic mechanical system performs dynamic motion on orbit. The first satellite of the project was "STARS," which was launched by the H-IIA rocket on 23, January, 2009. It was a mother-daughter satellite, a tethered satellite, and also a robotic satellite. These three main characteristics have been evaluated and verified successfully on orbit, though attitude control for a tethered space robot could not be performed due to shorter tether extension than expected. On 31, August, 2010, TSR-S (Tethered Space Robot -S) was launched by the sounding rocket S-520-25 from Uchinoura Space Centre. One of S-520-25 experiments is for a tethered space robot. The proposed attitude control approach for disturbances suppression and change of the desired attitude for a tethered space robot have been evaluated and verified. The second satellite of the project was “STARS-II,” which was launched by the H-IIA rocket on 28, February, 2014. It was also a mother-daughter satellite, a tethered satellite, and a robotic satellite as well as STARS. However, tether was 300m long (5m long on STARS) and Electro Dynamic Tether (EDT). 300m tether deployment was evaluated by orbital altitude change, though telemetry data from the satellites was not sufficient. Currently, the project is developing “STARS-C”, which will be deployed into orbit from ISS (International Space Station) in 2016. It is a 2U Cubesat, and one is a mother and the other is a daughter satellite. They are connected by 100m long Kevlar tether. Its primary purpose is to analyze basic tether dynamics motion on orbit experimentally. Also, the project just starts to develop “STARS-E”, which is an orbital space elevator. It consists of a mother and a daughter satellites, and a grandchild satellite, which is a climber to translate on tether. Technology demonstration of STARS-E can be applied to orbital transportation, transfer, and the first step for space elevator to Geo Situational orbit. This paper describes past mission results, future mission plans, and also future practical missions.

ARACMO: Tethered Mobility for Planetary Exploration
SPEAKER: unknown

ABSTRACT. To enable future robotic exploration systems to have greater mobility capabilities on difficult terrain such as craters, cliffs, gullies, and skylights, Tethers Unlimited is developing the “Advanced Regolith Anchoring for Cable-assisted Mobility” (ARACMO) Anchor. This device can launch hundreds of meters from a rover vehicle, self-right, autonomously anchor, and support high loads through the attached tether. This will enable the rover to rappel, climb, or maneuver over otherwise insurmountable terrain utilizing the stability that a strong anchoring point affords. In this paper we will present a design summary and preliminary test results for an ice-anchoring ARACMO system intended for integration into the JPL Axel Rover vehicle to enable enhanced exploration of Europa and its geologic double ridges, as well as a preliminary design for a rotary percussive anchoring version intended for rocky terrain such as on Mars.

Instant-Start Hollow Cathodes for Electrodynamic Tether Applications
SPEAKER: John Williams

ABSTRACT. Prototype hollow cathodes are described that have been developed and tested for Electrodynamic Tether (EDT) applications that use a low-work-function, electron-emitting material for the insert that can be inexpensively formed in a simple one-step process. Cathodes equipped with this type of insert can be started instantly from room temperature. This paper discusses recent results obtained using cathodes with an outer diameter of 9.5 mm, although we have tested cathodes with 3.2 mm and 6.4 mm diameters as well. Data from an ongoing wear test is presented along with measurements made on two cathodes with different orifice channel lengths. The measurements included bias voltage and temperature recorded over a range of emission current and flow rate of argon. Efforts to develop a steady-state, 1-D model of the insert and orifice regions are presented along with plans to extend the model to treat transients at startup and when the emission current changes.

10:20-10:40Coffee Break
10:40-12:00 Session 11: Space Tether Modeling Techniques I
Distributed Control Law for Nonovershooting Deployment of Tethered Satellites System
SPEAKER: unknown

ABSTRACT. This paper proposes a new distributed control law with input limitation for the nonovershooting and stable deployment control problem of space tethered satellites system. A dynamics of tethered satellites system based on the method of distributed control is developed by referring to dynamics of space tether deployment. Meanwhile, we design a nonovershooting deployment trajectory and propose a new distributed control law. Then we apply this control law to a series of simulation of deployment trajectory-tracking and analyze simulation results in different cases. The results show that the distributed control law can deploy the tethered satellites stably without overshoot and the tether always be kept positive that we desired. The effectiveness and advantage of the distributed control law is validated by computer simulation and this method provides a certain reference for applying it to future space tethered satellites deployment. 

Deorbit with Bare Tether System from High Eccentricity Initial Orbit: Analyses and Numerical Simulations
SPEAKER: Guido Pastore

ABSTRACT. The implementation of deorbit procedures for space debris mitigation is becoming more
and more urgent. This study is focused on deorbit from GTO, using a bare electrodynamic
tape tether, equipped with a hollow cathode. Objects to remove from GTO are, for example, dual-payload adapters, i.e. structures employed in heavy launches to GEO to house
two distinct payloads inside the fairing envelope. A computer code has been developed to
simulate deorbit from GTO, under simplifying assumptions, for a generic system. Simula-
tions consider only orbits with zero inclination, and implement the local in-plane rotation
about the system's center of mass, in addition to the global orbital motion. The system is
modeled as a dumbbell with rigid tether and two point masses. Dissipative perturbations
implemented in the code are electrodynamic Lorentz drag and aerodynamic drag. These
forces are enabled only below specific altitude thresholds, above which they become neg-
ligible. The local rotation is the main source of tension along the tether. The maximum
tension, at the system's center of mass, must not exceed a maximum value dictated by
the mechanical properties of tether material. Deorbit analyses are carried out for various
configurations in order to evaluate the system's dynamic behavior over time. Total deorbit
time is computed, and profiles of different parameters during the entire deorbit. Given that
system's geometry and total mass are generally constrained, or only slight modifications
are allowed, the options available to the designer are also constrained. This paper focuses
on system's dynamics and the effect of local dynamics on the tether tension. Particular
attention is paid to the maximum mechanical load on the tether, and the parameters that
affect it.

A New Control Law Based on Barrier Lyapunov Function for Deployment of Space Tether System
SPEAKER: unknown

ABSTRACT. Stable deployment of the space tether system is a key step for space tether satellites applications and missions. Many deployment devices and deployment control methods have been researched for decades. Among them, the tether tension feedback control is considered as an effective control strategy because of its simplicity, operability, rapidity, effectiveness. So a lot of articles were obtained by using tension control theory. While, usual simple feedback tension control may introduce an overshot in the tether length state, and even tether deployment velocity state may occurs negative condition, which are denied for tether deployment system. Up to now, none of the previous scenarios proposed a control law that gives an explicit system expression contained the above two state constraints. So a stable, fast and non-overshooting control law is necessary to the space tether deployment. Recently, the Barrier Lyapunov Function (BLF) method has emerged as an effective way to solve the state-constrained control problem. To avoid this situation, make the tether length state never transgress its full length and tether deployment velocity state never become minus, we introduce the Barrier Lyapunov function, which will grow to infinity when its arguments approach a designed limit in a strict feedback system. By ensuring boundedness of the Barriver Lyapunov Function in the closed loop, we ensure that the two states are not transgressed. The control arguments can be acquired offline by solving a static nonlinear constrained optimization problem. What’s more, due to these two states constrains are asymmetric about the zero, it is very suited to use asymmetric Barrier Lyapunov Function in the tether space system. We compare this control law with the simple feedback control law, and one based on Quadratic Lyapunov Function. We show that the novel control law has better performance than the former two scenarios on the three indices. A series of numerical examples are provided to illustrate the performance of the proposed control law.

12:00-13:30Lunch and Poster Session

Lunch provided in the Palmer Commons.

13:30-15:10 Session 12: Space Tether Modeling Techniques II
Collision Risks to and from Space Tethers

ABSTRACT. The collision cross-section between a space tether and a more typical space object scales with the length of the tether and the width of the other object. This cross-section is often 2-3 orders of magnitude larger than the area of the tether itself, and 2-4 orders of magnitude larger than the collision cross-section between two typical intact space objects. The collision cross-section of 2 tethers can be another 2-3 orders of magnitude larger, depending on relative orientation. The total collision risk also depends greatly on mission duration, orbit congestion, and use of active avoidance. Impacts that cut a tether are likely to end its mission, so space tether operators must be proactive about minimizing chances of collision, especially collisions between two tethers.

On the other hand, the effects of tether collisions on other objects are usually less damaging than collisions involving 2 typical space objects. As a rough rule of thumb, hypervelocity impact may disable satellites with a million times the impacting mass, but they may shred objects only up to a thousand times the impacting mass. The tether mass directly involved in a collision with a large space object is generally grams. Such impact may disable even ton-class satellites, but is unlikely to create much new debris. But even very light tethers can disable otherwise robust solar arrays, by severing the array or perhaps just its bus circuitry.

The main long-term cost of most debris collisions does not result from the chance of a collision of tracked debris directly with an operating satellite. About 90% of the cost is expected to come from later collisions involving gram-class shrapnel created by infrequent collisions of two large debris objects that shred each other. This shrapnel is far below current or planned detection thresholds, so it cannot be actively avoided. We don’t even know how many satellites have already been disabled by such gram-class shrapnel.

The paper also analyzes tape-like tethers, and tethers using multiple separated strands. For a given mass, they can be much more robust against failure due to impact by micrometeoroids. But failure rates due to debris impact are reduced less, because most of the ~7 km total width of objects in low earth orbit is due to tracked objects >2m across. Most of the cut risk to tape-like tethers is due to near-grazing impact by mm-class meteoroids or shrapnel. Multi-strand tethers can withstand that, but pose another issue: twice-cut free segments. Such segments can cut even tethers (including other tethers) with effective widths up to the length of the free segment.

The paper also analyzes the severance of the SEDS-2 tether after 4 days, and that of TiPS after 10 years. It ends with a discussion of liability issues, and recommendations on reducing tether collision risks. Prudent design and operation should let tether risks to other spacecraft be similar to those of other space missions, even if rules are tightened beyond the existing “25 year” rule.

Experimental Validation for the Deployment Behaviour of Orbiting Tethers Using an Air-Bearing Turntable
SPEAKER: Udai Bindra

ABSTRACT. The successful deployment and stabilization of a tether is a critical success criteria for all tethered missions. Although the deployment behaviour of the satellite under any control law being implemented, can be inferred from numerical simulations, there is no experimental verification for the same. The scope of this research is to develop an Earth based experiment that can imitate the behaviour of the tethers in space, during and after deployment. The experiment consists of an inclinable air-bearing turntable, whose inclination and rotation rate can be adjusted. This assists in controlling the magnitude of the gravitational, centrifugal and Coriolis forces acting along the tether. In order to scale down the size of the tether and the magnitude of forces acting on the tether in orbit, appropriate scaling factors are developed to help compare the motion of the deployed satellite in the experiment to that in orbit. This research aims to provide experimental verification for the deployment behaviour of satellites in space and can be used to validate untested control mechanisms for stabilizing the tether before it is sent into orbit.

Multiphysics Finite Element Analysis for Current Profile and Libration of Bare Electrodynamic Tether Systems
SPEAKER: unknown

ABSTRACT. This paper developed a multi-physical finite element dynamic model coupled with a discretized 2D OML model for the bare electrodynamic tether by consider the elastic, thermal, and electrical coupling effect on the dynamic flexible tether. In current paper, the hypothesis of the motional electric field Em is assumed constant along the whole tether is released and the difference of electron collection efficiency between connective elements is considered. Firstly, a discretized finite element model for the current and voltage profile is derived, and a high efficient iteration solver is developed for the two-boundary value problem of the discretized current model. It is verified through a benchmark study in which the electrodynamic tether behaviors a small vibration situation. The comparison results show that the newly finite discretized model is accurate and reliable. In addition, a sensitivity of the number of element is studied. Secondly, the verification of the new method is investigated when the electrodynamic tether exists a moderate vibration. It is interesting founded that the conventional method is overestimate for the current calculation when the system transform into a large transverse motion, moreover the difference of current and libration motion of whole EDT tether is significantly if no control strategy is applied to the EDT system.

Effect of Electromagnetic Force on The Deployment of Electrodynamic Tether System
SPEAKER: Jian Zhang

ABSTRACT. This paper studies the effect of the motion-induced-current on the in-plane libration of bare electrodynamic tethers when the tethers deploy downward. The tethers is modeled as a rigid, inextensible and massless rod, and the orbit of the mother satellite is assumed to remain on a circular orbit. The motion-induced-current along the electrodynamic tethers is calculated by using the orbital-motion-limited theory and International Reference Ionosphere-2012 model. The integer-order tether tension controller for inertial tethers’ deployment is used as a benchmark. The dimensionless Hamiltonian energy function of the electrodynamic tethers’ libration during the deployment is expressed, and according to this energy function, a simple switching on/off current is used to suppress the in-plane libration. The situations of different orbital altitudes and different length of the tethers are explored. Compared to the deployment of the inertial tethers, the analysis addressed that under the nearly same deployment rate, the situation taking the motion-induced-current into consideration can decrease the maximum in-plane angle than the inertial tethers’ situation. Moreover, the analysis shows that the effect in 400km orbit which has the higher electro density(about 5 °) is more significant than the effect in 500km orbit which has the lower electro density(about 2°). Compared to the short tether, the effect of the motion-induced-current is greater on the long tethers under the nearly same deployment time.

14:50-15:10Coffee Break
15:10-17:40 Session 13: Electric Sails for Interplanetary Exploration and Science
Using charged tether Coulomb drag: E-sail and plasma brake (Invited)

ABSTRACT. REVIEW: A voltage-biased metallic tether creates an electrostatic potential structure around itself. If put into flowing plasma, the electrostatic field deflects the trajectories of plasma ions. The resulting momentum transfer from plasma to the tether can be used for propulsive purposes. The electric solar wind sail (E-sail) is one such application. The E-sail has a set of centrifugally stabilised positively biased tethers in the solar wind. It enables propellantless propulsion in the solar wind, much in the same way as the photonic solar sail, but typically with order of magnitude higher thrust per propulsion system mass. The E-sail's high efficiency stems from the fact that the tether's electrostatic field penetrates a significant distance (some 100-200 m distance at 1 au) into the solar wind plasma while the tether that creates the electric field can be made very thin. As a result, the E-sail's virtual sail area can be millions of times larger than the physical area of the wires of which the tether is made. Thus, even though the solar wind's dynamic pressure is 5000 times less than the photonic pressure, the E-sail can achieve high thrust per mass. If using 20 kV voltage, the achieved thrust is some 0.5 mN/km while a kilometre of tether weighs about 10 grams.

Even though E-sail's thrust source - the solar wind - is highly variable, the E-sail's thrust varies much less, due to some nontrivial plasma feedback mechanisms. Furthermore, because the thrust is independently controllable in direction (by inclining the sail) and magnitude (by changing the voltage), the E-sail is accurately navigable and also able to tack sunward.

The E-sail works everywhere in the solar system except inside Earth's magnetosphere, because inside the magnetosphere there is no solar wind. However, in low Earth orbit (LEO), a closely related device called the plasma brake can be used for satellite orbit lowering and deorbiting. The plasma brake is a negatively biased Coulomb drag tether with moderate voltage. It uses the relative velocity between the orbiting satellite and nearly stationary ionospheric plasma to provide controllable orbit-lowering drag. As the E-sail, the plasma brake is also very efficient in terms of thrust per mass. Another important benefit of the plasma brake is that the tether is so thin that it is safe to other space assets in case of accidental collision.

In the presentation we review the development status of Coulomb drag tether propulsion and discuss some interesting application ideas.

MAGNETOUR: Surfing Planetary Systems on Electromagnetic and Multi-Body Gravity Fields
SPEAKER: unknown

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

ESTCube-1 lessons learned from the first Coulomb drag in-orbit experiment

ABSTRACT. LESSONS LEARNED: The mission of ESTCube-1, a one-unit CubeSat, was to perform the first in-orbit demonstration of the electric solar wind sail (E-sail). It was launched in May 2013 and was operational until May 2015. The E-sail is a propellantless propulsion system concept that uses thin charged electrostatic tethers for turning the momentum flux of a natural plasma stream, such as the solar wind or ionospheric plasma ram flow, into spacecraft propulsion. The E-sail payload on board ESTCube-1 consisted of a thin ten meters long snap-proof multi-wire metallic tether, an end-mass at the tip of the tether, a motor driven reel, a high voltage supply, electron guns and launch locks for the reel and the end-mass. The tether was planned to be deployed using centrifugal force provided by spinning up the satellite. The end-mass keeps the tether under tension and stretched. A camera monitors tether deployment by imaging the end-mass. The motor assists deployment of the tether.

In September 2014 attempts were made to deploy the tether from the satellite. However, the end-mass did not appear on camera images and angular velocity changes that should have accompanied its deployment were not observed, hence it was concluded that the tether experiment was not successful. The most probable reason for tether deployment failure is that the reel is not rotating either due to a jammed rotator or failed reel lock deployment. While preparing a similar payload for the Aalto-1 satellite, it was found that slip ring electric contactors can carve small pits in the slip ring during vibration testing and the small torque of the employed piezoelectric motor was not able to overcome the resistance. The problem was solved by implementing a launch lock that keeps the connectors away from the slip ring until released in space. However, due to the lack of diagnostic measures, the exact reason of deployment failure on board ESTCube-1 is not known. The following diagnostic measures were added to Aalto-1 payload: to detect whether launch lock for the reel has deployed, whether the reel is turning and whether the end-mass exits its enclosure.

In this study, we will present the overview of the tether experiment on board ESTCube-1 and implications for similar experiments in the future.

Sensitivity Analysis of Deployment Dynamics Parameters for the Electric Sail
SPEAKER: unknown

ABSTRACT. The deployment dynamics of a radially configured, spin stabilized, electric sail (E-sail) with a hub-mounted control actuator are investigated. Sensitivity of the deployment behavior to tunable deployment parameters, such as the deployment rate, spacecraft rate, tether orientation, and control effort, are determined.

The E-sail is an interplanetary propulsion concept that uses electrostatic interactions with solar wind protons to generate spacecraft acceleration. This is done through an array of 20-100 thin, charged tethers up to 20 km in length, each attached radially about the spacecraft hub and spin-stabilized. During the deployment of the E-sail, the system will experience a large change in inertia, and therefore will require that substantial energy and momentum are input to the system. A primary challenge for the E-sail deployment is determining a low-risk scheme to accomplish this, presenting a non-trivial task.

Two deployment configuration concepts have been shown in previous work. One concept is to stow the tethers on a single hub and spin them out in a tangential orientation, similar to a yo-yo despinner. The second concept has the tethers each on an individual spool, and unspools the tethers out at a radial orientation. Both concepts yielded feasible deployment behavior in initial simulations. However, the significance of specific deployment parameters to these deployment behaviors is not well understood, and therefore makes finding the optimal deployment paths difficult. This paper aims to determine the sensitivity of the deployment behavior to these parameters, and to determine optimal schemes for realistic deployments. For example, the tether orientation in a radially configured deployment is strongly correlated to the system spin rate and tether deployment rate. Tuning these two parameters, with no prior knowledge to their sensitivity, to achieve a desired tether orientation is difficult. Solutions to these parameter issues will be explored. Finally, further analysis of the control formulation will be considered. Thus far, control has been implemented using PID feedback control. Lyapunov control theory will be applied to the system to evaluate stability.

Refined Analysis of Electric Sail-Based Displaced Orbits

ABSTRACT. The Electric Solar Wind Sail (E-sail) is a propellantless propulsion system that is theoretically able to produce and maintain certain orbits of great practical importance, which are difficult (or even impossible) to generate with conventional thrusters. Within the set of those orbits, this paper focuses on circular displaced non-Keplerian orbits (DNKO) maintained by an E-sail, whose preliminary analysis has been discussed by Mengali and Quarta [1]. It is well known that Sun-centered DNKOs are very useful, for example, in deep space missions aiming at the observation of Sun’s polar regions. Many other potential application for DNKOs exist and the interested reader is referred to the comprehensive survey by McKay et al. [2].

The analysis of DNKOs of Ref. [1] is based on a simplified E-sail performance model, characterized by two main assumptions: the thrust modulus is independent of the spacecraft attitude and it varies with the Sun’s distance r as (1/r)^7/6 . However, more recent numerical simulations have shown that the thrust modulus scales proportional to the inverse distance from the Sun. In the second place, a more refined thrust model has been recently proposed in Ref. [3]. It consists of a polynomial expansion that accurately evaluates the variations of both the thrust angle and the thrust modulus as a function of the sail nominal plane orientation. In fact, according to Ref. [3], the maximum thrust angle achievable with an E-sail is estimated to be about 20deg.

The aim of this paper is to provide a systematic mathematical analysis of circular heliocentric DNKOs and to improve the results discussed in Ref. [1] by means of the polynomial approximation proposed in Ref. [3]. Figure 1 shows the relation between radial and transversal components of the thrust. A number of mission opportunities obtained by changing the heliocentric distance, the orbital period and the E-sail characteristic acceleration are investigated. The corresponding performance and attitude configurations required to maintain circular heliocentric DNKOs are calculated. A summary of the obtained results is shown in Fig. 2. Different mission scenarios are discussed, including Type II DNKOs [4] and heliostationary positions. For example, Fig. 3 shows the characteristic acceleration required to maintain a Type II DNKO as a function of the elevation angle and the heliocentric distance.

References [1] G. Mengali, A. A. Quarta, Non-keplerian orbits for electric sails, Celestial Mechanics and Dynamical Astronomy 105 (1–3) (2009) 179–195, doi: 10.1007/s10569-009-9200-y. [2] R. J. McKay, M. Macdonald, J. D. Biggs, C. R. McInnes, Survey of highly-non-keplerian orbits with low-thrust propulsion, Journal of Guidance, Control, and Dynamics 34 (3) (2011) 645–666, doi: 10.2514/1.52133. [3] K. Yamaguchi, H. Yamakawa, Study on orbital maneuvers for electric sail with on-off thrust control, Aerospace Technology Japan, the Japan Society for Aeronautical and Space Sciences 12 (2013) 79–88 . [4] C. R. McInnes, Solar Sailing: Technology, Dynamics and MissionApplications, Springer Praxis series in space science and technology, 1999, pp. 173–180.