Research ProposalPDF Available

Deep Space Propulsion With Electromagnetic Tethers - A Literature Study

Deep Space
Propulsion With
A Literature Study
Matthew Turnock
Deep Space Propulsion With
Electromagnetic Tethers
A Literature Study
Matthew Turnock
For the Spaceflight MSc Track
Student number: 4430913
February 14, 2020
Version 1.2
Nomenclature v
1 Introduction 1
1.1 Background...................................... 1
1.2 ResearchQuestion................................. 2
1.3 Structure ....................................... 2
2 Mission Heritage and EDT Principles 5
2.1 MissionOverview.................................. 7
2.2 Conclusions ..................................... 11
3 Environment Characterisation 13
3.1 Magnetic Field Characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.1 HMF Characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.2 Planetary and Interstellar Magnetic Field Characterisation . . . . . . 22
3.2 Ionosphere Characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Interplanetary Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Interstellar Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.3 Conclusions of Ionospheric Characterisation . . . . . . . . . . . . . . 25
3.3 Space Tether Hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Space Debris and Micrometeoroids . . . . . . . . . . . . . . . . . . . 26
3.3.2 Space Tether Degradation. . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.3 Conclusions of Space Tether Hazards. . . . . . . . . . . . . . . . . . 27
4 Tether Design 29
4.1 Composition ..................................... 30
4.1.1 Material....................................30
4.1.2 Type......................................32
4.1.3 Multiplicity..................................33
4.1.4 Conclusions of Tether Composition Analysis . . . . . . . . . . . . . . 36
4.2 ThrustGeneration..................................37
4.3 Stability / Pointing Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 Conclusions .....................................40
5 Supporting Spacecraft Parameterisation 41
5.1 Sizing of the Reference Spacecraft . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Discussion of Changes / Conclusions to the Reference Spacecraft . . . . . 45
6 Orbital Dynamics 47
6.1 Perturbations Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.1.1 Central Body Gravity Perturbations . . . . . . . . . . . . . . . . . . . 49
6.1.2 Atmospheric Perturbations . . . . . . . . . . . . . . . . . . . . . . . . 50
6.1.3 Third-Body Gravitational Perturbations . . . . . . . . . . . . . . . . . 50
6.1.4 Radiation Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.1.5 Conclusions About Perturbations. . . . . . . . . . . . . . . . . . . . . 53
iv Contents
6.2 Propagation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.2.1 Propagation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.2.2 Analysis of 2D or 3D Simulation . . . . . . . . . . . . . . . . . . . . . 56
6.2.3 Conclusions of Propagation Analysis . . . . . . . . . . . . . . . . . . 57
6.3 Integration Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.3.1 Conclusions of Integration Analysis . . . . . . . . . . . . . . . . . . . 58
7 Optimisation 61
7.1 Variation of EDT Spacecraft Applications / Mission Scenarios . . . . . . . . 61
7.2 Variation of (Physical) EDT Characteristics . . . . . . . . . . . . . . . . . . . 62
7.3 Optimisation Targets and Constraints . . . . . . . . . . . . . . . . . . . . . . 63
7.4 Optimisation Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.5 Gravity Assist Selection Method. . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.6 Conclusions .....................................64
8 Validation / Target Cases 65
8.1 ValidationCases...................................65
8.2 TargetCases.....................................66
8.3 Definition of Specific Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
8.3.1 MissionProfiles............................... 68
8.3.2 EDT Configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.4 Conclusions .....................................70
9 Analysis of Existing Tools 71
9.1 OrbitSimulation...................................71
9.1.1 Discussion of Remaining Tools . . . . . . . . . . . . . . . . . . . . . . 72
9.2 OptimisationTools..................................74
9.3 Magnetic Field Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
9.4 Conclusions .....................................75
10 Discussions and Conclusions 77
10.1 General Conclusions of the Literature Study . . . . . . . . . . . . . . . . . . 77
10.1.1 Assessment of Previous Work . . . . . . . . . . . . . . . . . . . . . . 77
10.1.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . 78
10.2 Reiteration of and Changes to the Research Question . . . . . . . . . . . . 78
10.3 Thesis Project Planning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
A Literature Study Planning 81
B Additional Smallsatellite Data 83
Bibliography 85
List of Abbreviations
ADCS Attitude Determination and Control System
API Application Program Interface
ASI Agenzia Spaziale Italiana (Italian Space Agency)
AU Astronomical Unit
ED ElectroDynamic
EDT ElectroDynamic Tether
EMF ElectroMotive Force
ESH Equivalent Sun Hours
GMAT General Mission Analysis Tool
GPS Global Positioning System
GTO Geostationary Transfer Orbit
HCS Heliospheric Current Sheet
HI Heliospheric Interface
HMF Heliospheric Magnetic Field
IM Interstellar Medium
ISS International Space Station
JAT Java Astrodynamics Toolkit
JAXA Japanese Aerospace eXploration Agency
LEO Low Earth Orbit
MAST Multi-Application Survivable Tether
MEE Modified Equinoctial Element
MiTEE Miniature Tether Electrodynamics Experiment
NASA National Aeronautics and Space Administration
NRL Naval Research Laboratory
OBP On-Board Processing
OEDIPUS Observations of Electric-field Distribution in the Ionospheric
Plasma - a Unique Strategy
OML Orbital-Motion-Limited
OOM Order Of Magnitude
PCM Point Circle Method
PMG Plasma Motor Generator
PROPEL PROPulsion using ELectrodynamics
RHS Right-Hand Side
RK Runge-Kutta
RW Round Wire
SEDS Small Expendable Deployer System
SOI Sphere Of Influence
SRP Solar Radiation Pressure
STARS Space Tethered Autonomous Robotic Satellite
Continued on next page
vi Contents
STK Systems ToolKit
STS Space Transport System
TBD To Be Determined
TiPS Tether Physics and Survivability
TOF Time Of Flight
T-REX Tether technologies Rocket EXperiment
TRL Technology Readiness Level
TS Termination Shock
TSS Tethered Satellite System
TT Tape Tether
TUDAT TU Delft Astrodynamics Toolbox
USM Unified State Model
UV Ultra Violet
VOE Variation of Orbital Elements
Contents vii
List of Symbols
Latin Symbols
[m] Satellite cross-sectional area
[m/s] Acceleration
[T] Magnetic field vector
[T] Parker magnetic field strength
[T] Radial component of magnetic field
[T] Azimuthal component of magnetic field
[m/s] Speed of light in vacuum
[-] Satellite reflectivity coefficient
[m] Average distance between 2 bodies in circular
orbits around a central body
[] Representing the function for an elliptic integral
of the second kind
[-] Unit vector from the Earth to the Sun
F[N] Lorentz force vector
[m/s] Satellite acceleration
[m/s] Spherical harmonic perturbation acceleration
in the radial direction
 [m/s] Spherical harmonic perturbation acceleration
in the azimuthal direction
I[A] Current vector
[-] Flattening spherical harmonic component
[m] Length of EDT
[kg] Mass
[m] Electron density
[m] Radius from central body (or radius of central
[m] Radius from central body
[K] Temperature
[s] Time
[m/s] (Solar wind) velocity vector
[T] Radial component of (solar wind) velocity
[W/m] Solar intensity
Greek Symbols
[deg] (Heliocentric) latitude
[ms] Standard gravitational parameter of a body
1.1. Background
Tethers of one form or another have been present in the space industry for many years, their
heritage dating back even to NASA’s Gemini programme [18]. In more recent years however,
the electrodynamic tether (EDT) has featured prominently in scientific investigations, as well
as being tested on board space missions, as a means of utilising magnetic fields in space to
provide low-thrust (near) propelantless propulsion [40], or power to a spacecraft at the expense
of kinetic energy [74].
In previous years, significant work has been done to assess the use of an EDT in planetary
magnetic fields, such as that of the Earth [37] or Jupiter [74], however very little has been
done to assess the use of an EDT for interplanetary or interstellar travel. There are also
currently significant problems in providing propulsion to spacecraft that wish to travel to the
edge of the Solar System and beyond, using current technology; with conventional chemical
propulsion one runs into the ”tyranny of the rocket equation” in which colossal spacecraft would
be required for deep space travel, to bring the required propellant to perform manoeuvres.
There are also alternative propulsion solutions such as solar sails [44], or electric propulsion
via very high specific impulse ion drives for example; in deep space both the solar sail and
electric propulsion systems run into the problem of very low solar intensity, to either sail from
or generate power from.
It is in this scenario in which an EDT could prove useful, as it is able to run without the use
of propellant, and also potentially without a net power consumption, and so could facilitate a
means of propulsion in deep space.
2 1. Introduction
1.2. Research Question
The research question has initially been chosen as the following:
Investigate the feasibility of electrodynamic space tethers as a means of propulsion applied to
possible future interplanetary and/or interstellar missions.
As part of this research question, the following subquestions can be raised:
What acceleration can realistically be achieved by an EDT in interplanetary and inter-
stellar space?
Which regions of space would an EDT spacecraft be suited to operating, and on what
kinds of missions?
What design concepts of an EDT are best suited to the above mentioned operating
The justification for choosing an interplanetary or interstellar application, instead of an Earth
or other planetary application, is that these kinds of applications for space tether propulsion
are relatively under-researched; this presents an opportunity for a thesis to explore these
possibilities. The reason to only consider the propulsive applications stems from the initial
prompt for the research, which showed that a mission to the ”edge of the Solar System” would
be infeasible with more conventional propulsion means.
1.3. Structure
The literature study is split into four main areas:
1. Introduction - this introduction chapter, in which the project is introduced and the research
question posed.
2. The analysis of thesis elements - in which all aspects relevant to the main thesis are
proposed and addressed, in Chapters 2 through 9.
3. The discussion and conclusions - in which the conclusions of the literature study are pre-
sented, the research question is reiterated (and adjusted if necessary), and the working
plan for the thesis is presented, in Chapter 10.
4. Appendices and bibliography - after the main report are the appendices which provide
some additional information for certain sections, such as the literature study planning in
Appendix A, and the bibliography lists all sources used in the generation of this report.
The introduction and conclusions sections are both fairly short and self-explanatory, however
the remaining chapters are briefly outlined as follows:
Chapter 2 - Mission Heritage and Introduction to EDT Principles - in this section the basic
working principle of an EDT for propulsion is briefly introduced, as well as a study of the
previously flown space tether missions, and EDT paper studies.
Chapter 3 - Environment Characterisation - in this section the various environmental
aspects relevant to an EDT are outlined. This includes the characterisation of magnetic
fields, ionosphere, and hazards in space.
Chapter 4 - Tether Design - the tether design section comprises all elements connected
to the physical design of the EDT. It includes tether composition and material, thrust gen-
eration techniques, and brief analyses of deployment mechanisms and attitude control
1.3. Structure 3
Chapter 5 - Supporting Spacecraft Parameterisation - this section briefly outlines a refer-
ence spacecraft that can be used as the baseline upon which the EDT can be designed
and mounted to.
Chapter 6 - Orbital Dynamics - in this section the orbital dynamics elements that are to be
simulated for the main thesis are analysed. Included are discussions on perturbations,
propagation techniques, and integration techniques.
Chapter 7 - Optimisation - here the aspects of the main thesis simulation that can be
modified, such as the intended mission or characteristics of the EDT components, are
addressed, to aid with the higher-level optimisation that will be done in the main thesis
Chapter 8 - Validation/Target Cases - in this section the specific cases are identified that
can be used to verify/validate the orbit simulation environment that will be developed. In
addition to this the target cases of the proposed EDT are outlined.
Chapter 9 - Analysis of Existing Tools - here existing tools for aspects of the final simu-
lation environment such as orbital simulation are identified and analysed, to determine
if they can be used.
Mission Heritage and EDT Principles
Gemini 11 was the first mission to explore the use of tethers in space, and demonstrate their
feasibility. Since then there have been a number of tether-based missions conducted, as
well as other planned or paper studies; it is important to first consider these missions before
performing further research.
The EDT functions on the basis of the Lorentz force, which states that a current moving per-
pendicularly through a magnetic field, will induce a force on the object with moving current;
another way to phrase that is that a conductive wire that is moved through a magnetic field
will have a current induced in the wire. The equation for this is shown in Equation 2.1 [58], in
which Frefers to the Lorentz force vector, to the total length of the tether, to a segment of
the tether, Ito the current vector through segment , and Bto the magnetic field vector
through segment .
IB (2.1)
It should be noted that in Equation 2.1, the integral is required to account for the change in
magnetic field strength over the tether, and also the change in direction of the tether, as it is
likely to flex as a force is applied to it. In interplanetary and interstellar space it is however fair
to assume that the change in magnetic field over the tether length is negligible.
6 2. Mission Heritage and EDT Principles
Figure 2.1: NASA artist’s impression of a space tether system anchored to the Space
Shuttle, similar to the TSS missions [56].
For the analysis here, both conducted missions as well as planned near-future missions are to
be considered; these are outlined in Table 2.1, which lists the mission name, launch date, and
mission type. In the following subsections, each mission along with its goals and contributions
to the field will be mentioned.
It should be noted that some previously conducted missions have been excluded from this list,
as a result of unrelated mission failures, or redundant information.
2.1. Mission Overview 7
Table 2.1: Conducted, planned, and paper-study missions giving a brief history of mission
Mission Name (Planned) Launch Date Mission Type
TSS-1 and TSS-1R (NASA)
1992 and 1996 Technology demonstrators (general
(NASA) [43] [10]
1993 and 1994 Technology demonstrators (general
PMG (NASA) [17] 1993 Technology demonstrators (ED
OEDIPUS (NASA) [10] 1995 Scientific experimentation (tether dy-
TiPS (NRL) [62] 1996 Scientific experimentation (tether dy-
namics and long-term survivability)
MAST (Tethers Unlimited +
Stanford Uni.) [32]
2007 Scientific experimentation (tether
long-term survivability)
T-Rex (JAXA) [90] 2010 Technology demonstrator (OML the-
STARS missions (Shizuoka
Uni.) [79] [87]
2009 - 2014 Technology demonstrator (tether ex-
tension and dynamic motion analysis)
PROPEL (NASA) [58] - Technology demonstrator (ED tether)
ISS Reboost (journal) [37] - ISS stationkeeping concept study
Jovian Capture (journal)
- Concept for capture into Jovian Sys-
2.1. Mission Overview
In this section a brief overview of the previously mentioned missions, as well as their goals
and useful information gained from them, can be found.
TSS-1 and TSS-1R
The Tethered Satellite System (TSS) was a collaborative mission between NASA and the Ital-
ian Space Agency (ASI) intended to investigate plasma-electrodynamic processes in space,
as well as the orbital mechanics of a gravity-gradient stabilised system of two satellites linked
by a long conducting tether. The TSS-1 mission had limited results, since the tether deploy-
ment was terminated at only 268 m of the planned 20 km; therefore only the results of the
TSS-1R mission are to be considered here. [83]
In February 1996 TSS-1R launched aboard STS-75, into a 300 km circular orbit. Over a
period of five hours after being released from the Space Shuttle, the tether was deployed
to a length of 19.695 km, before breaking near the top of the deployer boom. Despite the
breakage, TSS-1R was able to collect useful data during the tether deployment [83]. The
primary findings from TSS-1R are that it is indeed possible to facilitate current flow in a tether
connecting two spacecraft, by using the Earth’s magnetic field, as well as ionospheric electrons
to complete the circuit; this current flow could potentially be used for power generation, or in
reverse for propulsion. The specific voltage measurements made also revealed some errors
in the theoretical ionospheric plasma and magnetic field models, namely the Parker-Murphy
model. In this case the errors showed that ED tethers could provide a much larger propulsive
force, for a given current flow, than previously predicted [83].
8 2. Mission Heritage and EDT Principles
The SEDS (Small Expendable Deployer System) project began as a Small Business Inno-
vative Research contract awarded to Joe Carroll by NASA MSFC, and flew as secondary
payloads on Delta-II GPS satellite launches. SEDS-I in March 1993 was released into an ec-
centric orbit with perigee altitude of 190 km, and apogee altitude of 720 km, whereas SEDS-II
in March 1994 was released into a circular orbit at 350 km altitude [43].
SEDS-I demonstrated a 25 kg payload could be deployed at the end of a 20 km-long tether,
and a deployment mechanism could be used such that the tether was kept taught, and fully
deployed without tether breakage. The main mission objective however was to further study
tether dynamics both in space and during reentry, after the tether was cut from the main space-
craft; both of these objectives were successfully completed [43].
SEDS-II demonstrated the feasibility of deploying the tether using an active closed-loop control
law, to bring it to a specific position, along a predetermined trajectory, instead of simply allowing
the tether payload to drift, as in SEDS-I; the active control was achieved using the release
braking mechanism during deployment. The secondary objective of SEDS-II was to study
the long-term evolution of the tethered system. In the first of these objectives SEDS-II was
successful, with the final deployment velocity being 2 cm/s (compared to the 7 m/s of SEDS-I),
which prevented large tensions at the end of deployment. In the second objective however
after five days the tether was (unintentionally) cut, allegedly by a micrometeroid or space
debris. [43]
The PMG (Plasma Motor Generator) in June 1993 was launched into an eccentric 207 x 922
km Low Earth Orbit (LEO), and set out to determine the feasibility of using an ED tether system
for power generation and propulsion in LEO. In this objective the mission was successful, using
a 500 m tether it was the first mission to demonstrate measurable current generation and
propulsive force from ionospheric plasma. The mission also highlighted significant changes
in current generations between night and day [17].
OEDIPUS (Observations of Electric-field Distribution in the Ionospheric Plasma - a Unique
Strategy), a diagram of which is shown in Figure 2.2, was launched in 1989 and 1995 respec-
tively for OEDIPUS-A and OEDIPUS-C. They were suborbital sounding rocket flights designed
primarily to investigate plasma physics in the upper atmosphere, with the secondary objective
to study the flight dynamics of the tether experiment [43].
2.1. Mission Overview 9
Figure 2.2: OEDIPUS spacecraft diagram [34].
TiPS (Tether Physics and Survivability) was a mission launched in June 1996 into a 1022
km circular orbit, consisting of two small mases connected by a 4 km tether; the purpose
of the mission was to investigate on-orbit tether motion, as well as long-term survivability. In
the former objective the mission was successful, mostly confirming anticipated results with the
exception of some unexpected bowing and rotation [62]. Regarding the latter, the mission was
also successful, as the tether survived until 2006, much longer than the planned three-year
mission time; showing that long-term operations of LEO tethers is indeed feasible [10].
The MAST (Multi-Application Survivable Tether) is a collaboration between Tethers Unlimited
Inc. and Stanford University’s Space Systems Development Laboratory; launched in April
2007 into a polar 647x782 km orbit, the primary mission objective was to use CubeSat space-
craft connected by tethers to better understand the survivability of tethers in space. Com-
munication with the picosatellites failed and the mission terminated after only two months of
operation, and so detailed measurements intended to be made by the ”gadget” which was de-
signed to traverse up and down the tether, could not be made. Despite this it can still be seen
that the tether remains intact, due to the proximity of the spacecraft to this day. [32].
The T-Rex (Tether technologies Rocket EXperiment) is a sounding rocket launched in 2010 as
an international collaboration between the USA, Europe, Japan and Australia to demonstrate
novel ”Origami” folding techniques for deploying an EDT, as well as verification of electron
collection theories used to facilitate current flow, such as OML (Orbit Motion Limit). In both of
these objectives the mission was successful with rapid tether deployment, as well as revealing
potential difficulties in handling the complex behaviour of a flexible tether in space. [90]
STARS Missions
The STARS (Space Tethered Autonomous Robotic Satellite) series of missions are cubesat
technology demonstrators, to assess the feasibility of using an EDT as a deorbiting device;
more specifically to study tether deployment via gravity gradient, electrical current gathered
by an EDT, attitude control and further tether deployment / retrieval using tether tension [87].
10 2. Mission Heritage and EDT Principles
STARS-I was launched in 2009, and STARS-II in 2014; the missions were partially successful
but experienced faster-than-expected orbital decay, postulated to be caused by the tether
becoming tangled during deployment [79].
PROPEL is currently a paper study for a proposed mission to study the use of an EDT in LEO
for six months [58]. PROPEL uses a spacecraft host flying in formation with an endmass,
connected by the EDT; its mission goals are to demonstrate the capability of EDT technology
for (near) propellantless propulsion for various orbital manoeuvres, as well as orbital power
harvesting, and formation flight. These mission goals aim to fully characterise and validate
the integrated EDT propulsion system, qualifying it for use in future missions.
Figure 2.3: The PROPEL mission profile [58].
ISS Reboost
The ISS reboost study is a paper study outlining the potential use of an EDT as a means of
station-keeping on the ISS, to counter atmospheric drag and other orbit perturbations; written
in 1998 the application to the ISS of course did not eventually occur [37]. The study concluded
that an EDT reboost system has advantages over other conventional propulsion systems, po-
tentially saving the program $2B over 10 years, however several issues were also identified,
such as the shift of ISS centre of mass that could affect microgravity research, safety con-
straints during orbital rendezvous, and power availability [37].
Jovian Capture
An example of a paper study outlining the use of an EDT in interplanetary space can be found
in Schadegg et al [75]. This mission would plan to use an EDT as propulsion and power
generation in order to aid capture into the Jovian system, and to reduce the eccentricity of a
captured orbit. An EDT could also be used as a propulsion system for a spacecraft performing
a tour of Jupiter’s moons in a similar manner, as outlined in Sanmartin et al [74].
2.2. Conclusions 11
2.2. Conclusions
To conclude the above summary, it is clear that there has been quite a substantial level of work
done in the realm of scientific study and technology demonstrators for tether concepts in LEO.
These concepts include EDT’s used for propulsion, as well as more general concepts such
as deployment techniques, tether dynamics, and long-term survivability; all of this research
provides a valuable resource for potential tether designs to be taken forward in the coming
thesis study.
However, there has also never been a mission conducted, or officially planned (there have
only been conceptual paper studies), to test these tether concepts in interplanetary space;
this presents significant impacts to consider when designing for this new regime, for exam-
ple different survivability concerns. The demonstrations do place the concept of EDT’s as
a propulsion technique at Technology Readiness Level (TRL) 7, corresponding to a ”system
prototype demonstration in a space environment” [54] since there are currently no missions
using the concept as part of a wider system.
Environment Characterisation
As previously stated, one of the major justifications for investigating the use of tether propulsion
is for use in deep space; therefore the potential environments to investigate must be properly
characterised, after which potential design regions can be selected for a basic investigative
mission profile. In this section both of these things will be done, and based on the operational
requirements of an EDT; the following environmental conditions shall be investigated:
Magnetic field strength, (relative) speed, and direction - this is required as the strength
and direction of the Lorentz force are directly related to the strength, speed and direction
of the local magnetic field [35].
Characteristics of the local ionospheric plasma - in all applied EDTs, the current through
the tether is facilitated using electron collection / emission by utilising the surrounding
plasma, as shown in Figure 3.1; therefore naturally the relevant characteristics of the
plasma such as electron density must be known.
Hazards - hazards to an EDT are ever-present, and must be characterised in the in-
terplanetary and interstellar medium to be able to assess the expected longevity of a
proposed mission. The most common of these are space debris and micrometeoroids,
which have been postulated to be the cause of previous tether mission failures, such as
the SEDS-II mission [43]. Also present is the potential for UV and high-energy radiation
from the Sun to degrade certain types of tether material, particularly polymer fibres [29].
14 3. Environment Characterisation
Figure 3.1: The essential physics of an EDT utilising electron emission / collection for circuit
completion [58].
3.1. Magnetic Field Characterisation
For the thrust that is be generated from an EDT, one of the most important aspects is of
course the local magnetic field strength. There are in general three regions where magnetic
fields could exist in the scope of this research; planetary magnetic fields such as that around
the Earth, the heliospheric magnetic field (HMF) generated by the Sun, and the interstellar or
galactic magnetic field beyond the influence of the Sun. Due to the mission statement outlined
in Chapter 1, only the interplanetary and interstellar environments will be considered in detail
It is also important to note that most of the characterisation in this section is to do with the field
strength, since this is the most variable / difficult parameter to obtain; the field direction can
be determined implicitly by the model used. As well as this, the spacecraft velocity relative to
the field is also known to be simply the relative velocity between the spacecraft and the Sun,
in the interplanetary case, since the magnetic field lines are (approximately) stationary with
respect to the Sun. The previous statement is not true in the interstellar case however, as the
IM (Interstellar Medium) moves at approximately 25.7 km/s relative to the Sun.
3.1.1. HMF Characterisation
In general, the HMF is carried out into space by the solar wind, and directly above the surface
of the Sun is a region of super-radial expansion, in a spatial region approximately bounding the
corona, the magnetic field dominates the plasma flow and undergoes super-radial expansion.
At the source surface, the magnetic field and plasma flow become purely radial, and regions of
space further out than this become the heliosphere, where the magnetic field and plasma flow
become approximately spiral in shape. To illustrate these stages see Figure 3.2, also shown
3.1. Magnetic Field Characterisation 15
on the diagram are the vector equations for the magnetic field
and solar wind velocity
each region of the heliosphere; the equations will be further discussed later in the section [65];
it should also be noted that at the source surface, the solar wind is not corotating with the Sun,
and as such both the magnetic field and solar wind flow both become purely radial, hence the
lack of a tangential term to the shown equations.
Figure 3.2: Heliospheric magnetic field development regions. Shown in blue and red are the
regions of opposing polarity, separated by the heliospheric current sheet (HCS), shown as
the green dashed line [65].
The source surface typically occurs at approximately a few solar radii from the Sun [65], and so
only the heliosphere region of the magnetic field will be considered further. The spiral geometry
of the HMF shown here is the steady-state approximation given by the Parker model, which
assumes an idealised solar wind with exactly radial outflow with constant speed, independent
of radial and latitudinal position [65]. In addition to this, the footpoints of the magnetic field lines
are assumed fixed in the photosphere, rotating with the Sun; this allows the field to be split into
a radial component and azimuthal component , twisting the HMF into an Archimedian
spiral, in the solar equatorial plane [65].
With these assumptions, ”a magnetic field line at a heliographic latitude has the form of a
spiral wrapped on a cone whose centre axis is the solar rotation axis, and whose angular half-
width is °” [15]; a more helpful illustration of this description is shown in Figure 3.3.
16 3. Environment Characterisation
Figure 3.3: 3D illustration of the ideal Parker spiral HMF; the black, red, and blue lines
represent heliocentric latitudes of 0° (equatorial), 25° and 60° respectively [82].
It should also be noted that the rotation axis of the Sun is tilted by 7.25° compared to the
ecliptic [52], which should be taken into account when performing magnetic field calculations.
The difference that this tilt makes to the magnetic field strength can be simply calculated from
the cosine, which shows that accounting for the tilt, the field would only be 0.8% weaker than
if it were not accounted for; as will be shown in Figure 3.6, the variation in the field due to
even minor changes in solar wind speed can produce changes orders of magnitude larger,
therefore the effect of this tilt can be safely neglected.
For the remainder of the characterisation, the Parker model can be used, since it serves as
a good first-order approximation for the magnetic field, and has been validated, particularly in
the outer HMF, by Voyager 1 and 2 data [15].
According to Parker’s model, the strength of the magnetic field varies as shown in Equation 3.1
[15]. is the Parker magnetic field strength as a function of heliocentric radius , time
and latitude ;is the radial component of the (yearly average of) magnetic field at
1 AU, as a function of and ;is the (yearly average of) the solar wind speed at and
3.1. Magnetic Field Characterisation 17
 (3.1)
The first term on the right-hand side (RHS) of Equation 3.1 represents the radial HMF compo-
nent, which decreases with the inverse square of ; the second term represents the tangential
HMF component, which decreases with the inverse of [15]. Therefore Equations 3.2 and
3.3 hold true,
It can also be shown that in the distant heliosphere (i.e. beyond around 10 AU), is inversely
proportional to , and proportional to [15]; also the HMF has no latitudinal component in
the Parker model, due to the assumption of radial solar wind [65].
As a preliminary characterisation of the HMF, the Parker model can be used, and for a given
value of and , the magnetic field strength at a radius can be found using Equation 3.4;
only the values of  and are required to be known, with being the heliocentric radius
of these measurements.
 and  are dependent on the solar wind speed , and the latitude . Assuming an
equatorial spiral (i.e. °), the components can be calculated using Equations 3.5 and 3.6;
and refer to the total magnetic field strength and azimuthal angle of the HMF to the radial
direction respectively, at .
 cos (3.5)
 sin (3.6)
Both and vary depending on the activity of the Sun; for the purposes of this study the
maximum and minimum values of each using historic data can be used to characterise the
HMF. The magnetic field strength has been measured over time, and is shown at a distance of
1 AU in Figure 3.4 [65]; it can be seen that the variation has extreme (yearly average) values
approximately as shown in Equation 3.7.
18 3. Environment Characterisation
Figure 3.4: Variation of Solar magnetic field strength over time at 1 AU, from 1965 to 2015.
The red and white lines show the yearly and Carrington-rotation averages respectively; the
black histogram shows the monthly sunspot number [65].
Observations of the HMF also allow the confirmation of the Parker spiral angles shown in
Figure 3.5, such that the extreme variations are approximately as shown in Equation 3.8.
Figure 3.5: Probability distribution functions for for different solar wind speed intervals;
where the angle to HMF is 0° and 180°, the HMF flows directly outwards from and inwards
towards the Sun respectively. The solid curves show the results of hourly OMNI observations
of the near-Earth HMF, covering the period 1965 – 2012. Vertical dashed lines show the
equivalent ideal Parker spiral angles [65].
 (3.7)
3.1. Magnetic Field Characterisation 19
°° (3.8)
Using the initial condition variations of Equations 3.7 and 3.8, along with Equation 3.4, the
strength of the HMF can be characterised as shown in Figure 3.6.
Figure 3.6: Characterisation of HMF, using Parker model. Four cases are considered for the
variation in historic conditions. Also shown on the figure are the radial distances of some
Solar System features.
It should be noted that the calculations made in Figure 3.6 approximate the range of values
measured by the Voyager 1 probe as it covered similar distance ranges, as shown in Fig-
ure 3.7.
20 3. Environment Characterisation
Figure 3.7: Magnetic field strength measured by Voyager 1 between 1978 and 2001 (left);
the dots represent measured data, the solid line represents a specific calculation of the
Parker model by Burlaga et al, and the upper and lower dashed lines represent Parker model
calculations for 400 and 800 km/s solar wind speed respectively. Also the labels V1 and V2
represent Voyagers 1 and 2 respectively. The distance at which Voyager was at any given
time can be inferred by the distance over time graph (right) [15].
At 75-90 AU is the termination shock (TS), where the solar wind speed becomes subsonic,
with respect to the Sun, due to interactions with the IM [11]. Therefore beyond this point it
is clear that the Parker model cannot be used (as assumes a constant solar wind velocity).
There are however other models such as that used in Ferreira et al [24] that can be utilised;
considering the heliospheric interface (HI) as the region between termination shock and the IM,
the HI can be split into three regions, namely the nose, poles, and tail, as shown in Figure 3.8.
The solutions of the Ferreira et al model, along with a reference Parker model, can be seen in
Figure 3.9.
3.1. Magnetic Field Characterisation 21
Figure 3.8: Diagram of the heliospheric interface, showing the nose, poles and tail, with the
Sun at the centre. Adapted from [24].
Figure 3.9: Magnetic field strength computations for the different HI regions [24].
Figure 3.9 shows that in all HI regions, the magnetic field strength rapidly increases, before
suddenly dropping down to 0, as the HI is exited. Comparing the Parker solution shown in
Figure 3.9 to the one in Figure 3.6, Ferreira et al appears to use conditions favouring a slightly
stronger magnetic field. In addition to this, the agreement between models closer to the Sun
22 3. Environment Characterisation
than the IM is very good. As a reference, the magnetic field strength in geostationary orbit is
approximately 10 or 15 nT [22].
3.1.2. Planetary and Interstellar Magnetic Field Characterisation
As previously mentioned, planetary magnetic fields will not be considered here in detail, how-
ever it is known that planets with non-negligible magnetic fields, such as the Earth or Jupiter,
have field strengths many OOMs larger than either interplanetary or interstellar fields; approx-
imately 25-65µT at the Earth’s surface and LEO [25], and around 10 or 15 nT at geostationary
altitude [22], more detailed modelling can be done at a later date on a planet-by-planet ba-
Beyond the heliosphere lies the interstellar (or galactic) magnetic field. According to Beck and
Wielebinski [12], the interstellar magnetic field is known to vary from 0.6 nT in the vicinity
of the Sun, and increases to or 2-4 nT in the region of the galactic centre. These values are
of a similar OOM to the values at the edge of the heliosphere shown in Figure 3.9, with the
notable exception of the large spike in strength near the HI near the nose; this may be a region
favourable to maintain flight in to more effectively perform manoeuvres with the EDT.
Since any interstellar travel in the scope of this research is likely to be close to the Sun, the
interstellar magnetic field strength can be assumed to be of the order 0.6nT; more detailed
modelling can be done during the thesis proper, if necessary.
From the characterisations described above, the following conclusions can be shown:
Figure 3.6, supported by Equations 3.2 and 3.3, shows that the HMF is first dominated by
the radial component which varies as , and is then dominated by the azimuthal
component which varies as ; with the inflection between dominant regions occur-
ing at approximately 1 AU.
Figure 3.6 also shows that the magnetic field strength can vary by roughly one OOM at
all radial positions, depending on the solar activity defined by and .
According to Equation 3.1, the radial component is independent of latitude , while
the azimuthal component is proportional to cos . Therefore latitude does not play
an important role in HMF strength below around 1 AU, but should be considered above
around 1 AU.
In the heliospheric interface, before reaching interstellar space, there is a magnetic field
strength spike compared to the regular HMF, shown by Figure 3.9. This could potentially
offer a good region in which to utilise an EDT. It should also be noted that the increase in
magnetic field strength becomes smaller, but over a larger distance, as one progresses
from the nose region, through the poles to the tail region of the HI.
It is preferable to use an EDT in planetary magnetic fields where possible, due to the
increased strength compared to deep space.
Travel using an EDT in interstellar space is equally feasible as in the outer HMF, due to
the similar OOM of the magnetic field in both regions.
As shown in Figure 3.2, the magnetic field lines steadily deviate further from the radial
direction (with respect to the Sun); in the produced Lorentz force this will tend to cause
cosine losses in the level-pitch (i.e. prograde for a circular orbit) direction, and so this
should be taken into account during mission planning.
3.2. Ionosphere Characterisation 23
The relative velocity used by the Lorentz force can be considered relative to the Sun in
the interplanetary case, and relative to the IM in the interstellar case.
The implications of these conclusions on the potential mission profile are as follows: the more
rapid increase in magnetic field strength below 1 AU implies it could be advantageous for a
mission to first drop into the inner Solar System to utilise higher thrust levels before venturing
into the outer Solar System. Also the linear drop off of HMF strength beyond around 10 AU
implies an EDT could be feasible at much larger distances than a solar sail, with solar intensity
that drops off with the inverse square of distance. The dependency of magnetic field strength
on cos implies that it would be advantageous to have a smaller solar orbital inclination where
possible. The high magnetic field strength around certain planets implies an EDT could be
used for touring missions around for example Jupiter, or to escape the Earth environment
before venturing further into deep space.
3.2. Ionosphere Characterisation
The main characteristic to consider when addressing the ionosphere is the electron density,
since this is a major factor for electron emission / collection used for EDT propulsion [58].
Secondary to this is the local temperature, which is an important factor for some assumptions
made during EDT calculations [49].
3.2.1. Interplanetary Ionosphere
The electron density in the interplanetary ionosphere is directly characterised by the solar
wind, and unless close to the corona of the Sun, can be considered to follow a 1/relationship
with distance from the Sun (in the Solar equatorial plane) [76]. Direct measurements of the
interplanetary electron density can be seen in Figure 3.10, whose data is taken from NASA’s
Viking probe [51].
24 3. Environment Characterisation
Figure 3.10: Electron density profile around the Solar equator, up to 1.40 AU, upper AU
scale added from the base figure found in Muhleman [51]. Data is taken from NASA’s Viking
spacecraft, where the solid dots represent data points directly, the open dots represent the fit
of the model outlined in Muhleman [51], and the solid line represents the expected 1/r
From Figure 3.10 it can be seen that at distances larger than 100 Solar radii, the electron
density perfectly follows a 1/rrelationship; therefore it can be reasonably said that this elec-
tron density can be extrapolated with this relationship out to the border between interplanetary
and interstellar space.
3.2. Ionosphere Characterisation 25
3.2.2. Interstellar Ionosphere
The transition from interplanetary to interstellar space is sharp across the heliopause, and can
be seen in Figure 3.11 using measurements from Voyager 1 and 2.
Figure 3.11: Electron density measurements from Voyager 1 (black dots) and Voyager 2 (red
dots) [30].
The temperature of the local IM is quite variable, measured to be = 6680 1490 K by
Redfield [68], and around 8000 K by Mathis [47].
Mathis also estimates that the local IM electron density to be = 0.025 cm [47]; similarly
Spitzer estimates the electron density to be 0.02 cm 0.025 cm [80]. These values
are of course much smaller than the inner Solar System values presented in Figure 3.10, which
is around 10 cm near 1 AU.
3.2.3. Conclusions of Ionospheric Characterisation
Clearly, the electron density of the inner Solar System is much higher than anywhere else con-
sidered, and so this would be the ideal place for a (conventional) EDT to function. However,
there is also a significant increase in electron density as one crosses the heliopause, imply-
ing a higher electron density in interstellar space compared to the far reaches of the Solar
26 3. Environment Characterisation
3.3. Space Tether Hazards
For any interplanetary or interstellar mission, the longevity of the spacecraft should be given
consideration, due to the long time periods in which the spacecraft is in cruise; this is particu-
larly true for an EDT, due to its size. In this section the potential hazards to an EDT in deep
space are outlined.
3.3.1. Space Debris and Micrometeoroids
In previous tether missions, space debris and micrometeoroids have posed a significant threat
to spacecraft survivability, as mentioned in Chapter 2. It is known that in Earth orbit, the particle
density of orbital debris and micrometeoroids of diameter larger than 1 µm is approximately 12
km across altitudes varying from 500 - 10000 km [39]. It is also known that throughout the
Solar System there exists a dust cloud, with particle density at 1 AU of objects in the same size
range (above 1 µm) is ”a few per km” according to page 208 of Schwenn et al [77]; this is non-
negligible and therefore micrometeoroid impacts are a potential hazard to an interplanetary
Characterisation of micrometeoroid spatial density
According to Drolshagen [23], a number of models are available for use in interplanetary space,
although Drolshagen focuses on near-Earth applications. A very common model is the Grün
model, although this is only applicable to the region around 1 AU, so will not be considered;
similarly is the IMEM/Dikarev model, which only works up to 10 AU. The model which is rele-
vant to use in the current context is the Divine (and Divine-Staubach) model, which operates
in ranges from 0.1-20 AU, on mass ranges of 10 g - 1 g. During the thesis proper, this
model can be used as described in Divine [21], in order to provide an estimate for the mi-
crometeoroid density and as such basis for a risk assessment in the inner and mid-outer Solar
In the region between 20 AU and interstellar space there is very little data on micrometeoroid
density, and so models are not readily available to describe it; in this case a conservative
estimate can be assumed in which the density value is constant, and the same as the value
given by the Divine model at 20 AU.
In interstellar space, the meteoroid density is also considered roughly constant, in which dust
grains between 0.1 and 1 µm have a spatial density of 1-1000 km, according to Chapter 11
of Matloff [48].
Risk assessment outline
According to Khan et. al. [38], a tether can be severed by particles ranging in size from
1/6 to 1/2 of the tape tether diameter, and so assuming the tether is no less than a few mm
in diameter (a reasonable assumption), then all micrometeoroids larger than around 0.1 mm
should certainly be modelled.
Since the likelihood of the survivability of a tether is dependent on many factors such as the
tether design and material, it is difficult to determine fully the probability of a catastrophic
mission failure due to micrometeoroid impact, without performing a full probability analysis for
every tether design. Therefore this risk will be incorporated into the final analysis quantitatively
as a relative failure risk, taking into account the micrometeoroid density over the length of the
mission, and the tether length, as shown in Equation 3.9; ,,,, and  refer to the
relative risk, EDT length, total mission time, micrometeoroid spatial density across time step
, and a to be determined reference relative risk value (for example a baseline mission).
3.3. Space Tether Hazards 27
 (3.9)
Using this approach it is possible to compare different mission profiles and EDT solutions,
without the need to rigorously calculate the failure probability.
3.3.2. Space Tether Degradation
In the past, space tethers have needed to consider the degradation of the tether over time
due to the influence of atomic oxygen and UV radiation; since atomic oxygen is only found in
LEO [29], it can be ignored for the purposes of this research. UV radiation on the other hand
is an ever present threat close to the Sun, and only reduces with a relationship moving
away from the Sun; UV radiation also only generally affects polymer fibres and not metals
[70]. Having identified UV as an essentially unavoidable hazard, mitigation efforts are further
discussed in Chapter 4.
3.3.3. Conclusions of Space Tether Hazards
Two major hazards to space tethers have been identified: impact hazards and tether degra-
dation. The former of these is most pressing, as impacts present a hazard to all types of
space tethers, and due to the length of an interplanetary or interstellar mission, significant
steps should be taken to mitigate the risk of catastrophic failure. To help account for this, a
risk assessment method was also outlined to be used.
The degradation due to UV exposure is less serious, as it generally only effects polymer-based
fibres, however this hazard should be considered when choosing the tether material.
Tether Design
In order to properly test the feasibility of an EDT, an appropriate design should be chosen upon
which further work such as survivability analyses can be conducted. There are a number of
aspects to consider in this design process, which are outlined as follows:
Survivability - this essentially refers to the likelihood of a catastrophic spacecraft failure
as a result of the hazards discussed in Section 3.3.
Spacecraft dynamics - this refers to the aspects of the spacecraft that are complicated
by using a large EDT, such as manoeuvrability and attitude stability; it also refers to more
tether-specific concepts such as the required tensile strength of the tether as well as its
Spacecraft longevity - this is complementary to spacecraft survivability, but covers a
broader range of topics such as deterioration of components over long time scales, and
the overall power usage that the spacecraft can support.
Dimensions / parameterisation - this refers to the determination of the dimensions of the
EDT itself to allow the concept to be feasible, for example the tether length.
As well as the above design considerations, the following components must be specifically
addressed during the design stage:
Tether composition - this refers to the physical composition of the tether such as its
material, as well as other design considerations directly related to the tether such as its
shape (for example a tape or simple cylinder).
Thrust generation / current flow modes - this refers to the specific method the spacecraft
uses to generate a Lorentz force. For example a bare tether vs a closed tether.
Stability / pointing method - naturally a long tether such as is considered in this research
presents significant ADCS problems, which must be directly addressed.
In the following sections, the above components will be further addressed.
30 4. Tether Design
4.1. Composition
The tether composition is split into three distinct components: material, tether type, and tether
multiplicity, each of which are further expanded upon below.
4.1.1. Material
The tether material selection is of course an important aspect, also included in this section
are if a single-material tether is used, such as for the PMG mission [17], or a composite tether
containing separate load-bearing and conducting components, such as the one used by TSS-
1R, shown in Figure 4.1 [55].
Figure 4.1: TSS-1R composite tether diagram [55].
Table 4.1 shows a number of different materials that could be used for an EDT, including prop-
erties such as (ultimate) tensile strength and (mass) density; the conductivity of the material
is also shown, to show if it is suitable to use the material as the current-carrying component
of the tether, or only as a load bearing component.
4.1. Composition 31
Table 4.1: Example materials for EDT construction [9] [92].
Material Tensile
Electric Conductivity
Aluminium-2024 0.22 - 0.46 2780 79 - 165 Conductive
Copper 0.07 8920 7.8 Highly conductive
Carbon nanotube 62 1340 46268 Conductive / semiconduc-
tive along tube axis
Zylon 5.8 1540 3766 Non-conductive (unless
made a conductive textile)
Spectra 2000 3.5 970 3608 Non-conductive
M5 Fibre (PIPD) 5.3 1700 3118 Non-conductive
As previously mentioned, there has been a historic precedent to use a single material for both
the load-bearing and current-carrying components of the tether, as well as a composite de-
sign using different materials for both. Therefore the merits of each type of design must be
considered; for example a single material solution would be very simple, but may add consid-
erably to the overall mass of the tether. Similarly, depending on the deployment mechanism
and dynamics of the eventually deployed system, the tensile load may be very low, imply-
ing a single-material solution, or very high, implying a composite solution to handle the extra
loading. Some potential configurations to consider are as follows:
A single-material copper solution - this would be ideal from the perspective of the Lorentz
force generation aspect of the EDT, as copper is a very good conductor, however it must
only be applied to designs which apply a very low tensile load, due to the fact that copper
has a very low tensile strength, as well as a high density, as shown in Table 4.1
A single-material aluminium or carbon nanotube solution - this has some of the advan-
tages over the previous copper solution, since both are sufficiently strong and have
(some) conducting properties, although their function as a current-carrying component
is of course less ideal than copper. These solutions could be used for a medium-high
loading scenario.
A full composite solution with a copper inner component, and a stronger load-bearing
component such as M5 fibre - this solution provides both the favourable conductivity of
copper, and good tensile strength by the fibre. The use of a fibre instead of metal also
allows the tether to be less brittle, and therefore is able to flex more if necessary. This
kind of solution can be used in all loading cases, but the use of multiple components is
more complex than a simple tether, and would pose challenges to implement into a tape
tether for example (see later sections for discussion on the tape tether).
Another consideration to make when discussing the tether material, is protection against UV
light, and atomic oxygen, as mentioned in Section 3.3. Since atomic oxygen is only found in
LEO as a result of Earth’s upper atmosphere, only UV degradation needs to be considered;
in addition to this, metals are not generally affected by UV radiation [70], so degradation only
needs to be considered for polymer materials such as Zylon, which are generally heavily af-
fected by UV. It is known that polymers exposed to UV radiation lose tensile strength over
time, as demonstrated in Table 3 of Gittemeier et al [29], in which the maximum tensile load
dropped from 386 N for unexposed Zylon, to as low as 306 N for Zylon exposed to UV radiation
32 4. Tether Design
for 518 ESH (Equivalent Sun Hours), or around 20 days.
Therefore it may be preferable to use a metal such as Aluminium as the EDT material, but
in the case that a polymer fibre is used for the EDT, a UV resistant coating such as Nickel
should be used, which showed some promise in protecting Zylon [29], but despite this, further
research must be done to determine if these coatings are truly resistant.
4.1.2. Type
There are a number of types of space tether commonly presented in literature; these are as
Single round wire - this is a single wire of certain diameter, which can be a single material
wire akin to a single core electronic cable, or a composite wire such as the TSS-1R tether
shown in Figure 4.1.
Woven cable - this is similar to the single round wire, but consists of multiple single wires
woven together like a rope.
Tape tether - this is, as the name implies, a tape-like (rectangular) tether, with a compar-
atively much larger width than thickness; a diagram of a tether of this kind can be seen
in Figure 4.2.
Single-cable tethers are currently the type that are used in many historic missions, likely due
to their simplicity and relative infancy of using tethers in space outside of the context of tech-
nology demonstrators. However, tape tethers provide significant advantages over the more
conventional wire tethers. For example, tape tethers are more resistant to fatal micromete-
oroid impacts [38]; in addition to this they may provide a more effective electron collection
surface for bare tether designs.
4.1. Composition 33
Figure 4.2: Illustration of a tape tether, being impacted by debris [38].
4.1.3. Multiplicity
To address the reliability and survivability of a tether design, particularly tape tethers, espe-
cially one envisioned for interplanetary or interstellar travel with very long transit periods, it
is necessary to consider using more than one tether. This can either be done using one or
more entirely redundant tethers, or by other means. In literature, a prominent solution to this
is a double-wire solution, in which two wires are used knotted together at regular intervals, as
shown in Figure 4.3.
34 4. Tether Design
Figure 4.3: Comparison between a single tether solution (left), and double-knotted tether
solution (right) [66].
Another proposed solution is to use a multiline design using many individual lines, with cross-
linked secondary tethers to distribute the load in case of a single failure. This solution was
pioneered by Tethers Unlimited, and is known as the Hoytether; it can be formed either into a
tape-tether type design, or tubular tether design, as shown in Figure 4.4; this design was used
in the MAST mission mentioned in Chapter 2.
4.1. Composition 35
Figure 4.4: Hoytether multiline tether design from Tethers Unlimited [84] [33]. The left-most
image shows the hollow tubular design, the centre image the multiline tape tether design,
and the far-right image the damaged multiline tether, with secondary lines being used to
redistribute load.
The survivability of such a multiline tether compared to an equivalent single-line tether can be
seen in Figure 4.5, from which it can be clearly seen that the multiline tether vastly increases
the probability of tether survival.
36 4. Tether Design
Figure 4.5: Lifetime comparison of equal-weight single line and failsafe multiline tethers for a
low-load mission [84].
4.1.4. Conclusions of Tether Composition Analysis
Regarding the choice of tether material, it is quite clear that some kind of composite
solution would be preferable, especially for a tether many km long. But in the case of a
tape tether it may be necessary to use a single material, in which case aluminium would
be preferable, since it has good specific tensile strength, and it is an electic conductor.
Also regarding tether material, a polymer fibre should be avoided wherever possible,
since significant UV damage can be caused to these kinds of materials, and the effec-
tiveness of UV-protective coatings for them is dubious at best [29].
For the type of tether to be used, in any case the tape-tether design would be preferable
to increase spacecraft survivability. However, in light of the strength concerns implied
by the tape tether solution, it is likely that a single-wire or woven-cable solution will be
implemented to allow for a composite cable, making use of the Hoytether design shown
in Figure 4.4 in order to increase survivability. Further calculations into the required
survivability will need to be completed however.
Regarding multi-strand tethers, it is almost certain that some kind of multi-strand tether
will need to be implemented, in order to allow the tether to survive for many years, such
as is required for an interplanetary or interstellar mission.
4.2. Thrust Generation 37
4.2. Thrust Generation
Regardless of tether design, thrust generation is done on the basis of exploiting the Lorentz
force, as described in Chapter 3; therefore a current must flow through the tether. This can be
done in three main ways:
Constant current utilising an insulated tether - the basis for this current flow is to collect
electrons or positive ions on one end of a tether, and emit them at the other. In this case
these charged particles come from the surrounding ionosphere, but the tether does not
interact with them directly [27].
Constant current utilising a bare tether - like the insulated tether design, this works on
the basis of particle collection and emission, but in this case collects electrons from the
ionosphere directly on the tether, using it as an anode [73].
Transient current - unlike the previous two methods, transient current does not rely on the
external ionosphere to produce a current. Instead it uses an internal electricity source,
such as batteries, to send a current from one end of the tether to the other. It is transient
since a constant current cannot be achieved in this manner, however also unlike the
other methods it does not require an overall input of electrical power to function; hence,
aside from efficiency losses, a transient current system could have no net energy input
required. In addition, a transient current solution for an EDT has not yet been proposed,
but is possible in theory (E. Lorenzini, personal communication, Nov 6, 2019).
Both the insulated and bare tether designs rely on the emission / collection of charged particles,
with an example operation shown in Figure 4.6.
These are three examples of current generation, but it is of course conceivable that other
methods exist. The insulated tether provides an attractive option as the simulation is relatively
simple; however the collection / emission devices required on either end of the tether add
significant mass, which could be avoided by the use of a bare-tether solution. Therefore for
these reasons it is unlikely to utilise the insulated tether option.
38 4. Tether Design
Figure 4.6: Operation of a (partially) bare tether EDT envisioned for power generation on the
ISS [46].
The remaining methods require significantly more investigation to ascertain which is more
feasible for the research to be done in this study. For example the power requirements of
the bare tether design may be unsuitable to use in distant interplanetary / interstellar space;
similarly the non-constant nature of a transient current design may require the repeated re-
orientation of the tether, which could prove to be infeasible.
4.3. Stability / Pointing Method 39
4.3. Stability / Pointing Method
For an EDT, the Lorentz force acts directly on the tether, and is not necessarily uniform [72],
causing tether deformation in a free tether system; even with a uniform load distribution, which
is the classical estimate, tether bowing still occurs [72], as shown in Figure 4.7. Therefore
some method of stabilising or controlling the tether spacecraft must be devised to ensure the
tether remains taught, and in the correct orientation.
Figure 4.7: Illustration of a distributed load causing EDT bowing [72].
In previous space tether designs, used in Earth orbit or even Jupiter orbit [75], they rely on the
use of gravity-gradient stabilisation to maintain tether orientation; naturally, without an exceed-
ingly long tether and/or very large end-masses, the Solar gravity-gradient would be insufficient
to ensure a taught tether, and would be non-existant for interstellar missions. Therefore an-
other control / stabilisation method must be utilised.
One alternative method is that used in Pearson et. al. [67], in which the EDT utilises spin-
stabilisation; this increases the potential thrust that can be achieved by a tether system without
significant deformation (compared to a gravity-gradient stabilised approach), as well as allow-
ing any orientation plane desired for a given manoeuvre. The main issue however, is that
the spacecraft is of course not always in the orientation which would provide maximum thrust,
as the tether would not always be perpendicular to the magnetic field. Despite this, Pearson
asserts that tethers could spend between 50-75% of their time closer to the correct orientation
than away from it [67]. Figure 4.8 shows a few possible EDT thrust vectors for an Earth-based
spin-stabilised EDT mission.
Other stabilisation methods have not yet been found in literature, however the spin-stabilisation
method appears to be a feasible solution.
40 4. Tether Design
Figure 4.8: Diagram showing possible spin planes for an Earth-based spin-stabilised EDT
4.4. Conclusions
Based on the above analysis, the following conclusions can be drawn about the design process
of the EDT:
The tether composition is likely to be a Hoytether-type multi-line tether in order to en-
sure good survivability of the EDT using composite cables to provide both strength and
electrical conductivity; alternatively some kind of knotted tape-tether solution could be
employed, as this also has good survivability, but may require the use of a single material
in the tether.
Regarding thrust generation, the transient current solution is currently favoured, and will
be further investigated; however, since this has never been employed either in a historic
mission or paper study, it is important to also consider one of the other solutions. In this
case a (partially) bare tether solution would be employed, as it has been shown to be
more efficient than an insulated tether solution.
The spacecraft is most likely to make use of a spin-stabilised configuration in order to
keep the spacecraft in tension; primarily because no other option is readily apparent
for interplanetary or interstellar travel. This in itself presents some complications to the
spacecraft control system, but these are outside the scope of the current research thesis.
Supporting Spacecraft Parameterisation
In order to analyse the feasibility of an EDT, it is also necessary to have a reference spacecraft
upon which the EDT can operate; this section aims to develop such a reference spacecraft.
The spacecraft is to be sized based on historic interplanetary missions, including the sizing of
each spacecraft subsystem; an example of the Cassini interplanetary spacecraft can be seen
in Figure 5.1.
Figure 5.1: Cutaway diagram of Cassini spacecraft [61].
42 5. Supporting Spacecraft Parameterisation
5.1. Sizing of the Reference Spacecraft
Table 5.1 shows the typical mass and average power distributions across subsystems for in-
terplanetary spacecraft. For the most part it provides a good initial estimate for the mass and
power requirements for most spacecraft subsystems; for example the on-board processing re-
quirements for an EDT spacecraft would be similar as for most other types of spacecraft.
Table 5.1: Part of table A-1 and A-2 from New SMAD [91], showing typical subsystem mass
and average power distributions distributions for an interplanetary spacecraft.
Subsystem % dry mass % total power
Payload 15 22
Structure and Mechanisms 25 1
Thermal Control 6 15
Power (including harness) 21 10
Telemetry Tracking & Command 7 18
On-board Processing 4 11
Attitude Determination and Control Subsystem (ADCS) 6 12
Propulsion 13 11
Other (balance and launch) 3 0
Average dry mass (kg) / Average power (W) 888 749
However, the estimations made in Table 5.1 use historical data from spacecraft such as Cassini,
which are very large spacecraft of many hundreds of kg; this type of spacecraft is not particu-
larly suited to having an EDT as primary propulsion system. It is for this reason that a number
of nanosatellites (some interplanetary) and small-satellites were selected to provide an alter-
native mass and power distributions for the reference spacecraft; the satellites used for this
parameterisation are outlined as follows:
The MEMS (MicroElectric Mechanical Systems) satellite, weighing 2.6 kg, is a paper
study for a CubeSat nanosatellite utilising cold gas thrusters for orbit control in Earth
orbit [41].
The ESTCube-1, weighing 1.1 kg, is an Estonian CubeSat launched in 2013 to demon-
strate the use of a solar sail in Earth orbit [42].
The ADR (Active Debris Removal) satellite, weighing 23.4 kg, is a paper study for a
cubesat used to manage space debris for future mega-constellations [13].
The Solar Sail 1 and 2 spacecraft, weighing 280 kg and 343 kg respectively, come from a
paper study utilising the Solar wind as a means of interplanetary propulsion. The different
values used come from the initially presented 0.1 mm/sacceleration variant (Table 2 in
Janhunen [36]), as well as a 1 mm/sacceleration variant (Table 5 in Janhunen [36]).
It should be noted that in this case the data was not used for the power distributions,
as the paper is intended as a mass budget model, and so the power distributions are
somewhat unclear.
The mass and power distributions based on these are shown in Table 5.2, and it should be
noted that the spacecraft used and data about them can be found in Appendix B.
5.1. Sizing of the Reference Spacecraft 43
Table 5.2: Mass and power distribution averages of small and nanosatellites [13] [36] [41]
[42] . Further description of the values used can be found in Appendix B.
Subsystem % dry mass % total power
Payload 26.4 27.9
Structure and Mechanisms 19.0 0.5
Thermal Control 1.5 0.0
Power (including harness) 13.5 3.3
Telemetry Tracking & Command 9.2 24.9
On-board Processing 2.9 5.7
Attitude Determination and Control Subsystem (ADCS) 6.6 8.4
Propulsion 20.0 27.5
Other (balance and launch) 0.4 0.0
Average dry mass (kg) / Average power (W) 130 117
Of course, the estimations made in Tables 5.1 and 5.2 begin to lose relevance for an EDT
spacecraft when considering subsystems such as propulsion or power. Therefore, for the
purposes of the analysis done in this research, the following methodology was taken in order
to roughly parameterise the supporting spacecraft:
It was first determined qualitatively, which spacecraft subsystems would be significantly
affected when adopting the use of an EDT, compared to the average interplanetary
The mass and power of these relatively unaffected subsystems were then determined by
using the average mass and power values of those subsystems for historic spacecraft.
The mass and power requirements of the unaffected subsystems were totalled up and
could then be considered as the ”base spacecraft” upon which the other relevant sub-
systems can be designed to.
The first stage of this methodology is outlined in Table 5.3.
Table 5.3: Summary of the spacecraft subsystems directly affected by the use of an EDT.
Subsystem Affected?
Payload No
Structure and Mechanisms No
Thermal Control No
Power (including harness) Yes
Telemetry Tracking & Command No
On-board Processing No
Attitude Determination and Control Subsystem (ADCS) No
Propulsion Yes
Other (balance and launch) No
The justification for these choices is in many cases self-evident, there are however a few which
must be further explained:
Structures and mechanisms - Of course the structure and required mechanisms of an
EDT system on board a spacecraft are very different compared to that of the average
44 5. Supporting Spacecraft Parameterisation
spacecraft. However, it is assumed in this case that any structural or mechanical re-
quirements unique to the EDT are taken on in the design of the EDT itself, instead of as
part of this subsystem.
Thermal control - It could be argued that the use of a km-long EDT could substantially
affect the thermal qualities of a spacecraft and therefore the thermal control system.
However, since most of the heat generation and dissipation is done away from the tether
itself, by dedicated components, this can be neglected at the current stage of research.
Power - Depending on the implementation chosen for the EDT, the EDT itself may require
significant power inputs to function properly; similarly depending on the mission it may
provide an opportunity to provide power to the spacecraft itself. Therefore, naturally the
power system is heavily affected by the use of an EDT in the design.
ADCS - Of course the ADCS challenges of using an EDT in a spacecraft are significant.
However, these are mostly related to the stabilisation and pointing of the EDT, which
would typically not be done actively due to the large size of the EDT. Therefore the
active portion of ADCS should be comparable to that of a regular spacecraft.
The completion of the subsequent stages of the presented methodology results in the base
spacecraft parameterisation shown in Tables 5.4 and 5.5. It should be noted that even in the
small satellite case, it is certainly possible that a smaller satellite could be considered, since
the large solar sail used in the averages skews the results somewhat.
Table 5.4: Summary of base spacecraft parameterisation for conventional satellites, upon
which the power and propulsion subsystems can be designed.
Subsystem Subsystem Mass (kg) Subsystem Power (W)
Payload 133 165
Structure and Mechanisms 222 8
Thermal Control 53 112
Power (including harness) TBD TBD
TT&C 62 135
On-board Processing 36 82
ADCS 53 90
Propulsion TBD TBD
Other (balance and launch) 27 0
Base spacecraft total 586 592
5.2. Discussion of Changes / Conclusions to the Reference Spacecraft 45
Table 5.5: Summary of base spacecraft parameterisation for small satellites, upon which the
power and propulsion subsystems can be designed.
Subsystem Subsystem Mass (kg) Subsystem Power (W)
Payload 34.3 32.7
Structure and Mechanisms 24.7 0.6
Thermal Control 1.9 0.0
Power (including harness) TBD TBD
TT&C 12.0 29.3
On-board Processing 3.8 6.6
ADCS 8.5 9.8
Propulsion TBD TBD
Other (balance and launch) 0.5 0.0
Base spacecraft total 85.7 79.0
5.2. Discussion of Changes / Conclusions to the Reference Space-
Presented in Section 5.1 is a fairly flexible estimate of the mass and power budgets for the ref-
erence spacecraft, allowing for both large traditional spacecraft, as well as small and nanosatel-
lites. These values are of course subject to change as the EDT develops, however the EDT
will be developed in such a way that its own sizing attempts to line up with the sizing of the
rest of the spacecraft. However, if for example the spacecraft would only be feasible for a very
barebones spacecraft (i.e. a reduced payload) then this would also be considered in the main
thesis project.
Orbital Dynamics
To determine the feasibility of using an EDT for propulsion (and/or power generation), a number
of orbital simulations can be expected to be run; in this section all the elements related to
creating this simulation are specified. The different classes of elements to consider can be
split into three main categories; namely the selection of relevant orbit perturbations, analysis
of propagation techniques (including the choice of orbital elements), as well as an anlysis of
the possible integration techniques.
For the purposes of this analysis, it is assumed that the spacecraft begins its journey in a
circular Solar orbit at 1 AU, but not in orbit around the Earth. It is also assumed that the
spacecraft only travels through the interplanetary or interstellar medium; it does not come
in close proximity (i.e. inside the sphere of influence) with other bodies such as planets or
asteroids, so that disturbances such as atmospheric drag can be effectively neglected.
48 6. Orbital Dynamics
Figure 6.1: Juno spacecraft trajectory diagram [59].
6.1. Perturbations Selection
There are a number of perturbations which can be considered in an orbital simulation, and it
must be decided for each one if it should be included or ignored. The following list of potential
orbital perturbations is taken from Chapter 20 of Wakker [89]:
Non-point mass gravitational perturbations.
Atmospheric perturbations.
Third-body gravitational perturbations.
Radiation perturbations - solar and albedo.
In order to determine if a perturbing force should be included, the main criterion is to compare
its intensity to that of the force exerted by a possible EDT; since a specific destination is not in
mind, the required accuracy of the simulated orbit is such that a useful conclusion about the
use of EDTs can be made.
6.1. Perturbations Selection 49
According to Pearson et al [67], it is possible to obtain 500 mN of thrust from a 100 kg tether in
LEO; similarly according to Johnson et al [37], it is possible to obtain 500-800 mN thrust from a
200 kg tether in LEO. To determine EDT acceleration with distance the following assumptions
are used:
A 200 kg tether can produce 500 mN thrust in LEO [37], which has an approximate
magnetic field strength  = 45 µT [25].
According to SMAD [91], the propulsion system of an interplanetary spacecraft is 13%
of dry mass. Using the tether mass as propulsion system mass, this produces a total
spacecraft mass of 1538 kg, assuming there are no propellants (i.e. dry mass equals
wet mass). It should be noted that information regarding the exact mass distribution of
tether-based satellites is very difficult to come by, so although the 13% figure given by
SMAD is probably not ideal, it is sufficient for the current analysis.
The thrust produced by the spacecraft scales linearly with magnetic field strength, which
is true if other factors do not change [35].
Heliospheric magnetic field strength follows the profile shown in Figure 3.6, with median
values for and taken.
Using the first two assumptions a baseline acceleration can be found to be  = 0.325
mm/s, corresponding to the baseline magnetic field strength . Using the remaining
assumptions, the EDT acceleration can be simply found at radius using Equation 6.1.
 
This equation can then be combined with the magnetic field data described in Section 3.1 to
approximate the potential acceleration of an EDT spacecraft, in order to compare against the
accelerations caused by other sources.
6.1.1. Central Body Gravity Perturbations
In many orbital simulations, gravitational bodies are treated as simple point masses. In reality
this is not the case, meaning the shape and mass distribution of a body can influence the
gravitational force exerted on an orbiting body; a common way to treat these gravitational field
irregularities is to use the concept of Spherical Harmonics (SH) [89].
Figure 6.2: Diagramatic representation of spherical harmonics. From left to right are P,
P, and P [26].
SH perturbations are generally strong near the surface of the central body; for example the
50 6. Orbital Dynamics
SH component for flattening on the Earth produces a maximum perturbing acceleration 
of 2.73 cm/sat an altitude of 250 km, which then quickly drops off to  of 8.3310
m/sat geostationary altitude [89]. Using similar computations for the Solar term, which
is  according to Rozelot et al [71], shows that the maximum ac-
celeration at 0.1 and 1.0 AU is -2.3610 -2.3610 m/srespectively. These numbers
show that the Solar SH perturbations can be considered negligible, and the Earth SH pertur-
bations at low altitude could require consideration, depending on the final mission profile to be
It should also be noted that certain otherwise negligible perturbations, such as those found at
geostationary altitudes, can become significant when a spacecraft is placed at the same posi-
tion relative to the surface of the orbited body, such as for geostationary orbits [89]. However,
the mission profile considered for interplanetary EDTs does not have behaviour such as this,
and so these can safely be ignored.
In order to properly calculate the Solar SH perturbations in Figure 6.5, Equations 6.2 and 6.3
[63] can be used to calculate  and  respectively, in which only  is taken
as it is always the larger of the two.
 
6.1.2. Atmospheric Perturbations
Low-altitude orbits around the Earth and other bodies with atmospheres can induce atmo-
spheric drag perturbations to the orbit. The mission profile for this research is predominantly
conducted outside the Earth system, where any atmospheric drag can be completely ne-
glected. According to Wakker [89], atmospheric drag can also be completely neglected above
1000 km altitude from the Earth; since using the EDT to escape the Earth system is a possi-
bility, and the thrust provided is small, atmospheric drag should be considered at lower Earth
altitudes, ie below 1000 km, if necessary.
6.1.3. Third-Body Gravitational Perturbations
As well as the central body in an orbit simulation, it may also be necessary to take into account
Third-body perturbations. To calculate the magnitude of this acceleration, the well-known
equation for gravitational acceleration can be used, shown in Equation 6.4; refers to the
gravitational acceleration of the body in question, to the gravitational parameter of the same
body, and to the distance of the spacecraft from the body.
Using this simple equation however presents a problem, namely that it is not known the ra-
dius to each planet at any given time without the use of simulation or planetary ephemerides.
Therefore as a simple estimate, the Point Circle Method (PCM), also known as the Whirly-Dirly
corollary can be used [81]. This gives the average distance between two bodies in circular
,around the Sun using Equation 6.5, in which and are the orbital radii of the first
and second body respectively, and is an elliptic integral of the 2nd kind [81].
6.1. Perturbations Selection 51
Equation 6.5 shows a screenshot from a YouTube video demonstrating the average distances
over time of Venus, Mars and Mercury to the Earth [78].
Figure 6.3: Screenshot from a YouTube video showing the Wirly Dirly Corollary for the
distance from Earth to each Venus, Mars, and Mercury [78].
Using this method it is possible to estimate the average distance a spacecraft would be to
any given planet as it travels through the Solar System; of course the method is not perfect
but it does present a reasonable estimation for a representative disturbing acceleration for the
purposes of this analysis.
6.1.4. Radiation Perturbations
Perturbations from Solar radiation are an important consideration to make, as a Solar sail is
another propelantless method of propulsion that could be considered for interplanetary travel.
The radiation acceleration applied to a spacecraft is given by Equation 6.6 [89];
is the satellite
acceleration, the satellite reflectivity, the radiation intensity, the satellite cross-sectional
area, the spacecraft mass, the speed of light (in vacuum), and the unit vector from the
satellite to the Sun.
 (6.6)
In order to apply this equation, it is necessary to know a number of the spacecraft-specific
parameters such as satellite reflectivity; for this the TiPS EDT satelite discussed in Chapter 2
can be used as a representative spacecraft, as shown in Figure 6.4. Its components and
properties are as follows:
52 6. Orbital Dynamics
The ”Ralph” endmass, with mass 42 kg and dimensions 69 x 36 x 18 cm [62].
The ”Norton” endmass, with mass 10 kg and dimension 69 x 36 x 18 cm [62].
The tether itself, which has mass 5 kg, is 4 km long, and has a diameter of 2-3 mm (in
the following calculations 3 mm is used) [62].
Figure 6.4: Graphic of the US Naval Research Laboratory’s TiPS tether satellite. Note that
only a small part of the 4 km tether is shown deployed [53].
To determine the Solar radiation intensity at a particular distance from the Sun , a 
relationship can be used, as shown in Equation 6.7 [89]; is the solar intensity at distance
from the Sun .
For each parameter required in Equations 6.6 and 6.7, the following values are used and
= 1.5, since for most spacecraft [19].
= 1367 W/m[64].
= 1 AU, since this is where is measured at.
= 12.5 m, this is the sum of above described components of TiPS, assuming the
largest sides of the spacecraft are facing the Sun.
= 57.6 kg [62].
6.1. Perturbations Selection 53
=m/s [64].
6.1.5. Conclusions About Perturbations
Using the calculation methods from the previous sections, the different perturbations can be
compared against each other, at varying distances from the Sun. This can be seen in Fig-
ure 6.5, which shows accelerations for each perturbation, normalised with the Solar acceler-
ation at that distance. For reference, the Solar acceleration at 1 AU is 0.006 m/s.
Figure 6.5: Summary of different perturbation intensities varying with distance from Sun.
Results are normalised with the Solar gravitational acceleration. Third-body perturbations of
various bodies are indicated by dashed lines, and other perturbations (as well as estimated
EDT acceleration magnitude) can be seen by solid lines, colour coded as shown in the
From Figure 6.5, the following conclusions can be made:
In the inner Solar System (< 1 AU), the EDT acceleration is small, being much smaller
than SRP, but larger than third-body perturbations.
In the middle-outer Solar System (≈1 - 30 AU), EDT acceleration is of similar magnitude
as other perturbations such as third-body.
In the far outer Solar System (30 AU), the EDT acceleration is generally larger than
SRP, and all 3rd body accelerations, with the exception of Jupiter, until past ≈100 AU.
The above observations show that the EDT in this configuration has a potential use in the inner
54 6. Orbital Dynamics
Solar System, with magnitudes greater than many other perturbing accelerations, but unlikely
to be competitive with alternative propulsion such as a solar sail. This is demonstrated by the
fact that the radiation perturbation is much stronger than the EDT force, and in this case the
radiation force is not intended as a means of propulsion.
It can also be concluded that the EDT has some use in the middle-outer Solar System, but
less so than in the inner Solar System, as the EDT force becomes of similar or smaller in
magnitude than many other perturbations such as third body or radiation.
Finally it can be concluded that the EDT becomes a vastly more viable means of propulsion
in the far reaches of the Solar System, as it becomes orders of magnitude stronger than all
perturbing forces. There are also methods such as increasing tether length, and increased
current through the tether, which may be able to further increase the viability of a deep space
6.2. Propagation Analysis
There are two main aspects of propagation to consider here; firstly are the propagation tech-
niques themselves, and secondly is to consider if a full 3D simulation is needed, or if a simpler
2D system could be used instead. These considerations are split into different subheadings
6.2.1. Propagation Techniques
A series of propagation techniques are known for use in space simulations, which also deter-
mine the choice of state representations which are to be used. A useful diagram illustrating
osculating orbits, and a unified state model representation can be seen in Figure 6.6. The
propagation techniques to be considered are briefly summarised below:
6.2. Propagation Analysis 55
Figure 6.6: Diagram of an osculating orbit, a concept used in many propagation schemes
such as Encke (left) [89], and a diagram of the vectors used in a USM representation (right)
Cowell - This is arguable the simplest propagation scheme, simply consisting of a direct
numerical integration, usually in rectangular coordinates. Due to the simplicity of the
method it can be used in almost any circumstance [89]. The method is often used for
highly perturbed motion / chaotic motion, when other more sophisticated methods lose
their advantages.
Encke - This is another classical method of orbital propagation, and relies on the use of a
reference orbit, usually modelled in Keplerian elements, upon which only the deviations
are integrated numerically [89]. The method is often used for short-term propagations,
or orbits with minor deviations from Keplerian orbits.
Variation of Orbital Elements (VOE) - This method relies on considering the motion of the
satellite to be continuously transitioning between osculating Keplerian orbits, to produce
the final true orbit [89]. In this way, the orbit is represented as a Keplerian orbit with
constantly changing parameters. The method is often used for perturbed motion far
from the singularities inherent in a Keplerian orbit representation.
Modified Equinoctial Elements (MEE) - In the VOE method, singularities are present at
various geometries, such as when eccentricity is 0 (a circular orbit), or when inclination
is 0° or 180°. The MEE method aims to remove these by ”merging” Keplerian elements,
such that only the inclination-based singularities persist [20]. In addition to this, the
singularities can be avoided by certain formulations of the MEE [16]. The model is often
used for perturbed motion near singularities that would arise from Keplerian propagation.
Unified State Model (USM) - Like the MEE method, USM aims to remove singularities
56 6. Orbital Dynamics
from the VOE method by merging parameters. This is achieved using a 4-parameter
representation for a 3-dimensional orbit orientation, or a 3-parameter representation for
2 dimensions; in this method all singularities are removed [20]. The method is often used
for perturbed motion near both Keplerian and MEE singularities.
From this brief outline, the Encke method can be immediately discounted, since the use of
an EDT, or indeed any propulsion system, intends to deviate from a particular reference orbit.
Therefore propagation errors as time goes on will tend to increase.
The Cowell method is an attractive option due to its simplicity and robustness, however the
large state derivative values, and variations in them, can lead to large numerical errors, and a
difficult-to-adapt timestep.
Both VOE and MEE present useful advantages in reduced numerical errors compared to Cow-
ell, however in the scope of this research it is likely that the spacecraft will be in a low-inclination
orbit around the Sun - a regime where both VOE and MEE can encounter singularities. These
singularities are unavoidable for VOE, however the singularities near an inclination of 180°
for MEE can be avoided by using a retrograde formation of the equinoctial elements [16].
Therefore although VOE is attractive, it is likely to be ignored due the issue with singularities,
however MEE is certainly a strong contender, especially since a singularity can only be found
in the retrograde case, and can be avoided if necessary.
USM provides a solution with higher numerical accuracy than Cowell and Encke, but without
the singularities encountered in VOE and MEE, therefore it is naturally a very attractive option.
One issue with USM is the increased complexity compared to other methods, which must be
taken into account when deciding upon a propagation scheme.
6.2.2. Analysis of 2D or 3D Simulation
A second consideration to make about propagation besides the technique, is whether a full
3-dimensional simulation is required, or if a 2-dimensional approach is sufficient; examples of
these simulations can be seen in Figure 6.7 [88]. For the scope of the research to be con-
ducted, it is envisioned that the spacecraft will travel exclusively on or near the solar ecliptic;
the justification for this is that in Chapter 3 it was found that the HMF is generally stronger
at lower latitudes and therefore lower inclination orbits. It is also known that there will be
negligible out-of-plane forces acting on the spacecraft.
6.3. Integration Techniques 57
Figure 6.7: Example of a 2d orbit simulation (left), and a 3d orbit simulation (right) [88].
6.2.3. Conclusions of Propagation Analysis
The main conclusions of the above analysis are as follows:
Either a Cowell, MEE, or USM propagation scheme should be used for the orbit simula-
tion. Further analysis must be done to determine if the increased numerical accuracy of
the USM method is justified by the increased complexity compared to Cowell or MEE.
Other methods were discounted due to the likelihood of encountering singularities, or
poor numerical accuracy.
In the propagation scheme, a two-dimensional orbit approach can be utilised, assuming
the spacecraft travels in a single plane.
6.3. Integration Techniques
Integration of the satellite equations of motion is of course essential for any numerical simula-
tion, and for this there are a number of different integration techniques that can be considered.
The scope of this research is not to perform a full specific optimisation analysis, and therefore
a quantitative analysis of integration methods is not justified; however it is possible to qualitita-
tively compare the different kinds of integrator in order to pick an appropriate one. According
to Montenbruck and Gill [50] there are three major categories of integrator, suitable for use in
space simulations:
Runge-Kutta (RK) methods - these are particularly easy to use and may be applied to a
wide range of different problems.
Multistep methods - these have a high efficiency, but require storage of past data points
and specific knowledge of the problem; an example of these are the Adams-Bashforth
Extrapolation methods - these are well known for their high accuracy, and are powerful
single-step methods such as Bulirsch-Stoer.
In order to compare the different methods a selection of their performances are plotted in
Figure 6.8 [50]. The specific integrators that are compared are as follows [50]:
58 6. Orbital Dynamics
DOPRI8 - an 8th order RK4-family integrator.
ODEX2 - an extrapolation method intended for use with second-order differential equa-
DE - a variable order and stepsize multistep method integrator.
FILG11 - an 11th order RK4-family integrator, with implementation similar to DOPRI8.
It is known that most of the simulations performed in this research will be of higher eccentric-
ities, therefore the focus when choosing an integrator will be on the high eccentricity regime
(i.e. e=0.9). It is also known that extreme simulation accuracy is not required for the research,
therefore focus will be given to low / mid level accuracy, from 6 digits up to around 10 dig-
Figure 6.8: Performance diagram of several single- and multistep methods for test cases
e=0.1, the lower set of curves, and e=0.9, the upper set of curves. The number of function
calls is plotted versus the relative accuracy in digits [50].
From Figure 6.8 it is clear that all integrators have similar performance (i.e. fewer function calls)
for lower accuracy levels, before diverging more strongly for higher accuracies. However it
can be clearly seen that in the considered accuracy range the FILG11 and DE methods are
superior in accuracy compared to ODEX2 and DOPRI8; incidentally this is also the case for
the e=0.1 case. Therefore either the FILG11 or DE integrator will likely be used in future
6.3.1. Conclusions of Integration Analysis
The main conclusion of the above analysis is that either the FILG11 or DE method will be used
for future simulations; however it can also be said that the FILG11 method will be favoured
over DE, since FILG11 is from the RK4 family of integrators, and therefore would be simpler to
6.3. Integration Techniques 59
implement (and is already implemented in toolboxes such as Tudat [85]) than the DE method,
which is a multistep integrator.
Optimisation of a specific mission profile by, for example, attempting to achieve the smallest
Time Of Flight (TOF), is beyond the scope of the research of this project. However, there
are two main areas where mission properties can be changed, in order to ”optimise” for a
preferable or feasible overall direction for an EDT mission to take. These are the different
scenarios / applications that the EDT can be applied to, and the specific (physical) properties
of the EDT that can be varied; both of these will be addressed in this section.
7.1. Variation of EDT Spacecraft Applications / Mission Scenarios
The EDT propulsion system can be applied to a number of different applications / scenarios,
to establish which applications the EDT is most feasible in, or to establish in which stages of a
mission an EDT would be useful. Some potential simulation scenarios are outlined and briefly
described below:
Basic low-thrust propulsion from 1 AU - this is the most straightforward application of the
EDT, in which a low-thrust simulation is created, and the EDT is simply allowed to thrust
in the prograde direction; an example of this is shown in Figure 7.1 [14].
EDT after conventional propulsion kick stage - this is also a fairly simple application, in
which the EDT spacecraft is given an impulse from a kick stage, which is commonly used
for interplanetary spacecraft [45].
Using gravity assists in combination with EDT - as with many other interplanetary mis-
sions, an EDT spacecraft could make use of planets such as Jupiter to gain additional
Initial travel to the inner Solar System - as described in Section 6.1, the EDT has the
best potential performance in the inner, and far outer Solar System; therefore it could be
advantageous to first venture to the inner Solar System before being propelled into the
outer Solar System.
”Loitering” around areas of high propulsive potential - certain regions of the Solar System
provide a high potential for the EDT to create a high thrust. For example, as described in
Section 3.1, the magnetic field strength peaks along the border between interplanetary
and interstellar space (i.e. the heliosphere). Therefore a trajectory that rides the line
along the heliosphere may be able to utilise this increased field strength to achieve higher
62 7. Optimisation
Variations of the chosen direction upon leaving the Solar SOI - when leaving the SOI, the
interstellar medium has different properties in different directions, and so some directions
of travel may be favourable over others.
In the main thesis project each of these scenarios will be simulated, as well as combinations
of them, for example by using gravity assists in combination with travel into the inner Solar
System; the final choices of configurations considered can be found in Chapter 8.
Figure 7.1: A low-thrust spiral trajectory for Earth-Mercury transfer [14].
7.2. Variation of (Physical) EDT Characteristics
The second major set of parameters that can be varied for some level of optimisation, is the
components of the EDT itself, which are described in Chapter 4. Some examples of properties
that could be varied are as follows:
Tether length - according to the Lorentz equation, the longer the tether the stronger the
Lorentz force, so variations in long and short tethers can be investigated.
Tether current - also according to the Lorentz equation, a higher current induces a greater
Lorentz force, and variations to it could also be investigated.
Tether concept - the various conceptual aspects of the tether such as the use of a multi-
line versus a single-line tether, could be modified and the effects of which investigated.
In the main thesis project the various combinations of these variations will also be tested.
In order to reduce the number of combinations of simulation scenarios and tether variations,
the different scenarios can be tested with the same reference spacecraft, in order to determine
a few promising combinations of scenarios, which can then be taken to the next round of
testing, in which the EDT itself can be changed.
7.3. Optimisation Targets and Constraints 63
7.3. Optimisation Targets and Constraints
Within any optimisation problem, it is necessary to outline what is being optimised, and within
what constraints those goals should be achieved. The three main optimisation targets to be
considered can be outlined and justified as follows:
Mission transit time - this is essentially the length of time the mission is in transit to the
target location. It is obviously a major consideration, since it is of course better for a
spacecraft to begin performing measurements and producing useful data as soon as
Probability of mission survival - of course another consideration to make, especially with
a long mission such as is considered in this research, is how likely the spacecraft is
to survive. This is directly linked to the mission transit time, as spacecraft components
tend to degrade over time; but it is also related to mission decision that may cause the
spacecraft to suffer catastrophic failure as described in Section 3.3.
Spacecraft ”cost” - this indirectly refers to the effort required to launch and operate the
spacecraft. It generally refers to the size, mass, and power consumption of the space-
craft. In the context of this research, that entails the variation of parameters such as
overall tether length and the current passed through the tether.
The parameters related to these targets also form the optimisation constraints. For exam-
ple, the mission transit time should at maximum be within a human lifetime (in the case of a
non-interstellar mission). Similarly, the mission should also have a probability of survival that
justifies its cost, although since neither of these values can be readily quantified, some more
work must be done to determine the exact limits to be placed on them.
7.4. Optimisation Algorithms
Various optimisation algorithms are available to use for spacecraft trajectory analysis, espe-
cially for gravity assist-based trajectories which may potentially be utilised, according to page
57 of Hoving [31] one of if not the best candidate for the algorithm of choice is Differential
Evolution (DE).
DE algorithms come in a number of varieties however, many of which are already implemented
into Pagmo [1] (which will be used in the final thesis, as shown in Chapter 9); therefore in the
main thesis a brief analysis of these different DE varieties will be assessed and one cho-
7.5. Gravity Assist Selection Method
In order to generate solutions for gravity assist manoeuvres that could be desired by the mis-
sion concepts, for this see Chapter 8, a good method must be provided. Traditionally this
would involve the use of a Lambert solver, however this assumes that the propulsion is impul-
sive, which is naturally not the case for a low-thrust method employed by an EDT; therefore
another method must be utilised.
A particularly promising method is the Spherical Shaping Method for low-thrust trajectories;
the method is already implemented into Tudat [86], and is often used for low-thrust transfers
such as between Earth and Mars. In addition to this, the method has been used in the MSc
thesis of Hoving [31] in order to run simulations for multiple gravity assists using low-thrust
propulsion systems - the exact situation which is required of this research. Hoving notes that
there are limitations when the method is applied to non-small inclinations, however this is not
an issue in the current research, as all trajectories are anticipated to fly on or near the Solar
64 7. Optimisation
System equatorial plane. In addition to this, Hoving ran simulations for gravity assists using
moons in a planetary system, but naturally the concept can be scaled up to the Solar System
7.6. Conclusions
From the discussion in this section, the following conclusions can be drawn:
A number of physical components of the EDT can be varied, within a specific EDT con-
cept, to optimise the ”cost” of the EDT.
A number of mission scenarios can be explored, which will be further addressed in Chap-
ter 8.
The main targets and constraints for the EDT simulations are the mission transit time,
probability of mission survival, and ”cost”. Making the final optimisation a multi-objective
The primary optimisation algorithm to be used will be of the DE family, as it is best suited
to trajectory analysis, and is readily available to use in Tudat and Pagmo.
The spherical shaping method for low-thrust trajectories can be used for both regular
optimisation efforts, as well as for (multiple) gravity assist optimisations.
Validation / Target Cases
In this section two parts of the thesis are assessed; firstly the verification/validation cases,
which are used to demonstrate the capability of the developed simulation environment. Sec-
ondly are the target cases, which present some of the eventual goals which the EDT spacecraft
should achieve, in order for the research question to be considered answered.
8.1. Validation Cases
Once a simulation environment is created to test the feasibility of the EDT propulsion concept
in interplanetary or interstellar space, this simulation environment should be verified against
either a simpler (analytical) simulation, and/or validated against another simulation done by
other members of the scientific community.
Each component of the simulation environment can be verified individually; since the full sim-
ulation environment has not currently been created, it is difficult to say for sure which compo-
nents will be present to be verified, but the following list gives an idea of some of the major
Orbit simulation - the orbit simulation component can be verified by having no current
running through the EDT, and simulating a few orbit scenarios in the full simulation en-
vironment, and comparing those simulations against simulations made as examples in
Tudat for example. Some of those scenarios could include a simple circular orbit around
the Sun, or the simulation of a highly eccentric orbit around the Sun.
EDT thrust generation - using the Lorentz equation it is possible to analytically calculate
the thrust that should be produced by an EDT. A few points in the spacecraft trajectory
can be chosen, where this thrust can be analytically calculated and compared against
the simulation’s output of the generated thrust.
Magnetic field simulation - some locations where the magnetic field strength is (approx-
imately) known, for example data points collected by the Voyager spacecraft, can be
compared against the output of the magnetic field strength by the simulation.
Validation is somewhat more difficult, since there are no extensive calculations that have been
done for EDTs in interplanetary or interstellar space. However, some other scenarios such as
an Earth-based simulation can be used. Some previous simulations that could be emulated
to compare against include:
66 8. Validation / Target Cases
The brief calculations done in NASA’s interstellar EDT study [49].
The study done on GTO debris removal using an EDT [94].
The studies done on Jupiter capture and eccentricity reduction manoeuvres using an
EDT [75], an example manouvre of which is shown in Figure 8.1, and a tour of Jovian
moons using an EDT as propulsion [74].
Figure 8.1: Diagrams of a 50km length EDT spacecraft performing an eccentricity reduction
manoeuvre [75]. Orbit diagram showing where the EDT is thrusting (left); thrust is being
applied in the dark region, in the prograde direction. Plot showing eccentricity reduction over
time (right).
8.2. Target Cases
Based on the results of the perturbations analysis done in Chapter 6, it appears that an EDT
could be effectively applied either in the inner Solar System, or in the far outer Solar System
/ interplanetary space. In addition to this, the prompt for this research topic stemmed from
the lack of solutions for effective propulsion in the outer Solar System; therefore the target
cases will primarily aim to send a spacecraft on far outer Solar System / interstellar applica-
With these ideas in mind, a few mission targets can be considered:
Outer Solar System planets / planetoids - this includes sustained missions to the gas
giants such as Jupiter, or smaller planetoids such as Pluto; the distance from the Sun
can range up to around 50 AU. Missions at this range from the Sun are of course within
the scope of current technologies, and the application for EDTs would mainly be for
long-term planetary system tours around planets with a significant magnetic field such
as Jupiter or Saturn. The justification for these kinds of missions is that there is still a
large amount of research to be done on these bodies; in particular the very far-out bodies
such as Uranus or Neptune, neither of which have had a spacecraft sent to them since
”Mission to the edge of the Solar System” type scenarios - the inability to conduct a
mission of this kind with current technologies was the initial inspiration for the further
8.2. Target Cases 67
research into EDTs, and presents a good opportunity for an EDT to facilitate extended
research in the far reaches of the Solar System. For the purposes of this research the
”edge of the Solar System” is defined as the region where the Solar magnetic field is
still dominant over the interstellar one, that is within the heliopause. This ranges from
around 100 up to around 1000 AU, depending on the direction of travel from the Sun
(see Figure 3.8). Scientific study in this area of the Solar System could include study of
Kuiper-belt objects, or the interaction of the Solar wind with the interstellar medium.
Near-solar interstellar travel - for the purposes of this research, this includes regions
beyond the previous definition of the edge of the Solar System, but still within the grav-
itational influence of the Sun. It includes distances from the Sun ranging upwards from
about 1,000 AU; no spacecraft has been to these far reaches of the Solar System, and
would present a prime opportunity for close-up study of elements of the Oort cloud, while
on an extended mission in the area.
Far-solar interstellar travel - this refers to the possible application of an EDT to true
interstellar travel from one star system to another. For the purposes of this research,
the star system in consideration would naturally be the closest one, Alpha Centauri,
comprised of a triple-star system 4.3 light years (275,000 AU) from the Sun.
Figure 8.2: Distances (in AU) from the Sun of different portions of the Solar System [60].
The aim of all of these target cases would be to identify the EDT concepts that would make the
aforementioned missions feasible, as well as to quantify the parameters of the spacecraft that
would be required - i.e. the mass, size, power consumption etc. In addition to this, the use
of additional propulsion sources, such as an initial booster, or the utilisation of gravity assists,
can be investigated to further aid the feasibility of such concepts.
In the main thesis, the specific completion criteria to consider one of these target cases to
be successful will be further determined and outlined; in addition the feasibility of each target
case can be assessed.
In addition to simply having the above target cases, the final simulated missions can be com-
pared against previously outlined missions with similar goals, but using alternative propulsion
means. An example of this is the interstellar heliopause solar sail reference mission proposed
by ESA [44]. In this case their mission reaches interstellar space by aiming for the nose of the
68 8. Validation / Target Cases
heliosphere, and is intended to reach that location (i.e. a distance of 200 AU from the Sun)
within 20 years; if the proposed EDT missions can achieve results competitive with these
results by ESA, then the concept can certainly be considered viable.
8.3. Definition of Specific Cases
In light of the above discussion of potential target cases, as well as the optimisation consid-
erations discussed in Chapter 7, it is clear that all permutations of these possible solutions
cannot be explored; therefore a few specific cases are to be defined, to restrict the scope of
the final thesis.
The simulations will be conducted in two phases: firstly by choosing a specific EDT configu-
ration which will be tested on a number of selected mission profiles; secondly after a (brief)
analysis of the results produced from the first phase, the most promising mission profile will be
used in order to test the feasibility of a number of selected EDT configurations. This two-phase
approach allows for a range of variations of EDT implementations to be assessed, without the
need to fully simulate and analyse all possible permutations; it should be noted however that
it could be possible for certain combinations of EDT configuration and mission profile that will
inevitably not be tested may prove to be more feasible than those tested, however the two-
phase approach provides a good baseline to determine if the overall concept of an EDT could
be feasible at all.
Each selection of EDT configuration and mission profile can be further split into two cate-
gories: nominal testing and additional testing. The nominal testing cases are those cases
which should certainly be assessed for the thesis, whereas additional testing refers to those
cases which could be assessed, if time permits.
8.3.1. Mission Profiles
In this section the previously mentioned nominal and additional concepts for mission profile
are to be defined; these are shown in Table 8.1, which presents the mission type, abbreviated
designation, and mission target.
Table 8.1: Summary of nominal and additional mission profiles for investigation during the
Mission Type Designation Mission Target
Nominal SSO Far outer Solar System, HI, IM
Nominal InGA Far outer Solar System, HI, IM
Nominal SOKGA HI, IM
Additional EDGE HI only
Additional Alpha-C Alpha Centauri
To further expand on the selected mission concepts, they are outlined and justified as fol-
SSO - Nominal - Simple-Straight-Out - This profile is intended as the baseline, in which
the spacecraft starts in a 1 AU orbit around the Sun, and simply begins thrusting in the
prograde direction to see how far out the spacecraft can go before reaching the imposed
optimisation limits. It is unlikely to be particularly successful but acts as something to
compare other designs to.
InGA - Nominal - Inner Solar System, Gravity Assists - This profile is somewhat more
8.3. Definition of Specific Cases 69
complicated, and attempts to travel first to the inner Solar System, and then subsequently
fly to the outer Solar System. The profile also allows for the use of gravity assists, pri-
marily focused on the large outer planets such as Jupiter, to aid in increasing velocity.
The target for this profile is the same as SSO, which is simply as far out as it can get.
SOKGA - Nominal - Straight-Out with Kickstage and Gravity Assist - This profile is similar
to SSO, but in which the spacecraft receives an initial impulse from a kickstage, and is
allowed to utilise gravity assists; both of which are realistic possibilities if a mission were
planned in reality. The target for this profile is specifically further out areas such as the
HI and IM.
EDGE - Additional - Edge of the Solar System - This profile is intended to travel along
the ”edge” of the Solar System, in this case defined as the HI, to obtain extensive infor-
mation on the HI, by staying in or near it instead of simply passing through. The profile
has no limitations on potential concepts such as gravity assists, and is intended to use
information gathered from the nominal simulations to inform such decisions.
Alpha-C - Additional - αCentauri - This final profile is very ambitious and intends to send
an EDT spacecraft through the IM, and attempt to reach αCentauri. Like the EDGE
concept, there are no restrictions on possible mission concepts to be used, the decisions
for which are to be informed by knowledge from running the nominal simulations.
8.3.2. EDT Configurations
The same process carried out in Subsection 8.3.1 can now be carried out for the EDT con-
figurations. Table 8.2 shows the different EDT configurations for analysis, with the variable
elements of the configurations also outlined; RW and TT stand for Round Wire and Tape
Tether respectively.
Table 8.2: Summary of nominal and additional EDT configurations for investigation during
the thesis. RW stands for Round Wire, and TT for Tape Tether.
Configuration Designation Composition Multiplicity Thrust Concept
Nominal CHB Cu-Al, RW Hoytether Bare tether
Nominal CHTr Cu-Al, RW Hoytether Transient
Additional AlMB Al only, TT Hoytether (if viable) Bare tether
Additional AlMTr Al only, TT Hoytether (if viable) Transient
To further expand on the selected mission concepts, they are outlined and justified as fol-
CHB - Nominal - Composite Hoytether Bare tether - This configuration uses a composite
round-wire tether with a copper conducting core, and aluminium load-bearing compo-
nent; this is because a composite design like this has previous use, and a fibre-based
tether has the hazard of degradation. The tether also makes use of a Hoytether type
multiplicity concept, as it was shown clearly in Chapter 4 that the concept is superior
for survivability than other concepts. The configuration also makes use of a bare tether
concept, utilising electron collection and emission into the ionosphere; this was done
as the concept has been used in previous EDT missions, and is shown to be a better
solution than an insulated design.
CHTr - Nominal - Composite Hoytether Transient - This configuration is identical to the
CHB tether, but instead of the bare tether concept for thrust generation, the design uses
70 8. Validation / Target Cases
the transient thrust concept. This was done as the concept is very appealing, and is
novel ground for EDT missions.
AlMB - Additional - Aluminium Multiplicity Bare tether - This configuration is similar to the
CHB tether, but instead of a composite round-wire tether, it employs an aluminium-only
tape tether design. In addition to this the Hoytether concept for multiplicity is favoured,
but it is somewhat unclear if the concept is viable for tape tethers, and in the case that it
is not, then another multiplicity design shall be used, or even a design with no multiplicity.
AlMTr - Additional - Aluminium Multiplicity Transient - This configuration is identical to the
AlMB configuration, with the exception of using a transient concept for thrust generation,
as done in the CHTr case.
It should also be noted that there are a few elements common to all considered configurations,
due to having no viable alternatives; these common elements are as follows:
Control method - Spin-stabilised - As mentioned in Section 4.3, the only really viable
option for stabilisation and control of a large tether in deep space is a spin-stabilisation
method, and so this will be assumed in all cases.
Power generation - Nuclear - The spacecraft will require electric power generation, and
normally this is a point where considerable variability can come into the design. However,
in this case the spacecraft will generally be in deep space, where power generation
methods such as Solar cells are essentially useless; therefore nuclear power will be
used, either in the form of RTG’s, similar to those used on other deep space missions
[61], or future space-rate nuclear reactors such as the Kilopower series [28].
8.4. Conclusions
The conclusions of the section are as follows:
The different components of the developed simulation environment will be verified by
using simpler (analytical) simulations to compare the full simulation against.
The full simulation environment will be validated by running comparable EDT simula-
tions performed by other researchers, generally based around other bodies in the Solar
System (i.e. Earth and Jupiter).
There is a range of target cases, upon which the feasibility of an EDT can be tested, and
the specific success conditions, for example mission transit time, for these target cases
is yet to be determined.
The specific cases for mission profile and EDT configurations mentioned in Section 8.3
shall be the only ones tested in the final thesis, and will be done in a two-stage process.
Analysis of Existing Tools
For many aspects of modern research it is prudent to make use of technology and tools already
developed, to save time and increase performance compared to creating a new system. This
chapter explores some of the potential areas that tools to aid in the main thesis already exist,
and if they would be useful or not.
9.1. Orbit Simulation
Orbit simulation is one of the few cases where it is almost certain that an existing 3rd party
tool should be used - this is because there is a wide range of existing tools that can be used
depending on the use-case, and that the creation of a new tool from scratch would be very
time-consuming, and would likely not be as efficient or robust as those that already exist. With
this in mind there are a few potential software packages that could be used; this is by no means
an exhaustive list, but instead includes well-known packages and those that are free to use
(for TU Delft academics), with a variety of particularities surrounding them. The considered
packages are listed below with a brief description of them:
Tudat - referring to the TU Delft Astrodynamics Toolbox, Tudat is the C++ based orbital
dynamics and optimisation package developed in-house by the TU Delft astrodynamics
department [8].
Pykep - according to the documentation, Pykep is an ESA-developed scientific library
to provide basic tools for astrodynamics research. Its main focus is on computational
efficiency, being written in C++ and exposed to Python [7].
Poliastro - this is a (pure) Python package developed originally for a university project,
that provides a user-friendly API (Application Program Interface) for solving astrodynam-
ics problems, with a focus on interplanetary trajectories[69].
• Java Astrodynamics Toolkit (JAT) - This is a NASA-developed open source Java li-
brary used for space mission design, trajectory optimisation, and analysis of naviga-
tion, guidance and control systems. The toolkit also provides 2-D and 3-D visualisation
General Mission Analysis Tool (GMAT) - This is again an open source NASA-developed
software package designed for space mission design, optimisation and navigation. What
is different from the previously mentioned tools is that GMAT does not overtly use a
regular programming language, but it instead entirely utilises a GUI (Graphical User
72 9. Analysis of Existing Tools
Interface), with the option for custom scripting[57].
Systems Tool Kit (STK) - Developed by AGI, STK is a toolkit used for environment mod-
elling and mission design for land, sea, air, or space systems. Like GMAT it is a primarily
GUI-focused software package, and has a number of additional key modules which can
be installed [5].
Figure 9.1: Screenshot of GMAT while in-use [3].
A few of these tools can be immediately discarded from future considerations. The first of
these is JAT, the reasoning for this is that it provides a comparable set of functionalities as
some of the other tools considered such as Tudat or Pykep, but is written in the Java language,
which is somewhat less efficient than C++, while also being less user-friendly than Python. In
addition to this, the author has no previous experience working with Java, which adds a level
of complexity to the project with relatively little gain.
Another tool which can be discarded is STK - it provides a very similar experience as GMAT
being a full-mission GUI-based software package; however it is a paid commercial product (for
the relevant key modules required for orbit design), the license for which is rather expensive.
As with JAT, the author also has significant experience working with GMAT, which is not the
case for STK.
9.1.1. Discussion of Remaining Tools
Each of the above introduced tools has its own advantages and disadvantages, which will be
further discussed in the following paragraphs.
9.1. Orbit Simulation 73
Tudat of course has the obvious advantage of being developed by TU Delft students directly;
this means that any uncertainty about how to use the software, or if certain objectives can be
completed with it, can be easily ascertained by seeking help from TU Delft staff. Being written
in C++ Tudat is also highly efficient, and comprises useful optimisation algorithms as well as
simply performing simple orbit simulations. Another major advantage of this software package
is that the author does have significant experience working with it, meaning a large effort is not
necessarily required simply to become accustomed to using it. On the other hand, Tudat is a
work in progress, with some incomplete features, documentation that is lacking and/or difficult
to navigate, and an implementation that is not very user-friendly compared to more official
software packages. Tudat also offers no built-in visualisation capabilities, meaning the results
from simulations must be analysed separately from the simulations themselves, usually in a
simpler programming language such as Python or MATLAB.
Pykep, like Tudat, is written in C++ and prides itself on computational efficiency, meaning it has
the potential to run many simulations in a short time. Again like Tudat, Pykep also implements
a number of optimisation algorithms, and has been used by the ESA Advanced Concepts Team
on Global Trajectory Optimisation Competitions [7], giving it a good pedigree, and is known to
produce reliable results. In addition to the efficiency afforded by being written in C++, Pykep
retains a level of user-friendliness by being exposed to Python, meaning significant amounts of
time are not wasted compiling C++ code for example. Like Tudat however, it does not contain
any in-built visualisation techniques.
Poliastro, being a completely open source software package, has neither the pedigree afforded
by Pykep, or the ability to consult directly with the authors of the software like Tudat; as such
its reliability as a software package is questionable. Being written in pure Python, it is also
clearly less efficient than any of the other considered orbit simulation tools. However, one
main advantage of the package is its ease of use, and in-built 2D and 3D visualisations, as
shown in Figure 9.2, meaning it could be used as a supplemental or initial-analysis tool, with
the bulk of simulations performed by one of the more efficient software packages.
Figure 9.2: Example visualisation of NEOs in the Solar System created using Poliastro [6].
74 9. Analysis of Existing Tools
GMAT is the clear outlier compared to the other considered tools - instead of being a simple
module or set of modules for an existing programming language such as Python, GMAT is a
self-contained program, with no real direct access to the source code (although it does support
low-thrust missions by interface with outside programs). Simple scripting can be performed
with GMAT in its own scripting language, as well as the potential for MATLAB integration,
however the main method of using GMAT is by the GUI, an example of which is shown in Fig-
ure 9.1. The visualisations in GMAT are also generated automatically as a mission is created,
and can be very useful tools, however data plots for example cannot be directly created, and
must be made using exported data in another way, such as in a Python program. GMAT is
also primarily designed to fully map out a mission who’s basic plan is known, such as an Earth
observation satellite for example, and therefore the optimisation algorithms contained in the
program are less sophisticated than those for some of the other mentioned tools.
9.2. Optimisation Tools
Based on the conclusions made in Chapter 7, it is known that some optimisation algorithms will
be required to run the simulations in the main thesis. Obviously implementing these algorithms
directly would be inadvisable when there are a number of optimisation toolboxes available to
use; some examples include the suite of optimisation tools available in MATLAB, as well as
the Pagmo optimisation software package.
There are also a number of proprietary software, in particular used by NASA, such as the
Copernicus Trajectory Design and Optimisation Toolbox [93]; these toolboxes are attractive
due to their ease of use and interactive GUI, however they are hard to integrate into the use
of orbit simulation software such as Tudat, and require are generally intended for use by US
government organisations and universities, making it difficult to acquire the software.
Since Tudat has already been decided as the orbit simulation toolbox that will be used, it is
logical to then select Pagmo as the optimisation toolbox; Pagmo is a C++ toolbox developed
by ESA, with the specific intention of performing interplanetary trajectory optimisation [2], the
package is also available in Python as Pygmo. The reason to immediately choose Pagmo
as the toolbox of choice is that Tudat documentation already recommends using Pagmo as
the optimisation toolbox, the author already has experience integrating Pagmo routines within
Tudat, and of course Pagmo is written in C++, and so is relatively easy to incorporate into
a Tudat simulation. In addition to these reasons, Pagmo is a well-respected, reliable, and
extensive toolbox for trajectory optimisation, being developed by ESA, and easily usable with
its open-source licensing.
9.3. Magnetic Field Simulation
Another obvious contender to apply existing tools would be in the simulation of the interplan-
etary and interstellar magnetic fields. Various toolkits already exist for this use case for the
Earth magnetic field, such as the chaosmagpy Python package, which implements the CHAOS
magnetic field model along with visualisations etc. However, a similar kind of toolkit does not
readily exist for interplanetary and interstellar magnetic field applications.
The reason for this lack of tools is probably for two main reasons: firstly that the demand
for such a toolkit is not as prevalent either in industry or scientific endeavours, secondly is
that the distant interplanetary and interstellar magnetic fields are relatively simple to model,
compared to close-proximity planetary magnetic fields. The latter of these reasons means
that the development of a (series of) magnetic field models would be within the scope of this
study. In addition, by independently developing magnetic field models, it will be much easier
9.4. Conclusions 75
to integrate into the overall simulation framework that will be used for the project.
9.4. Conclusions
Based on the above analysis, the following conclusions can be drawn:
It is likely that GMAT will not be used as the primary simulation tool for this study, since
analysing the data from it is more difficult than other methods, and there are fewer pos-
sibilities for optimisation.
Poliastro will not be used as the primary simulation tool, however it could be used to
produce some useful visualisations, especially in the event that Pykep is used, which is
also Python based.
Both Pykep and Tudat offer a good solution for orbit simulation in this use-case, meaning
they would both be a suitable candidate. Although Pykep is attractive as it utilises high-
efficiency C++ code in a Python wrapper, the Tudat package will be eventually utilised.
This decision has been made due to the direct support available from TU Delft staff, as
well as the possibility to add to the Tudat package as a whole, instead of simply utilising
a third party package.
Pagmo is the natural choice to use as optimisation toolbox, owing to the fact that it can be
easily integrated into a Tudat simulation, as well as other factors previously discussed.
Discussions and Conclusions
10.1. General Conclusions of the Literature Study
10.1.1. Assessment of Previous Work
The major conclusion to take away from this literature study regarding previous work, is that
there have been extensive studies and experimentation into the use of EDTs for Earth-based
(especially LEO) applications, as well as some studies into their use in other planetary systems
such as Jupiter. However there has been little to no research on the use of an EDT directly
in interplanetary or interstellar space. The study that does consider the EDT as a means of
direct propulsion in interstellar space, namely Matloff [49], writes off the EDT as infeasible for
use in interstellar space; however this conclusion is only reached when considering an ”ark”
like starship, and so it is yet to be seen if an EDT would be feasible for a smaller microsatellite
type spacecraft.
These LEO studies are also predominantly focused on one of three things: firstly the physical
experiments as technology demonstrators to prove EDT feasibility, secondly as a means of
long-term station keeping, for example on the ISS, and finally as a means of space-debris
deorbit. Relatively few studies have been done on direct propulsion using an EDT.
It is also clear that the majority of (recent) studies focus on some variation of the bare-tether
EDT solution, as a means to complete the electric circuit using the ionosphere; no studies
have been done to assess the feasibility of a transient-current solution.
78 10. Discussions and Conclusions
10.1.2. Recommendations for Future Work
The recommendations for future work are as follows:
Study the feasibility of EDTs as a direct propulsion system in interplanetary space, since
no other studies have been done in this area, and determine if they are competitive
compared to other alternative means of propulsion.
Study the concept of a transient-current solution to completing an electric circuit for an
EDT. This kind of system has never been formally researched and presents a promising
solution to provide a propelantless means of propulsion, with little to no net spacecraft
energy usage.
Further study the research of an EDT propulsion system in interstellar space, particularly
in the context of a microsatellite or small scientific probe application.
Confirm during the thesis project that the applied tether solution is able to survive for
many years, despite the considerable risk of micrometeoroid impact.
Provide in the thesis project a starting point of EDT simulation analysis, using the concept
cases outlined in Section 8.3.
10.2. Reiteration of and Changes to the Research Question
The research question outlined in Chapter 1 remains mostly the same, with some minor
changes highlighted in bold as follows:
Investigate the feasibility of electrodynamic space tethers as a means of propulsion applied
to possible future interplanetary and/or interstellar missions; also assess the viability of a
transient-current solution for the electrodynamic tether.
As part of this research question, the following subquestions can be addressed:
What acceleration can realistically be achieved by an EDT in interplanetary and inter-
stellar space?
Which regions of space would and EDT spacecraft be suited to operating, and on what
kinds of missions?
What design concepts of an EDT are best suited to the above mentioned operating
How competitive is the EDT as a means of propulsion when compared against
both conventional chemical propulsion, and other alternative propulsion means?
10.3. Thesis Project Planning 79
10.3. Thesis Project Planning
In order to effectively plan the main thesis project, it is split up into themes, under which are
the topics of that theme, that can be allocated on a week-by-week basis. The themes and
topics are briefly outlined below:
1. Simulation development
a) Orbit dynamics modelling
b) Environment modelling
c) Thrust generation and tether dynamics modelling
d) Tether design modification modelling
2. Verification and Validation
a) Verification cases selection, development, and testing
b) Validation cases selection, development, and testing
c) Analysis of above verification and validation results
3. Simulations execution
a) Determination of all simulation cases and variations to run
b) Determination of success conditions from above run simulations
c) Implement and run simulations, and collect data
4. Data collection and analysis
a) Create useful plots and representations of data from the simulation output
b) Analyse data and assess feasibility of various solutions
5. (Comparisons)
a) Accumulate calculations or literature data from similar applications of for example
ion propulsion systems
b) Compare competitiveness of EDT solution to alternatives, for similar use-cases
6. General report completion
a) Finalise structure of report document, completing the intro, research question, etc.
b) Finalise the report, standardising the structure and adding in appendices where
necessary. Also make conclusions and recommendations for future work.
These topics are then assigned a week, in which the project is planned to start on 10 Feb,
or after approval of this literature study, and end around 12 July, at the end of the academic
year. Table 10.1 shows the timeline and distribution of the above topics, and of course there
is scope for this plan to change during the project.
80 10. Discussions and Conclusions
Table 10.1: Timeline of main thesis project using a weekly calendar.
Week Number Week Dates Topic Designation
07 10/02/20 - 16/02/20 1.a)
08 17/02/20 - 23/02/20 1.a)
09 24/02/20 - 01/03/20 1.b)
10 02/03/20 - 08/03/20 1.b)
11 09/03/20 - 15/03/20 1.c)
12 16/03/20 - 22/03/20 1.c)
13 23/03/20 - 29/03/20 1.d)
14 30/03/20 - 05/04/20 2.a)
15 06/04/20 - 12/04/20 2.b)
16 13/04/20 - 19/04/20 2.c)
17 20/04/20 - 26/04/20 3.a)
18 27/04/20 - 03/05/20 3.b)
19 04/05/20 - 10/05/20 3.b)
20 11/05/20 - 17/05/20 3.c)
21 18/05/20 - 24/05/20 3.c)
22 25/05/20 - 31/05/20 4.a)
23 01/06/20 - 07/06/20 4.b)
24 08/06/20 - 14/06/20 5.a)
25 15/06/20 - 21/06/20 5.b)
26 22/06/20 - 28/06/20 6.a)
27 29/06/20 - 05/07/20 6.b)
28 06/07/20 - 12/07/20 6.b)
Literature Study Planning
In order to ensure the timely completion of the literature study, ideally within the nominal 8
weeks, the report work was split into sections, and the time to spend on these sections roughly
estimated. Table A.1 shows this plan, in each column are respectively the topic, estimated
completion time in (working) days, and the start date and end date, both of which are split into
planned and actual dates.
It should be noted that weekends are not counted as working days, nor is the period from 18
Dec to 6 Jan, as this was the Christmas holiday period. Another important observation to
make is task (6b), optimisation; this was not initially envisioned as a dedicated section, but was
instead added part way through the literature study creation, and so did not have any initial
planning involved with it, indicated by the N/A terms. Finally, many of the later stages of the
report were being completed in parallel, so their end dates are in fact very close together.
82 A. Literature Study Planning
Table A.1: Literature study planning.
Topic / Estimated Completion Start Date End Date
Task Time (Days) Planned Actual Planned Actual
(1) Mission Heritage 4 24-10-19 24-10-19 29-10-19 30-10-19
(2) Environment Char-
4 30-10-19 31-10-19 04-10-19 06-11-19
(3) Orbital Dynamics 4 05-11-19 06-11-19 11-11-19 13-11-19
(4) Propagation and In-
3 11-11-19 13-11-19 11-11-19 28-11-19
(5) Tether Design 6 12-11-19 14-11-19 19-11-19 25-01-20
(6) Supporting Space-
craft Parameterisation
2 20-11-19 28-11-19 21-11-19 11-12-19
(6b) Optimisation N/A N/A 22-01-20 N/A 25-01-20
(7) Validation / Target
3 22-11-19 28-11-19 26-11-19 25-01-20
(8) Analysis of Existing
3 27-11-19 28-11-19 29-11-19 25-01-20
(9) Discussion and
3 02-11-19 23-01-20 04-12-19 26-01-20
(10) Complete Intro-
1 05-12-19 23-01-20 05-12-19 26-01-20
(11) ”Final Touches” 3 06-12-19 23-01-20 10-12-19 26-01-20
Additional Smallsatellite Data
In this appendix, the data used to parameterise a smallsatellite in Chapter 5 is shown. First a
brief description of the chosen satellites:
Table B.1: Mass distribution of each considered satellite for smallsat parameterisation [13]
[36] [41] [42].
Name Total
MEMS Sat 2.6 0.6 24.7 20.4 0.5 13.4 15.3 2.3 8.3 10.2 2.0
ESTCube-1 1.1 0.2 19.6 27.3 0.0 27.7 10.0 4.7 10.7 0.0 0.0
ADR Sat 23.4 2.3 9.7 17.1 0.0 1.4 1.4 6.4 5.3 58.8 0.0
Solar Sail 1 280.0 120.0 42.9 15.0 3.6 13.7 10.7 0.6 4.2 9.1 0.0
Solar Sail 2 343.0 120.0 35.0 15.0 3.2 11.2 8.7 0.5 4.3 22.1 0.0
Table B.2: Power distribution of each considered satellite for smallsat parameterisation [13]
[36] [41] [42].
Name Total
MEMS 2.2 0.44 20.00 0.00 0.00 8.18 45.82 10.36 9.27 1.09 0.00
ESTCube-1 8.09 4.2 51.92 0.00 0.00 1.85 28.43 3.71 14.09 0.00 0.00
IWSCFF 341.5 40.5 11.86 1.46 0.00 0.00 0.59 2.93 1.76 81.41 0.00
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The heliopause is the boundary between the hot heliospheric (solar wind) plasma and the relatively cold interstellar plasma. Pressure balance considerations show that there should be a large (factor of 20 to 50) density increase across the heliopause. Here we report electron density measurements from the Voyager 1 and 2 plasma wave instruments near and beyond the heliopause. The plasma density in the outer heliosphere is typically about 0.002 cm⁻³. The first electron density measured by the Voyager 2 plasma wave instrument in the interstellar medium, 0.039 cm⁻³ ± 15%, was on 30 January 2019 at a heliocentric radial distance of 119.7 au. The density jump, about a factor of 20, confirms that Voyager 2 crossed the heliopause. The new density is very similar to the first density measured in the interstellar medium by the Voyager 1 plasma wave instrument, 0.055 cm⁻³, on 23 October 2013 at a radial distance of 122.6 au. These small differences in the densities and radial distances are probably due to the relative locations of the spacecraft in the boundary layer that forms in the interstellar plasma just beyond the heliopause.
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