2005:147 CIV EXAMENSARBETE

Design Study for a Formation-Flying Nanosatellite Cluster

SARA GIDLUND

MASTER OF SCIENCE PROGRAMME in Space Engineering

Luleå University of Technology Department of Space Science, Kiruna

2005:147 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 05/147 - - SE

Design Study for a Formation- Flying Nanosatellite Cluster.

Centre for Large Space Structures and Systems Inc. (CLS3) 1425 Blvd. René Lévesque W-700 Montreal, Québec H3G 1T7 Canada

Abstract

Nanosatellites flying in formation vastly increase the capability of small satellite missions. The approach is within reach of technology, but there are severe challenges for the subsystems. The most demanding task is to implement effective control of the satellites. There are many options for solving the high and the low level control. The propulsion system and the communication system are the subsystems that will determine the constraints on the formation that may be used, and the duration of the mission. The mission of the cluster that the Centre for Large Space Structures and Systems Inc (CLS3) intends to launch will make use of existing technologies for nanosatellites and merge them with an in-house Guidance Navigation and Control system. The project will be developed as a collaboration between companies and organizations, in North America and Europe. The objective of the initial study was to summarize the state-of-the-art for the subsystems, and to stimulate discussions with potential partners. Negotiations with launch companies were also initiated. The satellites will fly in a circular or projected circular formation. In order to calculate the orbits of the satellites, it is of great importance to understand the Hill’s equations. Even though they do not include any of the major perturbations of the orbits, these equations are widely used for design of the control loops for formation-flying constellations.

Acknowledgements

This thesis would not have been completed if not for the guidance of Professor Hannah Michalska and the support of Björn Graneli. She was there to guide me on location, and he has been a great support, always calm, inspirational and encouraging. Björn Söderlund and Vladislav Ganine were also a great help. Thank you both for lighting up the days when the whole world seemed to rest on my shoulders, especially Björn Söderlund who had to put up with me 24-7. Thank you Dr Milind Pimprikar for taking me on, and giving me the opportunity to become a part of this interesting project, and thank you Rozita for the help with reports and presentations while in Montreal. Also thank you Roland Magnusson, for the use of your computer when mine crashed, and for your positive everything-works-out-in-the-end attitude. Last but not least, thanks to my parents: Without your loving care and support – where would I be today?

1. Table of Contents

1. Table of Contents...... 1 2. Abbreviations used...... 5 3. List of Figures...... 7 4. List of Tables ...... 9 5. Introduction...... 11 6 Introductory literature study ...... 13 6.1 Comparative analysis of Small Satellites...... 13 6.2 Comparison of formation flight missions ...... 15 7 Subsystems...... 17 7.1 GNC...... 17 7.1.1 Sensors...... 17 7.1.1.1 GPS ...... 17 7.1.1.2 Sun sensors...... 17 7.1.1.3 Star tracker ...... 18 7.1.1.4 Earth-horizon sensor ...... 18 7.1.1.5 Inertia sensors...... 18 7.1.2 Actuators...... 18 7.1.3 Control architectures...... 18 7.1.3.1 Centralized approach...... 19 7.1.3.2 Decentralized approach ...... 19 7.1.3.3 Executive controller approaches...... 19 7.1.3.3.1 Intelligent agent based system...... 19 7.1.3.3.2 Rule-based expert system...... 19 7.1.3.3.3 Flocking/Market-oriented programming system...... 20 7.2 Thermal ...... 20 7.2.1 Background...... 20 7.2.1.1 Passive Thermal Control ...... 20 7.2.1.1.1 Phase Change Devices ...... 20 7.2.1.1.2 Thermal Control Coatings...... 20 7.2.1.1.3 Multi Layer Insulation (MLI)...... 20 7.2.1.1.4 Thermal Doublers ...... 20 7.2.1.2 Active Thermal Control...... 21 7.2.1.2.1 Smart thermal coatings...... 21 7.2.1.2.2 Heat Pipe...... 21 7.2.1.2.3 Louvers ...... 21 7.2.1.2.4 Second-Surface Mirror...... 22 7.2.1.2.5 Electrical Heater...... 22 7.2.2 Design ...... 22 7.2.3 Specifications...... 23 7.2.3.1 From the launching company ...... 23 7.2.3.2 From the orbit...... 23 7.3 Structure & Separation ...... 24 7.3.1 Specifications...... 24 7.3.2 Design ...... 25 7.4 Power...... 25 7.4.1 Solar Cells...... 25 7.4.1.1 Multijunction cells...... 25 7.4.1.2 Thin films...... 26 7.4.1.3 Multiband solar cells ...... 26 7.5 OnBoard Data Handling (OBDH) ...... 26 7.6 Communication ...... 26 7.7 Propulsion...... 27 7.7.1 Colloid micro thrusters...... 27 7.7.2 Field emission electrostatic propulsion thrusters (FEEP) ...... 28 7.7.3 Micro pulsed plasma thrusters (μPPT)...... 28

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7.7.4 Miniature cold gas thrusters...... 30 7.7.5 MEMS solid propellant thrusters ...... 30 7.8 Payload ...... 31 8 Orbit selection...... 33 8.1 Hill’s equations and Clohessy-Wiltshire equations ...... 33 8.1.1 Derivation ...... 33 8.1.2 Homogenous solution ...... 38 8.1.3 Particular solution ...... 40 8.1.4 Discrete time ...... 42 8.2 THEONA...... 43 8.3 Trajectory deviation...... 44 8.3.1 Orbital disturbances ...... 45 8.3.1.1 Atmospheric drag ...... 45 8.3.1.2 Geopotential anomaly ...... 45 8.3.1.3 Solar pressure...... 47 8.3.2 Trajectory errors...... 47 8.3.2.1 Trajectory errors originating in position measurements ...... 47 8.3.2.2 Trajectory errors originating in velocity measurements ...... 48 8.3.2.3 Trajectory errors originating from thruster errors...... 48 8.4 Orbit manoeuvres ...... 50 8.4.1 Coordinate system...... 50 8.4.2 Velocity of satellites in orbits ...... 50 8.4.3 Coplanar manoeuvres...... 51 8.4.3.1 Apogee and Perigee raise manoeuvres ...... 51 8.4.4 Noncoplanar manoeuvres...... 52 8.4.4.1 Inclination change ...... 52 8.4.4.2 Change of the right ascension of the ascending node ...... 53 8.4.4.3 Combined inclination and RAAN change ...... 53 8.4.5 Combined coplanar and noncoplanar manoeuvres...... 53 8.4.6 Continuous thrust manoeuvres...... 53 8.4.6.1 Motion in the x-direction...... 53 8.4.6.1.1 Example ...... 54 8.4.6.2 Motion in the z-direction...... 55 8.4.6.2.1 Example ...... 55 8.4.7 Obtaining the desired relative distance ...... 56 8.5 Simulation ...... 56 8.6 Reports from the simulation program...... 59 8.7 Documents required from the launcher ...... 59 9 Radiation analysis ...... 61 9.1 SPENVIS...... 61 10 Discussion...... 63 10.1 Propulsion...... 63 10.2 Power...... 63 10.3 GNC...... 63 10.4 Thermal ...... 63 10.5 Radiation analysis...... 64 10.6 Launch...... 64 10.7 Over-all project...... 64 11 Future work...... 65 11.1 Time plan...... 65 Appendices...... 67 Appendix A Satellite Data ...... 69 A.1 Constella...... 70 A.2 Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions, DEMETER...... 71 A.3 DLR-TUBSAT ...... 72 A.4 Federation Satellite, FedSat...... 73 A.5 French Brazilian Microsatellite, FBM ...... 75

2 A.6 KITSAT-3...... 76 A.7 Leonid Meteor Satellite, LMS ...... 77 A.8 MICRO Satellite à traînée Compensée pour l’Observation du Principe d’Equivalence, MICROSCOPE ...... 78 A.9 MightySat II...... 79 A.10 MYRIADE...... 80 A.11 Near Earth Space Surveillance, NESS...... 81 A.12 ORION ...... 82 A.13 Ørsted Geomagnetic Research Satellite...... 83 A.14 PICARD ...... 84 A.15 PRoject for On-Board Autonomy, PROBA...... 85 A.16 RØMER...... 86 A.17 TechSat-21 flight experiment ...... 87 A.18 Tsinghua-1...... 89 A.19 ASUSAT1...... 90 A.20 Bitsy...... 91 A.21 EMERALD...... 92 A.22 Ionospheric Observation Nanosatellite Formation, ION-F...... 94 A.23 Magnetospheric Constellation, MC ...... 96 A.24 Mothership-Daughtership Space experiment...... 97 A.25 Munin ...... 98 A.26 Surrey Nanosatellite Application Platform, SNAP-1 ...... 99 A.27 Space Technology 5, ST-5...... 101 A.28 Three Corner Satellite, 3CS...... 102 A.29 Artemis ...... 103 A.30 Can-Sat ...... 104 A.31 The Canadian Advanced Nanospace eXperiment, CanX 1 ...... 105 A.32 Constellation Pathfinder ...... 106 A.33 CubeSat...... 107 A.34 MEMS Picosat...... 108 A.35 MEms-based PicoSat Inspector, MEPSI...... 109 Appendix B Structure ...... 111 B.1 The Design Criteria from the point of the launching company...... 112 B.2 Required documents from the launching company...... 115 B.3 Separation System...... 116 B.3.1 Drawing...... 116 B.3.2 Required documents from the launching company ...... 116 Appendix C Short summaries of important articles on orbit control...... 117 References...... 125 Books...... 125 Web pages ...... 125 Conference proceedings ...... 126 Journal Articles...... 127

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4 2. Abbreviations used

BPSK – BiPhase Shift Keying CLS3 – Centre for Large Space Structures and Systems COTS – Commercial off the Shelf FEEP – Field Emission Electrostatic Propulsion FSK – Frequency Shift Keying GNC – Guidance Navigation and Control LEO – Low Earth Orbit LV – Launch Vehicle MEMS – Micro Electro-Mechanical System NEMS – Nano Electro-Mechanical System OBDH – OnBoard Data Handling PEO – Polar Earth Orbit μPPT – Micro Pulsed Plasma Thrusters RAAN – Right Ascension of the Ascending Node RF – Radio Frequency SEU – Single Event Upset SHM – Space Head Module VLF – Very Low Frequency QPSK – Quadrature Phase Shift Keying

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6 3. List of Figures

Figure 7.2.1.2.2-1. Schematics of a Fixed-Conductance Heat Pipe. Figure 7.2.1.2.3-1. Open and Closed Louvers. Figure 7.2.2-1. The steps involved in designing the Thermal subsystem. Figure 7.3-1. The time schedule for the first efforts regarding the structural design. Figure 7.4.1.1-1. Structure of a Japanese triple-junction cell. Figure 7.4.1.3-1. Illustration showing the difference between Multijunction and Multiband solar cells. Figure 7.7.1-1. A schematic drawing of a Colloid Micro Thruster. Figure 7.7.2-1. Schematics of an FEEP. Figure 7.7.2-1. Schematics of an FEEP. Figure 7.7.3-1. Schematics of a Micro PPT. Figure 7.7.4-1. Drawing of a miniature cold gas thruster. Figure 7.7.5-1. Exploded view of a MEMS solid propellant thruster. Figure 7.7.5-2 a. 6×6 Loaded solid propellant thruster array from LAAS-CNRS. Figure 7.7.5-2 b. 6×6 Thruster array with resistors and metallic lines (2×2 cm) also from LAAS-CNRS. Figure 8.1-1. Relative motion coordinate system with the ‘centre’ satellite’s centre of mass as its origin. Figure 8.4.3.1-1. Apogee and Perigee raise manoeuvres. Figure 8.4.3.1-2. Hohmann transfer. Figure 8.4.6.1.1-1. Movement of remote satellite in the x-direction. Figure 8.4.6.2.1-1. Movement of remote satellite in the z-direction. Figure 11.1-1. The time schedule for the entire project. Figure B.3.1-1. Standard Adapter to Spacecraft attachment points.

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8 4. List of Tables

Table 6.2-1. Review of some related missions, either being planned or accomplished worldwide Table 7.1.1.2-1. Specifications for three Sun sensors. Table 7.1.1.5-1. Specifications for an inertial sensor. Table 7.2.3.1-1. The temperature and relative humidity in the different phases of launch preparation. Table 7.7.3-1. Flight and laboratory performance data, taken from [Burton 1998]. Table 7.7.4-1. The characteristics of a miniature cold gas thruster, with two different propellants. Table B.1-1. Acceleration on the satellite (and launch vehicle) during transportation. Table B.1-2. The acceleration experienced by the satellite during the different stages of the launch. Table B.1-3. Amplitude and duration of the Harmonic oscillations in the longitudinal axis (X) of the satellite. Table B.1-4. Amplitude and duration of the Harmonic oscillations in the lateral axis (Y,Z) of the satellite. Table B.1-5. The spectral density and duration of the Random vibrations of the launch. Table B.1-6. The shock spectrum at the satellite’s attachment points, * denotes the number of satellites that are in the same compartment. Table B.1-7. The acoustic loads on the satellite during launch. Table B.1-8. Third stage motor plume parameters affecting the satellite, maximum values.

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10 5. Introduction

Nanotechnology offers new ways for gaining enhanced capability and functionality in small satellites. One way of bringing advancements in nanosatellites a step further is to join a number of them into a cluster, thereby making them work as a virtual large satellite. Such a constellation has the potential of even surpassing the large satellites of today in some areas, since the separation distances between the satellites are not fixed, and the virtual aperture can be made as large as required. In order to accomplish this, however, it will be necessary to overcome significant technological challenges regarding the NEMS. The scope of this thesis is to investigate what is feasible with the technology on the market today. A pioneering effort in this field was the TechSat 21 program, comprising 35-40 clusters, each with 8 microsatellites. The intention was to perform both geolocation measurement with separation distances of about 5 km, and radar measurement with separation distances of about 500 m. The entire program was a joint effort of the US government and industry, but unfortunately the project was discontinued in 2003. The work already accomplished, though, is highly up to date and therefore references will be made throughout this thesis. In order to review the benefits of the new, as of present not fully developed concept of formation flying nanosatellites, the following innovations related to (a) nanosatellites and (b) clusters were identified. a) Nanosatellites There are several advantages in using nanosatellites in space missions, of which the most significant ones are: • Since the nanosatellites are light, the launch cost can be kept low. In addition, there is the option of ‘piggy-back rides’ with launches of larger satellites. • Nanotechnology enables the use of integrated systems, which will further reduce the weight and also improve the performance of the system. Further, the thermal control issue will be of lesser importance. • The latest technology may be used since low cost allow shorter lifetimes to be calculated (ranging from days to about one year). COTS products may be employed for the same reason, thus significantly contributing to the reduction of mission cost. Because of short lifetime the radiation environment, using COTS, is not as big an issue as for satellites exposed during several years. • The relatively short developing time for a nanosatellite allows more missions to be flown, with the latest technology, since the cost for each mission is accordingly reduced. • The use of nanosatellites reduces the problem of space debris, since the satellites are smaller and deorbit faster.

11 b) Cluster The notion of a formation-flying cluster offers a variety of new applications for small satellites. • An important application of these clusters might be syntheses of large apertures, allowing each satellite to communicate with the others and share the processing, communication, and payload in an aggregate thus forming a large ‘virtual satellite’. The cluster will have almost unlimited effective aperture, since the separation distance between the satellites can be varied. Therefore it can be used for performing a variety of tasks, such as geolocation, surveillance, communication and radar operations, previously done with larger and more expensive satellites. • For scientific missions, the cluster approach can be used for more thorough investigations in the atmosphere, ionosphere and the magnetosphere. For example, the ionospheric disturbances can be monitored when satellites in the cluster distribute information between them, since their relative positions are well determined. • The system architecture is highly adaptable. Since neither the geometry of the cluster, nor the number of satellites in the cluster are fixed, the cluster configuration can be adapted to suit the needs of an emerging mission. The flexibility in size of the virtual satellite is attractive for high value, and low cost missions. • The system performance can be slowly increased over time with a phased deployment and/or it may be tailored to meet evolving needs. • If one satellite is malfunctioning this is not crucial, since a replacement can be sent up at a relatively low cost. Alternatively the remaining satellites may be reprogrammed to perform the original tasks, a scheme customary called graceful degradation. New satellites can be added to existing ones in order to perform new tasks. • The satellites can be ‘mass-produced’, which will lower the production cost. • Furthermore, the deployment cost can be spread over a number of years, while the cluster still provides acceptable but ever increasing levels of performance.

12 6 Introductory literature study

6.1 Comparative analysis of Small Satellites

A number of small satellites were studied. Their characteristics are presented satellite by satellite in Appendix 12.3. Characteristics for nanosatellites are summarized below, in order to show the present level of development.

Sides: mostly within the rage of 10 cm to 50 cm Shape: cubic, box shaped, hexagonal, octagonal Weight: 1 to 10 kg Design life: 3 days to 1 year Mechanical/Structural subsystem: Most nanosatellites use Aluminium 6061 or possibly Aluminium 7075 rather than composite materials. This is mainly due to budget issues. Since most nanosatellite missions have short design lifetimes, they do not need the more radiation tolerant composite materials to an extent that would motivate the cost increase. Attitude Orbit and control subsystem: Most of the nanosatellites are three-axis stabilized, and most of them have magnetotorquers onboard for handling the orbit control. The torquers suffice, since the satellites have low mass. GPS is often used for the attitude determination. Magnetometers are also commonly used, but Star Sensors are found onboard only a few. Propulsion subsystem: Microthrusters are so far used on nanosatellites, often cold gas or plasma thrusters. There are also some nanosatellites without any propulsion at all, thus relying solely on the torquers. This is possible since most of the nanosatellites are in orbit as test beds for the different subsystems, requiring only that the satellite stays in orbit without very accurate attitude control. Since most missions are rather short the orbital decay is of no significance. Power subsystem: Almost all nanosatellites use GaAs solar cells. Some have Si cells because of the lower cost. If the satellite has low power consumption, or the orbit provides extended Sun visibility this is a fully functional solution. The batteries are most often Li-Ion or NiCad. Thermal control subsystem: Typically thermal control systems are passive. This is achieved with suitable thermal coatings and design considerations, in order to attain the required temperature balance for sensitive equipment. Telemetry, Tracking and Command: Most systems operate at UHF, but some also use the X-band, and others the S-band. Satellite Tool Kit (STK) is used for visualization of tracking at groundstations for some satellites. Other options are FreeFlyer from AI Solutions Inc or DSST from Draper Labs.

13 Data handling: Several different solutions for the onboard computer are available. Processors may be: Hitachi SH7709, Hitachi 8/3048, SpaceQuest FCV53, Intel 80C188EC, Power PC 750, Texas Instrument TMS320C50, Strong Arm SA1100. Payload: The most common payloads are CMOS-cameras, and instruments for investigation of the magnetosphere. At present most payloads are test platforms for different technologies for application with nanosatellites, such as new or improved processors, thermal coatings, communication devices, propulsion systems etc.

14 6.2 Comparison of formation flight missions

The table below lists the mission, payload and formation flight scheme for some of the state-of- the-art formation flight missions.

Satellite Mission Payload Formation flying The satellites will be released from the launcher stacked on top of each other. Initial tests will be done. Then the two satellites will be separated, but a tether will connect them. The instruments GPS, Colloid micro- onboard will be calibrated and further check-out Component characterization. thruster. Distributed of the subsystems will be performed. In the next Formation flying. health beacon. phase the tether is cut and the two satellites will fly Emerald Autonomous system. Instruments for in formation. In the last phase the Orion satellite Lightning and ionospheric science. lighting science that is launched at the same time will be included in the formation. More advanced formations will be tried out, where the Orion satellite will make the changes in position with regard to EMERALD, since it has a greater propulsion capability. Plasma Impedance Probe (PIP). Micro pulsed plasma thrusters. Gimballed Investigate the ionospheric disturbances. Two different formations will be attempted: magnetic attitude a) Leader-Follower ION-F Evaluate formation flying. control. Inter- b) Same Ground-track. Hardware evaluation. satellite communication and GPS. CMOS cameras. Stereoscopic imaging. CMOS cameras. 3 Corner Virtual-Formation Communications. Micropropulsion --- Satellite Automated Operations. experiment. MEMS Component validation. Heater Chip. Will be deployed into an along-track formation with separation distance 5 km, verifying position to 10 m accuracy. Then the sparse aperture sensing will commence along with onboard autonomy. The Autonomous formation maintenance and distance will then be decreased to 100-500 m and TechSat-21 reconfiguration. Sparse Aperture the satellites go into an elliptical 3-D Hill Sparse aperture sensing. sensing payload, an Flight configuration. After a while the separation Validate simulation with performance X-band antenna. distance is increased again. At the end of the experiment* modelling. lifetime the satellites will perform more riskful task such as autonomous formation changes and separation distances less than 100 m.

Validate modular COTS nanosatellite bus During the release phase the two other satellites concept. onboard the launch vehicle, Tsinghua-1 and Validate new manufacturing techniques and Nadzhda were pictured with the cameras. The technologies. satellite then went into orbit and was thoroughly Demonstrate 3-axis attitude control, checked out. It then increased its orbit with 3 km in precise orbit determination via GPS and Four CMOS APD- one month to rendezvous with Tsinghua-1. But, too SNAP-1 orbit manoeuvres. cameras. ORION much fuel was spent on maintaining orbit for it to Demonstrate rendezvous and relative orbit GPS receiver be able to perform formation flight. This was due determination via differential GPS. to an initial problem with the attitude control Demonstrate technologies and techniques system and to the greater fall ratio of SNAP-1 for formation flying. compared to Tsinghua-1. Instead the CMOS- Image Tsinghua-1 both at deployment and cameras were pointed towards nadir and Earth- rendezvous. imaging began. *Project has been discontinued. Table 6.2-1. Review of some related missions, either planned or already accomplished.

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16 7 Subsystems

7.1 GNC

A condition for the realization of a formation of nanosatellites is a light and very accurate ADCS- system. The relative positions are of greater importance than the absolute, since most of the control technologies for formation keeping are based on relative positions rather than the more uncertain absolute measurements. An increasing number of sensors and actuators using MEMS are available as COTS. They are, however, still very mission-specific. Most sensors are custom-made for a particular mission and then made available as ‘COTS’.

7.1.1 Sensors

7.1.1.1 GPS

The GPS sensor is the most common onboard nanosatellites. Since all of them so far fly in Low Earth Orbits, GPS is the most convenient method for absolute position measurements. The short mission duration also make it possible to use COTS GPS, making these systems very affordable. There are also missions that are using Differential-GPS for the relative position measurements.

7.1.1.2 Sun sensors

Three sun sensors and their specifications are shown below.

Developer Specifications Applied Microengineering Ltd, Great Mass: <10g Britain. 2003 Volume: <1cm3 Onboard mounting to within 0.02 degrees Operating temperature range: -50 to +80oC Field of View: 120o Accuracy: 0.12o Linearity: <0.1% of full scale Noise: <0.1o peak to peak Danish Technical University, Mass: <3g CubeSat. 2002 Field of view: ±70o Theoretical resolution: 0.07o Axis: two Dipartimento di Scienza e Ingegneria Sun-line est. error: 10-4 deg dello Spazio - Università di Napoli. Predicted accuracy: 1 arcmin

Table 7.1.1.2-1. Specifications for three different Sun sensors.

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7.1.1.3 Star tracker

Star trackers are very precise and provide lost-in-space ability. The downside is that they are rather heavy and use substantial computing power. It is not foreseen that the present mission will require this type of sensor.

7.1.1.4 Earth-horizon sensor

These sensors are rather crude, but they are small and light. They are often used when lost- in-space capability is required.

7.1.1.5 Inertia sensors

Offer high accuracy but require dumping of momentum. They are therefore combined with some type of actuators. Below an example is given.

Developer Specifications BEI technologies, Systron Donner Inertial Mass: 20g Division, California USA. Standard Ranges: ±200°/sec QDARS - MEMS Quartz Dual Axis Rate Input Voltage: + and - 5.0 Vdc Sensor Bias Stability: Model to <0.1°/sec Random Noise: .005°/sec/ Scale Factor Accuracy: ±1% Nominal Two Axes of Angular Rate Low Unit Price High Reliability Rugged Design

Table 7.1.1.5-1. Specifications for an inertial sensor.

7.1.2 Actuators

The most common actuators onboard a nanosatellite are magnetotorquers and/or some type of micropropulsion. An example of a MEMS-propulsion system is described in subsection 7.7.5.

7.1.3 Control architectures

In order for the formation to function smoothly a certain degree of autonomy is required. If all decisions concerning the formation would have to be taken by the ground control, the personnel needed to maintain the formation would be numerous and expensive. Also, the manoeuvres would depend on the communication window and would therefore take a long time to execute.

18 7.1.3.1 Centralized approach

The general idea is to control the satellite formation as one large entity. One satellite has the computation capability onboard and sends instructions to the other satellites. For the sake of redundancy there will most often be a hot backup satellite within the formation. The central entity may also be on ground. There is also the possibility of having the central entity program onboard all satellites in case the central satellite is lost, also called a hybrid approach.

7.1.3.2 Decentralized approach

With this approach the responsibility is distributed among the satellites in the formation. They make individual decisions on formation keeping and communicate with all satellites in the formation. This means that the overhead needed for inter-satellite communications will be larger than for the centralized approach. The advantage is that there will be no single weak point; if one satellite is lost the remaining will still function as a group even if some of the capacity is lost.

7.1.3.3 Executive controller approaches

There are several solutions for dealing with the scheduling and execution of events, of which three are described below.

7.1.3.3.1 Intelligent agent based system

In this approach efforts are directed towards defined goals. The functions of the satellite are broken down into agents, for example one for the propulsion system, one for the attitude determination system and so on. These agents are assigned to a goal and work individually or in collaboration with each other in order to achieve it. The approach makes possible the use of different techniques for different agents and still has them working together. Each agent can provide a solution on a low level, whereas on a higher level all can be integrated into a final decision. One important condition is that the agents need to be able to share information. This is done via message centres, where agents can post information or actions and request information or actions in return. The message centres can then match requests or post them at a higher level in order for solutions to be found. This approach was intended to be used on the TechSat21-program that was discontinued in 2003.

7.1.3.3.2 Rule-based expert system

Here the decisions are made based on the information available in the knowledge base. The knowledge base consists of facts and rules. The facts are supplied by the subsystems and stored in the base. The rules determine the type of actions to be performed based on a set of conditions; if the conditions are met, a certain type of action is performed.

19 7.1.3.3.3 Flocking/Market-oriented programming system

With flocking control the formation is maintained by maximizing an objective function that describes the well-being of the formation. Market-oriented programming seeks to minimize the use of resources by outsourcing the effort to the participants. With the case of formation flight the fuel would be the resource that is desired to be used equally throughout the formation.

7.2 Thermal

7.2.1 Background

7.2.1.1 Passive Thermal Control

7.2.1.1.1 Phase Change Devices

These devices use the latent heat of phase changes in a material for storing excess heat. Most often they consist of an aluminium container with some kind of wax inside. The device is best suited for electrical circuitry subjected to short power spikes. A disadvantage is that when the wax is molten it will not absorb more heat, and so the temperature of the electrical circuitry will start to rise.

7.2.1.1.2 Thermal Control Coatings

Included here are both thermal paints of different colours and foils of different metals. The advantages of using coatings are that they are lightweight and efficient, the disadvantage that they degrade over time. When choosing a coating it is of importance to choose the correct emittance, ε, and absorption, α. A high value of ε increases emission of heat, and a low value of α reduces absorption of solar radiation.

7.2.1.1.3 Multi Layer Insulation (MLI)

MLI consists of layers of aluminized Mylar or Kapton with alternate layers of coarse net. The main advantage is that the heat transfer between two surfaces can be reduced drastically, and therefore MLI is most often used for wrapping sensors and payloads in order to isolate them from other equipment. The rest of the satellite may then be subjected to greater temperature changes while the more sensitive parts are protected.

7.2.1.1.4 Thermal Doublers

These are in effect heat sinks made of a highly heat conducting material. The Doubler is in thermal contact with the device to be cooled, and dissipates the heat through radiation. It also works in the other direction, protecting the device from low temperatures. It can also be used on radiator surfaces in order to smooth the

20 temperature. Thermal doublers are best suited for devices that subjected to cyclic power dissipation.

7.2.1.2 Active Thermal Control

7.2.1.2.1 Smart thermal coatings

This is a new branch of thermal protection, still in the developing stage. The coatings change their properties when a voltage is applied. This gives the satellite the ability to have lower emission when the satellite is cold, and higher emission when the satellite needs cooling. Lab tests have shown promising results for the ability to change emission, making this option very interesting for nanosatellites in need of efficient and light thermal devices.

7.2.1.2.2 Heat Pipe

This device uses evaporation and condensation to transfer heat. A liquid contained in a pipe absorbs heat from a device and evaporates, whence the gas is transferred to a place at the other end of the pipe where the gas condensates in a radiator. The liquid is then transferred back to where the cooling is needed by capillary wicks. Heat pipes are very efficient and are at the same time light.

Figure 7.2.1.2.2-1. Schematics of a Fixed-Conductance Heat Pipe.

7.2.1.2.3 Louvers

Louvers work like blinds on the surface of radiators. They are covered with thermal paint and by opening them at different angles α and ε can be varied. The Louvers are operated by an actuator, which means they include moving parts that decrease the reliability.

Figure 7.2.1.2.3-1. Open and Closed Louvers.

21 7.2.1.2.4 Second-Surface Mirror

These mirrors work in two ways; they reflect the incoming energy while at the same time they dissipate the energy from inside the satellite. They are very efficient and now replace Louvers.

7.2.1.2.5 Electrical Heater

A thermostat is used for controlling the heater, which in turn heats the cold parts of the satellite. Electrical current generates the heat in a resistor. Because of this the on-time periods may be short. The advantage is that very precise temperature control can be achieved.

7.2.2 Design

The mass of the thermal subsystem is typically ~3-4 % of the dry mass, and should be kept less if possible. First of all the various temperature limits of the different subsystems and their components need to be determined, and then the heat generated by the components have to be calculated. The solar flux and albedo extremes on the satellites are taken from the radiation analysis. Then the thermal radiation extremes from Earth can be calculated. The heat equation can then be formulated and solved. The solution indicates the choice of thermal system. A good idea is to start with thermal paints and other passive systems. If these do not yield a stable and satisfactory design, active systems such as shutters and heaters should be considered.

Figure 7.2.2-1. Steps involved in the design of the thermal subsystem.

22 7.2.3 Specifications

When designing the thermal subsystem it is important to know what temperatures the satellite will be exposed to. Critical temperatures may arise while mounting the satellite to the launch vehicle as well as in space.

7.2.3.1 From the launching company

The temperature and humidity for different phases of the preparation of the satellite and launch vehicle are shown in table 7.2.3.1-1.

Phase Temperature range [oC] Relative humidity At the spacecraft processing facility 21 – 27 No more than 60 % During integration of satellite with 5 – 35 No more than 80 % Space Head Module Transportation of Space Head 10 - 25 No more than 80 % Module (inside the Transporter-Erector) At the Space Head Module 5 – 35 No more than 80 % processing facility (around the satellite) Load of the Space Head Module into 0 – 45 (no more than 30 min) No more than 80 % the silo, and mating with Launch 5 – 35 (no more than 5.5 Vehicle (Around the Space Head hours) Module) Inside the silo 5 – 25 (short term increase to No more than 80 % 35) Inside the silo (around the satellite) 5 – 30 No more than 70 %

Table 7.2.3.1-1. The temperature and relative humidity in the different phases of launch preparation. The thermal flux from the inner surface of the gasdynamic shield will stay below 1000 Wt/m2.

7.2.3.2 From the orbit

From the simulation program for the orbit calculation there will be a report on period in sunlight. That will be the base for the thermal calculations originating from the radiation from the sun.

23 7.3 Structure & Separation

In order to simulate the orbits and the control system with better accuracy, a rough geometrical outline of the satellites were required. The aerodynamic properties have an impact on orbit degeneration at Low Earth Orbits, which need be taken into account. The outline of the work is given below. A refined Nastran-model is not necessary, but something that would be compatible with the simulation program used for the control system. A brief summary of the materials to be used for the structure was also requested, in order that the first overview of cost and weight estimations for the satellites could be made.

Figure 7.3-1. The time schedule for the first efforts regarding the structural design.

7.3.1 Specifications

The total mass of each individual satellite should not exceed 10 kg, and possibly be kept at 8 kg, since then a low-cost launch opportunity would be within reach. The dimensions will depend on the shape, but should correspond to a cube of around 20x20x20 cm. Initially a hexagonal shape was discussed. This shape is used on many other missions and it would be time and resource saving to use the standard adapter at the launch vehicle. The aerodynamic calculations will show whether booms will be added for flight stabilisation and enhancing the aerodynamic properties.

24 7.3.2 Design

The design criteria for the structure and separation system according the launching company are given in Appendix 12.2.1, with comments on the interpretation. These were given to the person at CLS3 responsible for the structure and separation system to be included in his further work. In Appendix 12.2.2 and 12.3.2 the required documents from the launching company are given. The person in charge of the structure and separation system is also in charge of writing the appropriate documents and making sure that the launching company’s standards are adhered to. As mentioned above, it might be possible to reuse the separation system used for the former small satellites that have flown with the same rocket. One of the launch alternatives has an adapter for 10 to 20 kg spacecraft that might be usable. See drawing in Appendix 12.3.1.

7.4 Power

7.4.1 Solar Cells

Today the focus on solar cells is on the multijunction cells and thin films. There is also research being made on materials that absorb more than one band, making them even more efficient than the multijunction cells.

7.4.1.1 Multijunction cells

The principle of multijunction cells is that different cells with different bandgaps are stacked together in order to absorb more of the sunlight. The front cell exposed to the entire sun spectrum has the largest bandgap, and the second cell the second largest and so on. This configuration gives a better efficiency than homo- and heterojunction cells, reaching values of more than 35 percent in concentrated sunlight and around 30 percent in space applications.

Figure 7.4.1.1-1. Structure of a Japanese triple-junction cell.

25 7.4.1.2 Thin films

The most commonly used thin film solar cell is the amorphous-Silicon cell. The main advantages with these cells are that they are thin, light and flexible. They are also durable and naturally tolerant to radiation. The downside is that they have lower efficiency than other multijunction solar cells, around 10-15 percent.

7.4.1.3 Multiband solar cells

A new material, zinc manganese tellurium, ZnMnTe, with the ability to absorb more of the sunlight spectra is being developed to be used as a new type of solar cell that would be highly effective, reaching up to 50 percent accuracy. The light will not have to travel through the cell in order to reach the specific area where it is absorbed, but can be absorbed throughout the cell, which leads to higher efficiency.

Figure 7.4.1.3-1. Illustration showing the difference between Multijunction and Multiband solar cells.

7.5 OnBoard Data Handling (OBDH)

Collaboration was initiated with an institute of a Canadian university that would be involved with the building and the testing of the satellites. A discussion was also held regarding the subsystems they would be responsible for; the Onboard Computer as well as the Communication system were chosen at the outset. It was stressed though, that the satellites were to be built using a system-on- a-chip approach, since that approach minimizes mass and wiring.

7.6 Communication

The communication will be one of the limiting factors for the separation distances between the satellites and also the type of formation that can be achieved. Since there was no in-house expertise on this subsystem, the communication subsystem was assigned to the same researchers that were going to be in charge of the OBDH-system, see Chapter 7.5.

26 7.7 Propulsion

There exist four interesting potential types of propulsion that may be realized in the near future: • Colloid micro thrusters • Field emission electrostatic propulsion thrusters (FEEP) • Micro pulsed plasma thrusters (μPPT) • Miniature cold gas thrusters

7.7.1 Colloid micro thrusters

Colloid thrusters were first proposed in the 1960s, but were never used on any mission. This was mainly because the industry required high thrust, while the colloid thrusters provide low thrust and high accuracy. In order to attain high thrust levels, the colloid thrusters need between 12 and 100 kV, which resulted in packaging problems. Now that small satellites are in demand again, the colloid thrusters have come under consideration once more. The propellant is an electrolytic liquid most often consisting of a solvent and a salt, for example formamide or glycerol as solvent and sodium iodide (NaI) or lithium chloride (LiCl) as salt. Lately studies have been made on ionic liquids of high conductivity, consisting only of ions, with no solvent. A very strong electric field is used for extracting droplets, and/or single ions from the propellant supplied to the system via a needle. The field force works against the surface tension of the liquid, and possibly also a backpressure in the supply pipe, forming a jet that breaks up into droplets. The droplets are then accelerated further in the electric field to very high velocities, thereby creating the thrust. In most cases a cathode is added to the system for neutralizing the outgoing stream of ions.

Figure 7.7.1-1. Schematic drawing of a Colloid Micro Thruster. The use of one single needle is not enough; an array of needles has to be used in order to achieve sufficient thrust.

The target thrust range in current research is 1-20 μN with an Isp of 500 s.

27 7.7.2 Field emission electrostatic propulsion thrusters (FEEP)

The FEEP and the colloid thrusters operate almost in the same way. The main difference between the two is the propellant; the FEEP thrusters extract the ions from liquid metals instead of electrolytic solutions. Because of this the required electric field for the FEEP is higher than that of the colloid thrusters. The most commonly used metal is Caesium, since it has a large atomic number and a low melting point (29oC), but there are also some using Rubidium (39oC) or Indium (156oC). The problem with FEEP has been that they have not been suitable for Low Earth Orbits, since Caesium is an alkali metal and therefore reacts rapidly with water and oxygen, forming Caesium hydroxide (CsOH) and Caesium oxide (Cs2O) respectively. This can cause problems in two different ways: when the surface of the liquid Caesium is exposed to the atmosphere, and if there is water vapour inside the chamber before the first firing. The result may be that the jet is diverted, thereby decreasing the thrust. The altitude therefore had to chosen so that the level of oxygen and water in the atmosphere would be sufficiently low. Centro Spazio in Italy has performed a study of these effects, and they found that it was less than what had been expected. It is still of greatest importance, though, that the fuelling, the first wetting of the emitter and the first firing takes place in vacuum. The emitter has a slit where the ions leave, typically 1 to 2 microns wide and anything from 1 mm to several cm long. The accelerator is negatively biased by a few kV in order to obtain the ionization and acceleration required. Altering the voltage of the accelerator, above the threshold voltage, regulates the thrust. A neutralizer in the form of a cathode is necessary for balancing the ion flow.

Figure 7.7.2-1. Schematics of an FEEP. The Austrian Research Centre has been developing an FEEP that uses Indium as propellant, yielding a system that is a mix between the colloid thruster and the FEEP.

7.7.3 Micro pulsed plasma thrusters (μPPT)

There is more than one configuration available for the PPT. The three most commonly used versions are breech-fed, side-fed and coaxial. Independent of the configuration the PPT all function in the same way.

28 A spring is holding the propellant, a bar of TeflonTM, in place between an anode and a cathode. A capacitor is charged and then discharged, causing a large potential between the anode and cathode. This potential ablates part of the Teflon surface. The semiconducting spark plug is then initiated and gives rise to an arc between the anode and the cathode. The arc extends through the ablated Teflon and ionizes the gas. The high current in the arc generates a magnetic field, which in turn exerts a Lorentz force on the plasma. It is this force that accelerates the plasma to the high output speed. There is also some thermal expansion of the ablated Teflon that is not ionized by the arc, contributing to the exhaust velocity, but not to the same extent as the Lorentz force.

Figure 7.7.3-1. Schematics of a Micro PPT. The PPT have been around since the 1960s, and have been flown several times over the years. The pulses that can be achieved with the PPT are very short, and therefore very high precision can be attained. There are no moving parts, except for the spring holding the bar in place, and there are no specific handling requirements for the fuel since it is in a solid state. All this makes for a very safe and reliable propulsion system. The PPT are under scaling today and considered for several small satellite missions. It is also very suitable for larger missions with high accuracy pointing requirements. Some characteristics for a few existing systems are shown in table 7.7.3-1.

Thruster Eo [J] Isp [s] Ibit [μNs] mshot/Eo [μg/J]

LES-6 1.85 300 26 4.8 LES-8/9 20 1000 297 1.5 MIT Lab 20 600 454 2.8 MIPD-3 100 1130 2250 2 Primex-NASA 43 1136 737 1.5 IL PPT-3 Lab 7.5 600 450 10 Japan Lab 30.4 423 469 3.7 China Lab 23.9 990 448 1.9 Table 7.7.3-1. Flight and laboratory performance data, taken from [Burton 1998].

29 7.7.4 Miniature cold gas thrusters

These thrusters function as the larger cold gas thrusters, and are merely scaled to fit the needs of a smaller spacecraft A propellant is fed through a valve into a nozzle and then accelerated away from the satellite, creating the thrust, see Figure 7.7.4-1. In Table 7.7.4-1 the characteristics of a miniature cold gas thruster are shown, given two different propellants.

Figure 7.7.4-1. Drawing of a miniature cold gas thruster.

Company Propellant Thrust Impulse Life Specific Operating Nominal Operating span impulse voltage current temperature Surrey- 32.6g 45mN 22.3Ns >5years >60s 7-12Vdc 500mA Better than – SNAP Butane @ 0oC, max 20 oC to 120mN 50 oC @ 40oC Surrey- 33g Same as 34Ns Same as Same as Same as Same as Same as SNAP Ammonia above above above above above above Table 7.7.4-1. The characteristics of a miniature cold gas thruster, with two different propellants.

7.7.5 MEMS solid propellant thrusters

A solid propellant is stored in a combustion chamber in the lower part of the thruster segment. The propellant is ignited and the gas that results is accelerated in the nozzle to generate the thrust.

Figure 7.7.5-1. Exploded view of a MEMS solid propellant thruster. Solid propellants have many advantages: There is no leakage, no moving parts and low power is needed for ignition. The downside is that the thruster gives a one-time boost, although arrays of thrusters can compensate for this.

30

(a) (b) Figure 7.7.5-2 a. 6×6 Loaded solid propellant thruster array from LAAS-CNRS. Figure 7.7.5-2 b. 6×6 Thruster array with resistors and metallic lines (2×2 cm) also from LAAS-CNRS. The thrusters may be adapted to the specific mission, since the dimensions chosen for the chamber and/or throat will yield different thrust. The characteristics of the different types of fuel possible also vary. The thrust range seems to be in the order of a few μN to few tens of mN.

7.8 Payload

In the future formation flying nanosatellite clusters will be able to replace the larger satellites of today. It will also be possible to use clusters for stereoscopic imaging, geolocation and other tasks requiring a large aperture. For the present mission, the payload is not of first priority, rather the formation flight in itself. At present the payload has been dealt with only as a dummy, and in a later phase when the separation distances and other important features of the mission have been specified, the question of payload will be readdressed.

31

32 8 Orbit selection

8.1 Hill’s equations and Clohessy-Wiltshire equations

Hill’s equations were used for developing equations for rendezvous docking in the early 1960’s. They are only concerned with circular orbits and neglect the influence of nonlinear terms and long formation baselines. The formations derived by this equation are not viable for missions with long lifetime. One satellite is considered to be the ‘centre’ of the formation. The orbits of the rest of the satellites in the formation, called remotes, are accounted for relative to the ‘centre’. An interesting point is that the ‘centre’ satellite can be considered as virtual as well as real, depending on the mission requirements. A coordinate system that has the ‘centre’ satellite’s centre of mass as its origin is introduced; the x-axis is defined as the direction of motion for the ‘centre’ satellite, the y- axis as the out of plane vector, and the z-axis the radial direction towards the centre of Earth.

Figure 8.1-1. Relative motion coordinate system with the ‘centre’ satellite’s centre of mass as its origin.

8.1.1 Derivation

Newton’s law for gravitation [Newton 1713] is used for deriving the equations of motion expressed in a moving coordinate frame. The gravitational force is, in a non-rotating reference frame, Mm rv m v −= GF s −= μ s rv . (8.1.1-1) rg v)( r 2 rv r 3

where G is the universal gravitational constant, M the mass of the central body, in this case v Earth, ms the mass of the satellite and r is the radius vector from the centre of Earth. μ is defined as μ = GM , (8.1.1-2) Both sides can be divided by the mass for normalization, thus representing acceleration v v μ v rg v)( rf && −== r . (8.1.1-3) r 3

33 The equations are derived for a ‘chaser’ and a ‘target’, where for satellites flying in formation the ‘centre’ satellite will be the ‘target’ and the remotes will be the ‘chasers’. The target motion can be described by

v mt v F v −= μ r , (8.1.1-4) rg t )( 3 t rt which after normalizing yields,

v v μ v v rf −== r . (8.1.1-5) t )( &&trg 3 t rt For the chaser the motion will be defined by m Fv μ c v +−= Fr v , (8.1.1-6) rg vc )( 3 c rc v where F is the sum of forces acting on the satellite other than the gravitational force, such as thrust from the propulsion system or perturbations acting on the orbit, atmospheric drag, solar pressure and gravitational disturbances. Normalizing the equation yields v v v F fr v += . (8.1.1-7) && rgc c )( mc The chaser and the target are moving relative to each other, and the relative distance, s, and v relative acceleration, s&& , can be expressed as v v v −= rrs tc (8.1.1-8) v v v v vv F v ffrrs v +−=−= . (8.1.1-9) && && && c rgrgtc t )()( mc The chaser position vector may be expressed in terms of the target position vector. This can be done by linearizing the chaser acceleration for the target acceleration, using a Taylor expansion of first order v fd v vv rg )( vv v ff v += (− rr ), (8.1.1-10) c rgrg t )()( v tc rd vv =rr t v defining r as

⎡rx ⎤ ⎢ ⎥ rv = r . (8.1.1-11) ⎢ y ⎥ ⎣⎢rz ⎦⎥ If the rv vectors are defined as column vectors, the Jacobian matrix becomes [Wie1998]

34 v v ⎡∂f g1 ∂f g1 ⎤ ⎢ L ⎥ v ∂r ∂r fd v ⎢ 1 3 ⎥ rg )( = ⎢ ⎥ rdv v vMOM ⎢∂f g3 ∂f g3 ⎥ ⎢ L ⎥ ∂r1 ∂r3 ⎥ ⎣⎢ ⎦ . (8.1.1-12) The elements of the Jacobian must be derived separately for the diagonal elements and the other elements, since ri is not a function of rj. For the diagonal elements, i = j, and inserting equation 8.1.1-3 into equation 8.1.1-12 yields,

v 5 2 ∂f rg v )( ⎡ ⎛ 3 ⎞ − ⎤ μ ⎡ r ⎤ i μ −3 −+−= ++ 222 2 2rrrrrr −−= 31 i . (8.1.1-13) v ⎢ i ⎜ ⎟()izyx ⎥ 3 ⎢ 2 ⎥ rd j ⎣ ⎝ 2 ⎠ ⎦ r ⎣ r ⎦ For the rest of the elements, i ≠ j,

v 5 ∂f rg v )( ⎡ 3 − ⎤ μ rr ij ii μ ++−−= 222 2 rrrrr −= 32 . (8.1.1-14) v ⎢ ()zyx ij ⎥ 5 rd j ⎣ 2 ⎦ r rv v With as rt , the Jacobian from equation 8.1.1-12 may now be rewritten as

2 ⎡ rx rr yx rr zx ⎤ ⎢ − 2 2 3331 2 ⎥ ⎢ rt rt rt ⎥ 2 μ ⎢ rr xy ry rr zy ⎥ 3 J =− ⎢ 2 − 2 3313 2 ⎥ . (8.1.1-15) r ⎢ rt rt rt ⎥ 2 ⎢ rr xz rr yz rz ⎥ ⎢ 2 2 − 3133 2 ⎥ ⎣⎢ rt rt rt ⎦⎥ Inserting this in equation 8.1.1-10 yields

vv μ v v ff v −=− Js . (8.1.1-16) c rgrg t )()( r 3 and with this, equation 8.1.1-9 can be rewritten as v v μ v F s&& 3 Js +−= . (8.1.1-17) rt ms Transformation of the results to the moving frame can be done using a general kinematics equation for systems that are translated and rotating. The general expression for the second order time derivative being 2 xd xd vv *2* xd v ** dωv ()x * 2ωωω vvvv ×+×+××+= xv * , (8.1.1-18) dt 2 dt 2 dt dt where the * superscript denotes the rotating frame. Inserting sv and sv * along with equation 8.1.1-17 into equation 8.1.1-18, and rearranging, now gives

35 v*2* v** v v μ v sd * vvvv sd dω v * F 3 Js 2 ()s 2ωωω s =×+×+××++ . (8.1.1-19) rt dt dt dt ms v v The rt and ω vectors expressed in the moving coordinate system can be written as ⎡ 0 ⎤ ⎢ ⎥ rv = 0 , (8.1.1-20) t ⎢ ⎥ ⎣⎢− r⎦⎥ ⎡ 0 ⎤ v ⎢ ⎥ ⎢−= ωω ⎥ . (8.1.1-21) ⎣⎢ 0 ⎦⎥ where r is the distance to Earth, which will therefore be in the z-direction, while ω is the rotation of the satellite orbit. Using equations 8.1.1-20 and 8.1.1-21 for expressing the terms of equation 8.1.1-19, gives ⎡−ωz⎤ vv * ⎢ ⎥ ω s =× ⎢ 0 ⎥ (8.1.1-22) ⎣⎢−ωx⎦⎥ ⎡−ω 2 x⎤ vvv * ⎢ ⎥ ()ωω s =×× ⎢ 0 ⎥ (8.1.1-23) ⎢ 2 ⎥ ⎣−ω z⎦

⎡−ωz&⎤ sd v ** ⎢ ⎥ ωv =× 0 (8.1.1-24) dt ⎢ ⎥ ⎣⎢ ωx& ⎦⎥ −ωz v ⎡ & ⎤ dω * ⎢ ⎥ sv =× 0 (8.1.1-25) dt ⎢ ⎥ ⎣⎢ ω&x ⎦⎥ ⎡ 001 ⎤ ⎡ x ⎤ v* ⎢ ⎥v * ⎢ ⎥ Js = ⎢ 010 ⎥s = ⎢ y ⎥ (8.1.1-26) ⎣⎢ − ⎦⎥ ⎣⎢− 2200 z⎦⎥ For circular orbits ω will be constant over time, so the time derivative will be zero. Inserting 8.1.1-22 to 8.1.1-26 and the zero value of the time derivative of ω into equation 8.1.1-19 gives the following equations of motion in the x-, y- and z-direction respectively

36 Fx && 2ωzx & =− (8.1.1-27) ms

2 Fy && ω yy =+ (8.1.1-28) ms

2 Fz && & 32 ωω zxz =−+ . (8.1.1-29) ms The equations of motion in this coordinate system are known as the Hill’s equations [Hill 1878]. For circular orbits ω is defined as μ ω 2 = , (8.1.1-30) r 3

Defining the state vectors for in-plane (xi) and out-of-plane (xo) as

⎡x t)( ⎤ ⎢z ⎥ ⎢ t)( ⎥ xi = , (8.1.1-31) ⎢x& t)( ⎥ ⎢ ⎥ ⎣z& t)( ⎦

⎡ y t)( ⎤ xo = ⎢ ⎥ (8.1.1-32) ⎣ y& t)( ⎦ makes it possible to write equations 8.1.1-27 to 8.1.1-29 in the state space form. The general expression is known to be & Axx += Βυ , (8.1.1-33) where A is the transition matrix and B the input matrix. The Hill’s equations for in-plane and out-of-plane motion respectively can be written in the form ⎡ 00 ⎤ ⎡x& t)( ⎤ ⎡ 0100 ⎤⎡x t)( ⎤ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ 00 ⎥ z& t)( 1000 z t)( ⎢ ⎥⎡Fx ⎤ ⎢ ⎥ = ⎢ ⎥⎢ ⎥ + 1 (8.1.1-34) ⎢ ⎥ ⎢ ⎥ ⎢ 0 ⎥⎢ ⎥ x&& t)( ⎢ 2000 ω⎥ x& t)( mc ⎣Fz ⎦ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 2 ⎥ ⎢ 1 ⎥ ⎣⎢z&& t)( ⎦⎥ ⎣ − ωω 0230 ⎦⎣⎢z& t)( ⎦⎥ 0 ⎣ mc ⎦ ⎡ 0 ⎤ ⎡y& t)( ⎤ ⎡ 10 ⎤⎡y t)( ⎤ ⎢ ⎥ = ⎢ 2 ⎥⎢ ⎥ + ⎢ 1 ⎥[Fy ] (8.1.1-35) y t)( − ω 0 y t)( ⎣ && ⎦ ⎣ ⎦⎣ & ⎦ ⎣⎢ mc ⎦⎥ The Hill’s equations have been solved for various specific cases, with defined initial conditions.

37 8.1.2 Homogenous solution

A homogenous solution for the differential equations above can be derived using Laplace transformation. Keeping in mind that the Laplace transformations of a derivative and a second derivative are ( ′ ) −= fsFfL , (8.1.2-1) t s + )0()()( ( ′′ ) 2 −−= fsfFsfL ′ (8.1.2-2) t)( s + + )0()0()( respectively, the transformation of equations 8.1.1-27 to 8.1.1-29 turn out as follows

2 s &00)( s)( ωω zsZxsxXs 0 =+−−− 022 (8.1.2-3)

2 2 s &00)( ω YysyYs s)( =+−− 0 (8.1.2-4)

2 2 s &00)( s)( 0 ωωω ZxsXzszZs s)( =−−+−− 0322 . (8.1.2-5) Sorting out the different terms yields, in the frequency domain 1 1 1 1 s xX 0)( ()&0 −+= 2ωzx 0 + 2ωz0 + 2ωz&0 + ... s s 2 s + ω 22 ()ss + ω 22

2 1 + ()0 − 242 ωωω xz &0 222 (8.1.2-6) (ss + ω ) s 1 s = yY 0)( + y& 0 (8.1.2-7) s + ω 22 s + ω 22 s 1 1 2 . (8.1.2-8) s = zZ 0)( + z&0 ( 0 −+ 24 ωω xz &0 ) s + ω 22 s + ω 22 (ss + ω 22 ) In order to obtain the time domain response, an inverse Laplace transform may be performed on equations 8.1.2-6 to 8.1.2-8, resulting in

⎛ 4x&0 ⎞ 2z&0 x t)( ⎜ −= 0 ⎟sin6 ωtz − ()ωω &00 txzt +−+ ...36cos ⎝ ω ⎠ ω

⎛ 2z&0 ⎞ ⎜ x0 ++ ⎟ (8.1.2-9) ⎝ ω ⎠ y = cosωtyy + & 0 sinωt (8.1.2-10) t 0)( ω

⎛ 2x&0 ⎞ z&0 ⎛ 2x&0 ⎞ z t)( ⎜ −= 0 ⎟cos3 ωtz ω ⎜4sin zt 0 −++ ⎟ . (8.1.2-11) ⎝ ω ⎠ ω ⎝ ω ⎠ These equations, 8.1.2-9 to 8.1.2-11, are known as the Clohessy & Wiltshire equations. It can be seen that the solutions for y and z are oscillating, while there is a secular growth in x. This needs to be taken care of while specifying the orbits, since otherwise they will drift apart over time.

38 The homogenous solution to the state space form equations of motion, equations 8.1.1-34 and 8.1.1-35, can be derived by applying a Laplace transform of equation 8.1.1-33,

s s + =− Axxx s + Βυ s)()()0()( . (8.1.2-12) Rearranging gives

()s s =− xxAI + + Βυ s)()0()( . (8.1.2-13) With

−1 Φ s)( (s −= AI ), (8.1.2-14) the frequency domain solution becomes

x s = Φ s (x + + Βυ s)()0()()( ), (8.1.2-15) and the time domain solution

−1 −1 x t)( = L [Φ s x +)0()( ]+ L [ ΒυΦ ss )()( ]. (8.1.2-16) The first part of the solution is only dependent on the initial state while the second part depends only on the disturbances. The first part is therefore equations 8.1.2-9 to 8.1.2-11 in vector form. Another way of obtaining the general solution to equation 8.1.1-3 is

x φ tt )0()()( += xx p , (8.1.2-17)

where xp is the particular solution and ϕ(t) is a transition matrix that maps the initial state vector on the final state vector at time t. The transition matrix can be calculated from

A t)( φ t)( = e , (8.1.2-18) which is the general way of calculating this matrix. Comparing equations 8.1.2-17 and 8.1.2-

18, however it may be seen that the inverse Laplace transform of Φ(s) will equal ϕ(t). So for the in-plane and out-of-plane motions respectively this would yield ⎡ 4 2 ⎤ ()− sin61 ()ωω tt ()ω 3sin tt ()−− cos1 ()ωt ⎢ ω ω ⎥ ⎢ 2 1 ⎥ φ = ⎢ − cos340 ()ωt ()()ωt −1cos sin()ωt ⎥ (8.1.2-19) ti )( ⎢ ω ω ⎥ ⎢ ()()()− cos160 ()ωω t ωt − sin23cos4 ωt ⎥ ⎢ ⎥ ⎣ sin30 ()ωω t − sin2 ()ωt cos ()ωt ⎦ ⎡ 1 ⎤ ⎢ cos()ωt sin()ωt ⎥ φ to )( = ω . (8.1.2-20) ⎢ ⎥ ⎣− sin()cos ()ωωω tt ⎦

39 8.1.3 Particular solution

The propulsion system works with short pulses of thrust for orbit changes, so the particular solution for impulses is interesting for further investigation. Defining the input function as kkf Θ−Θ= , (8.1.3-1) t −tt 1 −tt 2 )()()( with k being the amplitude of the pulse and Θ the Heaviside’s step function, i.e. a pulse of amplitude k from t = t1 to t = t2. Laplace transforming equation 8.1.3-1 yields k F (1 −= ee −− 2stst ). (8.1.3-2) s)( s The particular solution in the frequency domain, that is, the second part of the right hand side in equation 8.1.2-16, will then for the in-plane and out-of-plane respectively be ⎡ 0 ⎤ ⎢ ⎥ 1 ⎢ 0 ⎥ = ΦΒυΦ F = ΦΒ ssisss )()()()()( = ... m ⎢F sx )( ⎥ s ⎢ ⎥ ⎣⎢F sz )( ⎦⎥

⎡ F sxs Φ+Φ F szs )()(4,1)()(3,1 ⎤ ⎢ ⎥ 1 F sxs Φ+Φ F szs )()(4,2)()(3,2 = ⎢ ⎥ (8.1.3-3) m ⎢ F sxs Φ+Φ F szs )()(4,3)()(3,3 ⎥ s ⎢ ⎥ ⎣⎢ F sxs Φ+Φ F szs )()(4,4)()(3,4 ⎦⎥

1 ⎡ 0 ⎤ 1 ⎡Φ F sys )()(2,1 ⎤ = ΦΒυΦ F = ΦΒ = . (8.1.3-4) ss sos s)()()()()( ⎢F ⎥ ⎢Φ F ⎥ ms ⎣ sy )( ⎦ ms ⎣ sys )()(2,2 ⎦

Only the last two columns of Φ(s) are needed for the in-plane equation and only the last column for the out-of-plane equation since the rest of the elements in Φ(s) are zero because of B (see equations 8.1.1-34 and 8.1.1-35). The first element in equation 8.1.3-4 is

1 11 k 1 −− 2 stst F sys )()(2,1 =Φ 22 ( ee )=− ... ms s sm + ω s

k 1 1 −− 2stst = 22 ( − ee ). (8.1.3-5) s ()ssm +ω The inverse Laplace transformation of equation (8.1.3-5) will in turn be ⎡ ⎤ −1 k 1 1 −− 2stst k 1 L ⎢ 22 ()− ee ⎥ = 2 ()cos()(ω()tt 2 cos()ω −−− tt 1 ). ⎣ms ()ss + ω ⎦ ms ω (8.1.3-6) This can be done for the elements in equation 8.1.3-3 and 8.1.3-4 and put into a matrix H, consisting of two four-element vectors for the in-plane motion and one two-element vector for the out-of-plane motion. Separating the x- and z-elements gives us two vectors for the in-plane motion

40 ⎡ 4 3 2 2 ⎤ ()cos()()ω()tt 2 cos()ω 1 (()()2 −−−+−−− tttttt 1 ) ⎢ω 2 2 ⎥ ⎢ 2 ⎥ ⎢ ⎥ 2 ()sin()()ω()1 sin()()ω 2 ω −+−−− tttttt 21 h = ⎢ ω ⎥ (8.1.3-7) 1 4 ⎥ ⎢ ()sin()()ω()sin()()ω 3 −+−−− tttttt ⎢ ω 1 2 21 ⎥ ⎢ 2 ⎥ ⎢ ()cos()()ω()tt cos()ω −−− tt ⎥ ⎣ ω 1 2 ⎦ ⎡ 1 ⎤ cos ω tt cos ω −−− tt ⎢ 2 ()()(()2 ()1 )⎥ h = ω (8.1.3-8) 2 ⎢ 1 ⎥ ⎢ ()sin()()ω()sin()ω −−− tttt ⎥ ⎣ ω 1 2 ⎦ ⎡ 2 ⎤ ()sin()()ω()tt sin()(ω ω −+−−− tttt ) ⎢ω 2 2 1 12 ⎥ ⎢ 1 ⎥ ⎢ ⎥ 2 ()cos()()ω()tt 2 cos()ω −−− tt 1 h = ⎢ ω ⎥ (8.1.3-9) 3 2 ⎢ ()cos()()ω()tt cos()ω −−− tt ⎥ ⎢ ω 2 1 ⎥ ⎢ 1 ⎥ ⎢ ()sin()()ω()sin()ω −−− tttt ⎥ ⎣ ω 1 2 ⎦ The particular solution for one pulse can then be written on the form 1 p1 = uHx ˆ , (8.1.3-10) ms where uˆ is a modified u, now containing only the impulse amplitude. If more than one pulse is applied, or if constant thrust is applied, the equations may be summed, thus describing a general solution. For each pulse the appropriate start and end times must be inserted. The general solution for the in-plane and out-of-plane motions becomes 1 ˆˆ , (8.1.3-11) x pi = ∑∑[()()11 i + hh uu 33 k ] ms ik 1 ˆ . (8.1.3-12) x po = ∑[()h u22 j ] ms j The summation is done over the x-, y-, z-axis, represented by index i, j, k respectively. In the case of a continuous thrust the solution to the equations of motion can be written as

⎛ 4x&0 ⎞ 2z&0 ⎛ 2z&0 ⎞ x t)( ⎜ −= 0 ⎟sin6 ωtz − ()ωω 36cos &00 ⎜ xtxzt 0 ++−+ ⎟ + ... ⎝ ω ⎠ ω ⎝ ω ⎠

2 ⎛ 4 3 2 ⎞ + z ()sin()tt +− γωωγ x ⎜ ()cos1 ()ω −− tt ⎟ (8.1.3-13) ω 2 ⎝ω 2 2 ⎠

41 y γ = cosωtyy + & 0 sinωt y (−+ cos1 ()ωt ) (8.1.3-14) t 0)( ω ω 2

⎛ 2x&0 ⎞ z&0 ⎛ 2x&0 ⎞ z t)( ⎜ −= 0 ⎟cos3 ωtz ω ⎜4sin zt 0 −++ ⎟ + .... ⎝ ω ⎠ ω ⎝ ω ⎠ 2 γ ()sin()ωωγ tt z (−+− cos1 ()ωt ). (8.1.3-15) ω 2 x ω 2

This is done by letting t1 be zero and the pulse width to be t. Here γx,y,z is the unit for force divided by mass.

8.1.4 Discrete time

Most controllers are designed in the discrete time domain. The design is simplified by the use of the equations of motion in the discrete time state space representation, compared with the equations for continuous time, equations 8.1.1-34 and 8.1.1-35. The discrete time state space representation is not an approximation of the continuous time equations, rather it gives the exact value at specific times. The input pulses from the propulsion system are constant in amplitude, a necessary condition for the calculation. The sampling time will be denoted T, and should be seven to ten times shorter than the minimum time for the fastest mode of the closed loop system. The next state starting at time t is considered as the t + 1 state. The state space model for discrete time may now be written as

t+ t += GuFxx t)()()1( . (8.1.4-1) The coefficient matrix, F, can be derived from equations 8.1.2-19 and 8.1.2-20 by setting the time t to T. The formal way of deriving it would be

A T )( F e == φ T )( . (8.1.4-2) The input matrix, G, is defined as

T A G = ∫ t)( Βdte . (8.1.4-3) 0

The product under the integral may be found in the last two columns of ϕi(t) for the in-plane motion and the last row of ϕo(t) for the out-of-plane motion (see equations 8.1.1-34 and 8.1.1- 35, and equations 8.1.2-19 and 8.1.2-20). Integrating this over the sampling time yields for in- plane and out-of-plane motion respectively ⎡ 4 3 2 ⎤ ()cos1 ()ω −− TT 2 ()− sin()ωω TT ⎢ω 2 2 ω 2 ⎥ ⎢ 2 1 ⎥ ⎢ ()sin()−ωω TT ()− cos1 ()ωT ⎥ 1 2 2 G = ⎢ ω ω ⎥ , (8.1.4-4) i m ⎢ 4 2 ⎥ s ()ω − 3sin TT ()− cos1 ()ωT ⎢ ω ω ⎥ ⎢ 2 1 ⎥ ⎢ ()()ωT −1cos sin()ωT ⎥ ⎣ ω ω ⎦

42 ⎡ 1 ⎤ ()− cos1 ()ωT 1 ⎢ω 2 ⎥ G o = ⎢ ⎥ . (8.1.4-5) m 1 s ⎢ sin()ωT ⎥ ⎣ ω ⎦

8.2 THEONA

In the 1980s-1990s Akim and Golikov at the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, developed a numeric-analytical satellite theory. Golikov, working for KIA Systems, later improved the theory and came up with a semi-analytical theory named THEONA, which stands for THÉOrie Numérique-Analytique. The theory uses the exact solution of the Generalized Problem of Two fixed Centres (GP2FC), created by Aksenov, Grebenikov and Demin. This exact solution is used as an intermediate orbit for the satellite motion, it is also called the Eulerian orbit since it was Euler who was first to formulate and solve the problem with two fixed centres in the plane case. The corresponding orbital elements are in the same manner named the Eulerian orbital elements. The problem is stated for two complex masses, m1 and m2, separated by a complex distance defined by the complex vectors r1 and r2 M m ()1+= iσ 1 2 M m (1−= iσ ) (8.2-1) 2 2

r1 = {}00 ()σ + ic

r2 = {00 (σ − ic )} (8.2-2) There are two modes of the GP2FC, one symmetric where σ = 0 and one asymmetric where σ ≠ 0. The asymmetric mode can be made to include the effects of both the second, third and partially the fourth zonal harmonics of Earth’s gravity field, if

2 ⎛ J ⎞ ⎜ 3 ⎟ (8.2-3) e JRc 2 −= ⎜ ⎟ ⎝ 2J 2 ⎠

J 3 2J σ −= 2 (8.2-4) 2 ⎛ J ⎞ ⎜ 3 ⎟ J 2 − ⎜ ⎟ ⎝ 2J 2 ⎠ where Re is the radius of Earth.

From the solution the intermediate orbit is chosen, which will therefore include the J2 and J3 effects. Other dynamical effects are also considered in the theory: air drag, gravity influence of other celestial bodies, the solar radiation pressure (with the shadow effects included) and the rest of the zonal, tesseral and sectoral harmonics of the geopotential model. This is accomplished by numeric-analytical integration of the differential equations for the Eulerian orbital elements.

43 Numerical-analytical integration is a step-by step method. The perturbation of each orbital element, in one orbit or more, is calculated analytically and then added to the orbital element within each step. Then the same process is performed within the next step based on the previous result and so on. THEONA can also take into account other disturbances of the satellite’s orbit, including: different types of manoeuvres, both impulse, long term and low thrust; input of orbit taken from tracking data; updates on the solar activity and geomagnetic disturbances; as well as changes in Earth’s equatorial frame, i.e. precession, nutation, pole motion etc. Orbits that are closely related through one or more orbital elements can be treated at the same time, allowing calculations to be made for clusters of formation-flying satellites. THEONA calculates the motion of one satellite, called a chief and then the calculations for the other satellites in the formation is expressed as deviations of this orbit. The chief can be virtual or real depending on the mission definition. If the chief is made virtual, its orbit is a mean of the orbits of the other satellites in the formation. The orbital elements of the other satellites are calculated analytically at each step based on the calculations done for the chief, thus decreasing the computational needs and at the same time achieving high accuracy. High accuracy can be attained since the disturbance is proportional to the distance, and the radius of the orbit is significantly larger than the distance between the satellites, making the relative motion better defined than the orbital.

8.3 Trajectory deviation

The deviation from the desired trajectory can come from one or more of the following causes: • Orbital disturbances: From atmospheric drag, the oblateness of Earth etc.

• Navigational errors: The difference between the actual position and direction, and the output from the attitude determination system.

• Control errors: The difference between the actual control system output and the desired, depending both on the navigation system and the attitude control system.

• Thrust vector errors: The deviation in thruster direction and magnitude from the desired values.

• Thruster failures: If the thruster breaks down for some reason, either leaving the thruster in on or off position.

44 8.3.1 Orbital disturbances

8.3.1.1 Atmospheric drag

The drag force on a satellite may be expressed as v v ρ 2 v −= ACvF rel , (8.3.1.1-1) D Drel v 2 vrel v where ρ is the density of the atmosphere at the specific altitude, vrel the velocity vector of

the satellite relative to the motion of the atmosphere, CD the drag coefficient and A the cross-section facing the direction of motion of the satellite body.

The shape of the satellite determines CD, for a sphere in the upper atmosphere it lies between 2.0 and 2.1 and for a flat plate in the upper atmosphere it would be around 2.2. v Note that vrel is not the same as the motion vector used in previous expressions, it is rather defined as the motion relative to the motion of the atmosphere. The atmosphere rotates faster at lower altitudes than at higher, because of the friction against Earth. A general expression for the relative motion would be ⎡dx ⎤ + ω y ⎢ dt Earth ⎥ ⎢ ⎥ v dy vrel = ⎢ −ω Earth x⎥ , (8.3.1.1-2) ⎢ dt ⎥ ⎢ dz ⎥ ⎣⎢ dt ⎦⎥

where ωEarth is the rotation of Earth around its axis. The parameter for the drag force expression most difficult to determine accurately is the density of the atmosphere. It depends on many variables and is therefore always changing: It depends, for example, on the temperature of the atmosphere and so the sun has great influence. At the illuminated side of Earth the atmosphere expands so that denser regions can be found at higher altitudes than on the dark side. There are different models, for example exponential, standard and Jacchia-Roberts, and in order to get the best results, simulations need to be performed with more than one model and then compared with one another. For an initial calculation of the orbits, however, an average value can be used. Since the satellites are flying close to each other, they are exposed to almost the same density. Most of the manoeuvres will take one orbit or more to complete, and therefore an average value will suffice. This will not be the case when designing the structure, since then the best aerodynamic properties possible are sought.

8.3.1.2 Geopotential anomaly

The gravitational field of Earth is disturbed due to the fact that the shape of Earth is not an ideal sphere, and also because its mass is not equally distributed. Models for the geopotential field including these effects are available, containing three different terms; the zonal, which depends solely on the latitude, the sectoral, depending on the longitude, and the tesseral, which depends on both. One model for the gravitational potential containing

45 only the zonal term, hence taking into account the oblateness of Earth, is expressed as follows

n μ ⎛ ∞ ⎛ R ⎞ ⎞ ⎜1−=Φ J ⎜ E ⎟ P (sinϕ)⎟ . (8.3.1.2-1) ⎜ ∑ n n ⎟ r ⎝ n=2 ⎝ r ⎠ ⎠ where μ is the gravitation of Earth, r is the distance between the centre of Earth and the satellite, Jn are the potential’s harmonic coefficients, RE is the equatorial radius of Earth, Pn are Legendre polynomials and ϕ is the latitude.

The term that is most important for low earth orbits is the J2 coefficient; it is more than two orders of magnitude larger than the other coefficients. It is therefore customary to speak about the J2–effect. It gives rise to a drift in the orbits, a secular growth of the RAAN, the mean anomaly and a rotation of the line of apsides (only of significance in elliptical orbits). It also causes oscillations of long and short periods in all the orbital elements. Below, the formulas for the secular growth of the RAAN, argument of perigee (describing the rotation of the line of apsides) and mean anomaly are given,

2 ⎛ RE ⎞ 2 −2 & J −=Ω 5.1 nJ 2 ⎜ ⎟ ()()1cos − ei (8.3.1.2-2) 2 ⎝ a ⎠

−2 & ⋅−≈Ω 1006474.2 − 2/714 ()(1cos − eia 2 ) (8.3.1.2-3) J 2

2 ⎛ RE ⎞ 2 2 −2 ω& J = 75.0 nJ 2 ⎜ ⎟ ()(+ 1sin54 − ei ) (8.3.1.2-4) 2 ⎝ a ⎠

−2 ω ⋅≈ a − 2/714 ( + 2 )(1sin541003237.1 − ei 2 ) (8.3.1.2-5) & J 2

2 3 ⎛ R ⎞ − E 2 2 2 & J += 75.0 nJnM 2 ⎜ ⎟ ()(11cos3 −− ei ). (8.3.1.2-6) 2 ⎝ a ⎠

μ n = (8.3.1.2-7) a

Here Ω& is the time derivative of RAAN in degrees per day, ω is the time derivative of J 2 & J 2 the argument of perigee in degrees per day, n is the mean orbital motion in degrees per day, RE the equatorial radius of Earth, a the semimajor axis in kilometres, i the inclination and e the eccentricity.

46 8.3.1.3 Solar pressure

The sun exerts a force on the satellite in the sun-satellite direction. This force is known as r r SP −= uApcF SR , (8.3.1.3-1)

where p is the radiation momentum flux and cR the reflectivity, A the cross section area of r the satellite exposed to the pressure and uS the unit vector in the sun-satellite direction.

The constant cR has a value between 0.0 and 2.0 depending on the reflectivity of the satellite. A value of one means that the satellite is a black body i.e. completely absorbs incoming light, 2.0 that it completely reflects incoming light and 0.0 that the satellite is translucent to the incoming light. This value can be quite hard to determine, since different materials have different values and the value might change with the temperature of the material. In addition the area exposed to the pressure changes over the orbit. The constant p depends on the distance to the sun and therefore varies over Earth’s orbit around the sun p ⋅= 1038.4 −6 N/m2 at aphelion

p ⋅= 1068.4 −6 N/m2 at perihelion. Since the force is directed from the sun, its value changes over the year and the orbit position. When the satellite enters the shadow of Earth it is zero, giving rise to disturbances in all the orbital elements. The most significant effects, however, are found in the inclination and the eccentricity. Since the effect is specific for the orbit and the time of the year, it needs to be calculated separately for each satellite. The solar pressure is of greater importance for higher orbits; at low Earth orbit altitudes it can be up to two or three orders of magnitude less than the influence from atmospheric pressure.

8.3.2 Trajectory errors

8.3.2.1 Trajectory errors originating in position measurements

From equations 8.1.3-13 to 8.1.3-15 the effects of measurement errors can be derived. An error in the position measurement can be thought of as a faulty value of the initial value in the equation. Therefore, a measurement error of Δxm will only lead to a trajectory error of Δxm, while in the y-direction a measurement error of Δym will lead to a trajectory error of

t)( Δ=Δ m cos(ωtyy ). (8.3.2.1-1)

Finally for a measurement error, Δzm, in the z-direction,

t)( 6 m (ω −Δ=Δ sin(ωttzx )) (8.3.2.1-2)

t)( zz m (−Δ=Δ cos34 (ωt)). (8.3.2.1-3)

47 8.3.2.2 Trajectory errors originating in velocity measurements

The same approach can be used for the velocity measurements as for the position measurements. The faulty value is introduced in equations 8.1.3-13 to 8.1.3-15, and then the effect on the trajectory is found. An error in the velocity vector, Δvxm, in the x-direction leads to the trajectory error ⎛ 4 ⎞ t)( Δ=Δ vx xm ⎜ ()ω − 3sin tt ⎟ (8.3.2.2-1) ⎝ω ⎠ 2 Δ=Δ (()ωtvz −1cos ). (8.3.2.2-2) t)( ω xm

An error, Δvym, in the velocity in the y-direction yields a trajectory error of 1 Δ=Δ sin()ωtvy , (8.3.2.2-3) t)( ω ym and the trajectory error for an error , Δvzm, in the velocity in the z-direction will be 2 vx (−Δ=Δ cos1 ()ωt ) (8.3.2.2-4) t)( ω zm 1 Δ=Δ sin()ωtvz . (8.3.2.2-5) t)( ω zm

8.3.2.3 Trajectory errors originating from thruster errors

The thrust is applied as force divided by mass in equations 8.1.3-13 to 8.1.3-15, so an error can occur both in the assumed thrust and the assumed mass. There is also the possibility that the thrust is applied for a longer period of time than nominal. The thrust error, Δγ, can also be expressed as a thrust error factor, εγ, the relationship between the two being

γ γ nom Δ+= γ (8.3.2.3-1)

γ = γ nomε γ (8.3.2.3-2) Δγ ε γ = , (8.3.2.3-3) γ nom with γnom as the nominal value of the thrust.

The time error can be expressed in the same manner, with tnom being the nominal time,

nom Δ+= ttt (8.3.2.3-4)

= tt ε tnom (8.3.2.3-5) Δt ε t = , (8.3.2.3-6) tnom

48 Including this in equations 8.1.3-13 to 8.1.3-15 yields the effect on the trajectory that the thrust error imposes. Thrust error in the x-direction will result in an actual trajectory of

⎛ 4 3 22 ⎞ x )( = xtact εγ γ ⎜ ()− cos1 ()tnom − tt εεω tnom ⎟ (8.3.2.3-7) ⎝ω 2 2 ⎠ 2 z = ()sin()− tt εωεωεγ , (8.3.2.3-8) tact )( ω 2 x γ tnom tnom thrust error in the y-direction amounts to 1 y = (− cos1 (t εωεγ )), (8.3.2.3-9) tact )( ω 2 y γ tnom and thrust error in the z-direction to 2 x = (t − sin(t εωεωεγ )) (8.3.2.3-10) tact )( ω 2 z γ tnom tnom 1 z = (− cos1 (t εωεγ )). (8.3.2.3-11) tact )( ω 2 z γ tnom Differentiating these equations after t, gives the error imposed on the velocities in the three directions. Thrust error in the x-direction yields ⎛ 4 ⎞ x& )( = xtact εγ γ ⎜ ()sin()tnom − 3tt εεω tnom ⎟ (8.3.2.3-12) ⎝ω ⎠ 2 z& tact )( = x γ (cos()t εωεγ tnom −1), (8.3.2.3-13) ω thrust error in the y-direction 1 y& tact )( = y γ sin(t εωεγ tnom ), (8.3.2.3-14) ω and thrust error in the z-direction 2 x& tact )( = z γ (− cos1 (t εωεγ tnom )) (8.3.2.3-15) ω 1 z& tact )( = z γ sin(t εωεγ tnom ). (8.3.2.3-16) ω

49 8.4 Orbit manoeuvres

8.4.1 Coordinate system

The same coordinate system as in 8.1 will be used throughout this chapter, see figure 8.1-1. • x-axis = movement in the orbital velocity vector • y-axis = out of plane vector • z-axis = vector pointing towards the centre of Earth

8.4.2 Velocity of satellites in orbits

The velocity of a satellite in orbit is determined using the specific mechanical energy v 2 μ ξ −= , (8.4.2-1) 2 r in the orbit. This can be solved for the velocity as

⎛ μ ⎞ v 2⎜ += ξ ⎟ . (8.4.2-2) ⎝ r ⎠ The specific mechanical energy for orbits that are not hyperbolic becomes, using the energy conservation law, μ ξ −= . (8.4.2-3) 2a This expression can be put into equation 8.4.2-2, obtaining 2 μμ v −= . (8.4.2-4) ar Using the known formula for r ()1− ea 2 r = , (8.4.2-5) + ecos1 υ and rearranging it as ()11 − e 2 = , (8.4.2-6) a (+ er cos1 υ) yields the following expression for the velocity

μ ⎛ 1− e 2 ⎞ v ⎜2 −= ⎟ . (8.4.2-7) r ⎝ + ecos1 υ ⎠

50 For a circular orbit this corresponds to μ v = . (8.4.2-8) circular r

8.4.3 Coplanar manoeuvres

Coplanar manoeuvre means that the orbit is changed in such a way that the orbital plane remains the same afterwards. This means, though, that the eccentricity, the semimajor axis and the argument of periapsis may change.

8.4.3.1 Apogee and Perigee raise manoeuvres

A tangential thrust in the velocity vector direction at perigee increases the semimajor axis, resulting in an increase of the orbit apogee. If the thrusting manoeuvre is performed at the apogee instead, the perigee will be increased.

Figure 8.4.3.1-1. Apogee and Perigee increase manoeuvres respectively. The delta-V required can be calculated from the final velocity minus the initial velocity,

final −=Δ vvv initial . (8.4.3.1-1) For an apogee increase this yields

⎛ 1212 ⎞ vvv =−=Δ μ ⎜ −−− ⎟ , (8.4.3.1-2) aRaise pp 12 ⎜ arar ⎟ ⎝ p 2 p 1 ⎠ and for a perigee increase the required delta-V will be

⎛ 1212 ⎞ vvv =−=Δ μ ⎜ −−− ⎟ . (8.4.3.1-3) pRaise aa 12 ⎜ ⎟ ⎝ a 2 a arar 1 ⎠ As can be seen from figure 8.4.3.1-1, the eccentricity increases with the apogee, and decreases with the perigee. A special case of apogee and perigee increase manoeuvres is the Hohmann transfer, where the initial and final orbits are circular. First an apogee increase is performed and when the satellite reaches the new apogee a perigee increase is performed, resulting in a new circular orbit with larger semimajor axis.

51

Figure 8.4.3.1-2. Hohmann transfer. The required delta-V for the transfer is calculated through summation of the two manoeuvres

⎛ 12 ⎞ μμ ⎛ 12 ⎞ ⎜ ⎟ ⎜ ⎟ . (8.4.3.1-4) aRaise vv pRaise μ⎜ −=Δ+Δ ⎟ μ⎜ −−+− ⎟ ⎝ 1 ⎠ 21 ⎝ 2 arrrar ⎠ There is also the possibility to thrust in the radial direction. This will increase or decrease the apogee or perigee, but without changing the semimajor axis, meaning that the orbital period is not changed.

8.4.4 Noncoplanar manoeuvres

These manoeuvres will affect the orbital plane, and therefore involves a change in the inclination and/or the right ascension of the ascending node. The thrust must be applied perpendicular to the motion in the plane; otherwise a change in the semimajor axis and/or eccentricity will occur as well. Pure noncoplanar changes, however, are quite fuel consuming so they are in most cases combined with in-plane changes. These types of manoeuvres are needed mainly for correction of orbit insertion errors and for compensating the J2-drift of nodes.

8.4.4.1 Inclination change

The change of inclination has to occur in either the ascending or the descending node, since the point where the manoeuvre takes place will be a part of the new orbit. No change of the other orbital elements occurs during a pure change of inclination. The delta-V required for a pure change of inclination can be calculated from

⎛ Δi ⎞ ΔviOnly sin⎜ ⎟ = , (8.4.4.1-1) ⎝ ⎠ vinitial cos22 φ fpa ⎛ Δi ⎞ iOnly =Δ vv initial φ fpa sincos2 ⎜ ⎟ . (8.4.4.1-2) ⎝ 2 ⎠ As can be seen in equation 8.4.4.1-1, for an elliptical orbit the delta-V needed is higher in either the ascending or descending node. This needs to be taken into account when choosing where to perform the manoeuvre, since noncoplanar orbit changes are ‘expensive’ regarding needed fuel.

52 8.4.4.2 Change of the right ascension of the ascending node

The change in the RAAN must take place in the middle of the arc between the two nodes since no change in inclination is desired. For an elliptical orbit a pure change of RAAN will include more than one burn. For a circular orbit the delta-V can be described as ⎛ϑ ⎞ vRAANonly =Δ cos2 ϑvinitial sin⎜ ⎟ , (8.4.4.2-1) ⎝ 2 ⎠ using

2 2 ϑ = coscos initial + sin ii initial cos(ΔΩ). (8.4.4.2-2)

8.4.4.3 Combined inclination and RAAN change

The formula for a combined inclination and RAAN change is ⎛ϑ ⎞ &iRAAN =Δ vv initial sin2 ⎜ ⎟ , (8.4.4.2-3) ⎝ 2 ⎠ with

ϑ = initial coscoscos final + initial iiii final cossinsin (ΔΩ) (8.4.4.2-4)

8.4.5 Combined coplanar and noncoplanar manoeuvres

Since noncoplanar manoeuvres are costly, they are most often combined with coplanar manoeuvres. The resulting delta-V can be obtained from the cosine law as

2 2 tot initial final −+=Δ 2 initial vvvvv final cosϕ (8.4.5-1) where φ is the angle between the velocity vectors.

8.4.6 Continuous thrust manoeuvres

Thrust is actually not applied instantaneously, but under some period of time. In the following examples Hill’s coordinate frame and equations of motion will be used.

8.4.6.1 Motion in the x-direction

In order to achieve motion in the x-direction of a remote-satellite with respect to the centre- satellite, an initiation thrust is first applied in the x-direction. Then the motion is controlled in the z-direction to attain the desired x-direction, and finally a counter-thrust is applied in the negative x-direction in order to stop the motion. In other words, a velocity, Vx, results in the x-direction between t0 and t1, corresponding to x0 and x1.

53 The equation of motion in the x-direction becomes

+= dtvxx . (8.4.6.1-1) t 0)( ∫ tx )(

The force per mass unit, γx,y,z, that has to be applied in order to keep the motion restricted to the x-direction can be calculated from the equations of motion, equations 8.1.1-26 to 8.1.1-28. The delta-V needed for this manoeuvre can be calculated as

t1 t1 t1 vtot =Δ x )( d + y )( d + z )( dτγτγτγ . (8.4.6.1-2) t τ t τ ∫∫∫ t τ 0 0 0

8.4.6.1.1 Example

As an illustration, the case with initial conditions

= & = vxXx x )0(000

00 = & zyzy &00 = γγ yx = 0,0,0, will now be discussed. The equation of motion in the x-direction becomes

+= dtvXx . (8.4.6.1.1-1) t 0)( ∫ tx )( Inserting the initial conditions into Hill’s equations yields an expression for the force per mass unit

γ tz )( = 2ωv tx )( . (8.4.6.1.1-2) The total delta-V that is needed for this manoeuvre is

t1 vtot =Δ z )( dτγ . (8.4.6.1.1-3) ∫t τ 0

Figure 8.4.6.1.1-1. Movement of remote satellite in the x-direction.

54 8.4.6.2 Motion in the z-direction

In order to move a remote-satellite relative to the centre-satellite in the z-direction, a thrust is exerted in the z-direction to initiate the movement. After this the motion needs to be controlled in both the x- and z-direction in order to keep the satellite moving in the z- direction, and in the end a thrust is applied in the negative z-direction to stop the motion. A velocity, Vz, is achieved in the z-direction between t0 to t1, corresponding to z0 and z1. In the z-direction the equation of motion will be

+= dtvzz . (8.4.6.2-1) t 0)( ∫ tz )(

The force per mass unit, γx,y,z, that has to be applied to keep the motion restricted to the z- direction can be calculated from the equations of motion, equations 8.1.1-26 to 8.1.1-28. The delta-V needed for this manoeuvre can then be calculated as

t1 t1 t1 vtot =Δ x )( d + y )( d + z )( dτγτγτγ . (8.4.6.2-2) t τ t τ ∫∫∫ t τ 0 0 0

8.4.6.2.1 Example

As an illustration, the case with initial conditions

00 = yxyx && 00 = 0,0,

= & = vzZz z )0(000 γ y = 0 will be discussed. The equation of motion for z becomes

+= dtvZz . (8.4.6.2.1-1) t ∫ tz )(0)( Inserting the initial conditions into Hill’s equations yields an expression for the force per mass unit

γ tx )( −= 2ωv tz )( (8.4.6.2.1-2)

2 tz )( −= 3ωγ ( tz + Ztv 0)( ). (8.4.6.2.1-3) The total delta-V that is needed for this manoeuvre is then

t1 t1 vtot =Δ x )( d + z )( dτγτγ . (8.4.6.2.1-4) t τ ∫∫ t τ 0 0

55

Figure 8.4.6.2.1-1. Movement of remote satellite in the z-direction.

8.4.7 Obtaining the desired relative distance

Satellites in orbits with different altitudes but the same inclination have different velocities, and thus a relative movement. This can be used if the satellites in the formation become separated too far, i.e. at launch. Since the satellites are at different altitudes this is a safe method for attaining the desired relative distance.

8.5 Simulation

The different stages of the mission need different types of control loops and will therefore have to be simulated separately. Dividing it into phases: • Separation from launch vehicle • Detumbling Determine how long it will take to detumble the satellites using the Attitude Control System. If possible, align the satellites in a loose leader-follower formation, and from that bring them to the circular/projected circular formation. • Initial checkout, Station-keeping • Formation initialization The main phase after release from the launcher is the initialization of the circular/projected circular formation. In the beginning only three of the satellites will be active in the formation. The fourth will be set to trail them. The initial orbits will have an altitude of ~400 km and an inclination of 69 degrees (Sea launch). The satellites do not have a formation programmed that they have to achieve at any cost; rather the orbits of the satellites after the detumbling will determine the formation. Calculating the desired orbit of the ‘centre’ satellite from the actual positions of the satellites is the first step. Then the orbits of the other satellites can be derived from the relative distances given by the mission requirements.

56 The initialization needs to be propagated first in the Hill’s frame in order to yield the reference orbits, which then will be propagated in the real frame, taking the perturbing effects into account. A control loop will be added for performing the changes in the most propulsion cost-efficient way. The delta-V for these orbital changes needs to be calculated as well as the number of orbits needed for obtaining the formation. Also, a thorough investigation of the effects of errors in the attitude determination system on the orbits is needed. In addition an estimation of the model of the perturbing forces is required, as well as the effects on the orbit not included in the simulation. Deliverables: • Script for calculating the reference orbits • Script for propagation in real frame • Control loop • Delta-V used • Number of orbits needed to perform the initialization • Measurement of error tolerance • Error in position due to propagation errors • Formation flight (three satellites) The second main phase is the first period of data acquisition for the payloads. First derive the reference orbits and propagate the orbits with perturbations. This has to be done first in the Hill’s frame in order to achieve the desired orbits, but also in the real frame to see how the perturbations will affect the orbits and the kind of counteractions to perform. A control loop has to be added that takes care of the orbit differences caused by the perturbations. The delta-V needed for maintaining the formation has to be calculated, as well as the time available until fuel is exhausted. Deliverables: • Script for calculating the reference orbits • Script for propagation in real frame • Control loop • Delta-V used • Measurement error tolerance • Error in position due to propagation errors • Manoeuvres The third main phase comprises the insertion of the fourth satellite into the formation. The fourth satellite should be manoeuvred into the formation, under the condition that the other three satellites also undergo position changes, thus minimizing fuel consumption and obtaining the predetermined relative distances. Derive the reference orbit changes needed in order to perform the manoeuvres as well as propagating the orbits and applying a control loop. Here the orbital changes need to be

57 propagated both in the Hill’s and the real frame in order take the perturbations into account. Calculate the delta-V needed. Deliverables: • Script for calculating the reference orbits • Script for propagation in real frame • Control loop • Delta-V used • Number of orbits needed to perform the initialization of the fourth satellite • Measurement error tolerance • Error in position due to propagation errors • Formation flight (four satellites) The fourth main phase is the second period of data acquisition of the payload. This time all four satellites will be active acquiring the data. Develop the control for formation keeping of all four satellites, building on the formation flying control loop for three satellites. Use the same type of reference orbits and propagation. Deliverables: • Script for calculating the reference orbits • Script for propagation in real frame • Control loop • Delta-V used • Measurement error tolerance • Error in position due to propagation errors • End-of -Life The fifth main phase is possible if there is propulsion left. Then experiments altering the relative distances and performing further data acquisition from all four satellites can be performed. Derive the orbit manoeuvres required for changing the relative distances of the four satellites, both in the Hill’s and the real frame. Use the model for the initialization manoeuvres for the fourth satellite. Calculate the delta-V needed.

58 Deliverables: • Script for calculating the reference orbits • Script for propagation in real frame • Control loop • Delta-V used • Number of orbits needed to perform the relative distance changes • Measurement error tolerance • Error in position due to propagation errors

8.6 Reports from the simulation program

The many results from the simulations need to be well documented. Some of the important parameters that can be obtained from the simulations will be: • Access report from ground-station(s) • Time in daylight • Illumination of the solar panels, power generation of the solar cells • Delta V calculation • Video for presentations

8.7 Documents required from the launcher

The launcher requires the following documents from the orbit simulations: • Parameters of the initial orbit in the injection point: inclination, apogee and perigee altitude with respect to earth mean radius (Rm = 6,371 km), argument of perigee latitude, ascending node longitude; • Injection accuracy requirements; • Spacecraft injection time constraints;

59

60 9 Radiation analysis

The team had not come in contact with SPENVIS, so a short description was produced. The decision of which program to use will be made by the persons in charge of the radiation analysis.

9.1 SPENVIS

SPENVIS stands for SPace ENVironment Information System. It is a www-based program that performs radiation analyses. It consists of nine packages, some made at ESA and ESTEC and also packages made by other agencies. The program can make a rather complete analysis of the environment surrounding the satellite. It also produces graphs and tables that can be used in reports. The nine packages include:

Coordinate generators Two generators are used, one for orbit generation and one for coordinate grid generation. Most of the different models used by the program require input generated in this package. The coordinates only have to be generated once and can then be used throughout the whole project.

Radiation sources and effects Trapped particles (included is a model for the anisotropy of trapped protons in lower altitudes) can be estimated together with solar protons during the mission for various mission segments. The damage of solar cells due to electron fluencies, the ionizing dose for various types of shielding, proton fluencies and non-ionizing energy for device degradation and LET spectra of cosmic ray particles for estimation of SEU-rates can also be calculated. There is also a tool for calculating effects on the shell of the satellite, which may be used for shielding distribution, and a tool for simulating the radiation transport through Multi-Layered Shielding.

Spacecraft charging DICTAT can be used to predict if there is a risk of electromagnetic discharges in a dielectric material. Three modules of ESPIRE are available, one for calculating the equilibrium potential, one for current collection and power loss of a solar array in LEO, and one for determination of various parameters affecting the LEO and PEO satellites.

Atmosphere and ionosphere Several atmospheric and ionospheric models can be used for finding the densities and temperatures at defined points and/or the densities and particle fluxes over the satellite orbit.

Magnetic field Various magnetic field models can be used to calculate parameters for orbits and for a specified set of points.

Meteoroids and debris NASA90 and ORIEN96 are models for orbital debris, as well as the Grün model for meteoroids. Wall penetration models are also included in the package.

61 Data base queries The in-flight data of several flown and flying missions are accessible.

ECSS space environment standard A copy of the standards for space environment from the European Cooperation for Space Standardization.

Miscellaneous The program includes a visualization of magnetic drift shells, electromagnetic radiation calculation on satellite surface, trapped particle models implemented on magnetic coordinate grids and coordinate transformations calculation and visualization.

62 10 Discussion

10.1 Propulsion

Two types of propulsion are discussed for the mission, one for the station-keeping and one for the formation-keeping. For the station-keeping the MEMS-thrusters will suffice. Staff from CLS3 will perform further investigation of the different options.

10.2 Power

It has been suggested that using fuel cells for powering the satellites will be a cost effective solution. This will depend on whether the mass of the fuel cells will be lower than that of the batteries and solar cells or, if the cells are heavier, if the cost of the fuel cells is lower than the launch cost of the extra weight. If the mission time is short enough the idea might be feasible. Further calculations as to the mission duration that would make the fuel cells a more cost effective option will be done at CLS3.

10.3 GNC

Hill’s equations are, as mentioned earlier, developed for docking of spacecraft and therefore not viable for longer missions. Most controllers are, however, based on these equations, so it is of great importance to understand them in full in order to evaluate the controllers. At the outset the orbit and control simulations were done by the team members. The simulation tool used was that of Princeton Satellite Systems. It was not powerful enough for extensive simulations, so collaboration with a Russian company was initiated. With their tool THEONA they would be able to do very extensive simulations for all the different phases of the mission. The literature referenced for this work included different control approaches, some on high- level control and some on low level control taking into regard saving fuel and/or time (summarized in Appendix 12.4). The research in this area is not extensive, and no circular/projected circular formation has yet been flown. In order to be able to determine the approaches most viable in the sense that they would be ready to be used within the desired timeframe of the project, collaboration with experts in Control Theory was initiated. The articles that the GNC-group of CLS3 found the most interesting were further investigated.

10.4 Thermal

The thermal testing and design will be delegated to a collaborating organisation, but investigations concerning the different methods for thermal control will be done within the company. Research on thermal paint has also been discussed with an external organisation.

63 10.5 Radiation analysis

A very thorough analysis of the radiation environment will have to be performed. This analysis will determine how much protection the MEMS-components needs, since the MEMS-devices are very sensitive to radiation degradation and SEUs. The low earth orbit and the relatively short mission duration, makes probable that radiation will not be an issue for other components.

10.6 Launch

Three launch options were under discussion. The first was inexpensive, but it was a shared launch and therefore altitude and inclination was already defined. The second and third was with another launch company, and would be more expensive. In return there was a window for altitude and inclination. There was further the possibility to share the launch as the primary mission. The second and third alternatives were within budget if the individual satellite masses could be kept around eight kilograms. If the total mass was higher than 40 kilograms the price increased rather drastically, since the launch could not be shared.

10.7 Over-all project

The efforts in the US concerning formation flight missions have been assigned to Universities and to different organizations related to the Department of Defence. University research often requires more time to develop new technologies, since students are involved only for short periods in the different projects. Every new research team has had their own view and much time is spent rearranging goals and strategies. In the wake of the discontinued TechSat21 mission, different companies and organizations have been interested in taking over and pushing it into the commercial sector. This would speed up progress and would bring new technologies to commercial breakthrough. CLS3 is a very ambitious small company with many contacts in well-established companies and organizations, and with the aid of CANEUS the project may become real. The project is in line with the general thinking concerning future satellite missions, in particular reduced cost and mass. It is very important that every aspect of groundbreaking ways of realizing satellite missions is thoroughly explored. If the market identifies affordable means of using Space, the industry will grow and new innovations and technologies for new applications evolve.

64 11 Future work

11.1 Time plan

The time schedule of the launching company regarding deliverables and documentation was used as a base for the time plan for CLS3’s project. The target was to launch the cluster in November 2005. The very tight schedule was justified by the fact that COTS-products and systems are to be used and that the whole project would be a joint effort between organizations from North America and Europe. This would be made possible by involving the CANEUS network. CLS3 would function as the ‘spider in the web’, keeping track of the project and being responsible for arranging the financing, as well as being in charge of the GNC-system. The time schedule below is preliminary and quite optimistic, but it offers a guideline as to the time available before launch. It is of greatest importance that the members of this collaboration are aware of the immense work that needs to be done. On the other hand the benefit would be that a functioning cluster would be the first on the market, thus having the chance of being used for profitable missions within the next few years.

65 Figure 11.1-1. The time schedule for the entire project.

66

Appendices

67

68

Appendix A Satellite Data

69 A.1 Constella (microsat) University of Surrey Platform

Length: 1 m Width: 1 m Height: 0.6 m Shape: pyramidal Weight: 70 to 140 kg Design life: 7 years, fuel for 10 years.

Mechanical/Structural subsystem: Standard trays or ad-hoc for the payload. Attitude and Orbit control subsystem: Designed for LEO. 3-Axis stabilized with momentum bias and pointing to nadir. Has three EarthHorizon sensors, two 3-axis magnetometers. Optional are GPS, Star camera, gyros or Sun sensors. Uses two momentum wheels and six torque coils. Reaction wheels are optional. Propulsion subsystem: N2 cold gas propulsion, 0.1 N. Power subsystem: 4 body mounted panels, either 70 W Si (peak 100 W) or 100 W GaAs (peak 140 W). NiCd battery of 200 Wh, for 14 V/28 V. Unregulated 14/28 V bus or a regulated 5 V bus goes to the payload. Thermal control subsystem: N.A. Telecommand and Telemetry: Hot redundant uplink, S-band Rx. Cold redundant downlink, S-band 0.1-4 W. Data handling: Onboard processor is an 80386EX. Can reload software and be reprogrammed in orbit. Homepage: http://centaur.sstl.co.uk/datasheets/Constella.pdf

70 A.2 Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions, DEMETER (microsat) CNES, ESTEC.

Length: 0.6 m Width: 0.6 m Height: 0.8 m Shape: block Weight: 120 kg Design life: 2 years. To be launched in 2004, from Baikonur with a converted SS-18 intercontinental ballistic missile.

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: LEO, 800 km polar orbit. Star sensor, gyros and reaction wheels. Propulsion subsystem: Hydrazine system. Power subsystem: GaAs cells on 2 deployable panels. Has a LiIon battery. Thermal control subsystem: Thermal control coating, THERME. Telecommand and Telemetry: Uses the S-band for transmissions. Maximum telemetry rate is 25 kbps. Data handling: A 10 MIPS microprocessor T805 is used as onboard computer. Also has Data Remote Processing PC (DRPPC). Payload: Earth observation satellite with the following instruments onboard: Electric sensors (ICE), magnetic sensors (IMSC), a plasma analyser (IAP), a Langmuir probe (ISL) and a particle detector (IDP). Homepage: http://smsc.cnes.fr/DEMETER/index.htm

71 A.3 DLR-TUBSAT (microsat) DLR

Length: 32 cm Width: 32 cm Height: 32 cm Shape: cubic Weight: 44.8 kg Design life: Launched with PSLV (2) on May 26th 1999.

Mechanical/Structural subsystem: Four compartments made of Aluminium. Attitude and Orbit control subsystem: Sun synchronous orbit, at 720 km with an inclination of 98 degrees. Three reaction wheels and three fibre optic laser gyros onboard for attitude control. Whithout ground station contact the satellite tumbles freely in order to receive sunlight on all solar panels. Propulsion subsystem: No propulsion. Power subsystem: Four NiH2 battery cells (Eagle-Picher) along with four solar panels that have a single string of 34 Si cells each. Thermal control subsystem: N.A. Telecommand and Telemetry: Satellite Control Centre (SCC), a transceiver unit in the VHF/UHF-band and a cross yagi antenna. Data handling: N.A. Payload: Earth observation satellite that has TV cameras onboard. Has two fore field cameras and a high resolution telescope. Homepage: http://www.ilr.tu-berlin.de/RFA/index.htm

72 A.4 Federation Satellite, FedSat (microsat) AUSPACE, Cooperative Research Centre for Satellite Systems (CRCSS)

Length: 50 cm Width: 50 cm Height: 50 cm Shape: cubic Weight: 58 kg Design life: 3 years. Launched with NASDA’s HII-A-202 on December 14th 2002.

Mechanical/Structural subsystem: The payload is accommodated on a platform based on the Space Innovation Limited MicroSILTM satellite bus. The payload shelf consists of two panels, one interfacing the subsystems and the other is for the payload itself. Attitude and Orbit control subsystem: LEO at 800 km with an inclination of 98.7 degrees. Uses a SIL Attitude control system, consisting of three magnetotorquers, MTR-25, (a NewMag 3-axis fluxgate magnetometer placed at the end of a 2.5 m long boom, four reaction wheels and three 2-axis digital sensors, ISS-256) and SACE-MDS Spacecraft Attitude Control Electronics. Propulsion subsystem: The momentum wheels, i.e. the magnetotorquers and the gyros, adjust the position. Power subsystem: NC4-2X8 NiCad battery with 16 cells provides a battery voltage of 20 V with a capacity of 4 Ahr. The battery is used along with a PCS28R-30 power conditioning system. 19.2 % efficiency GaAs/Ge solar cells are mounted on four sides. The cells produce 0.770 V each at EOL, and each string contains 28 cells. The 18 strings produce 29.26 V as total voltage and over 52 W at EOL. Thermal control subsystem: All subsystems are coated with a matte, black, non-conductive paint. The thermal coupling between the subsystems is through the mechanical interface and radiation. Telecommand and Telemetry: Uses the SIL S-band communications unit onboard, and the low cost SIL SGS-2.4 ground station. Uplink between 2925 to 2110 MHz and a downlink between 2200 to 2290 MHz. The redundant communication system onboard has been removed and instead the payload experiments in the UHF and Ka-band have been inserted in order to increase the experimental value and to minimize the weight of the communication subsystem. CCSDS/ESA chosen as communication system, since many ground stations use it worldwide. Data handling: Experimental onboard computer, with possibility for changing physical circuits via software control, the first in its kind. The groundstation is located in Adelaide, at the University of South Australia. Uses multi-channel signal analysis. DHS-848 is the Data Handling System used onboard, based around the INMOS T-80S transputer. A General Purpose InterFace, GPIF, provides serial data TC and TM collection to and from the payloads and subsystems, it also provides TTC.B.01 and RS422.

73 Payload: GPS receiver, NewMag, High performance computer, Ka-band transponder, Baseband processor, UHF Data Transfer system, a high efficiency solar cell experiment and a CD-ROM with a message from the Australian public. The experimental high efficiency solar panel is not a part of the satellite’s power subsystem. Homepage: http://www.auspace.com.au/projects/fedsat.htm http://www.crcss.csiro.au/fedsat/default.htm http://www.sdl.usu.edu/conferences/smallsat/proceedings/12/ssc98/6/sscvi2.pdf

74 A.5 French Brazilian Microsatellite, FBM (microsat) CNES, INPE

Length: 0.6 m Width: 0.6 m Height: 0.8 m Shape: box Weight: 100 kg Design life: 13 months Built on the MYRIADE platform, see that page for more details on the structure.

Mechanical/Structural subsystem: Using an already existing microsatellite platform. Attitude and Orbit control subsystem: LEO at 750 km at an inclination of 6 degrees. Has a Sun pointing payload. Uses a star sensor, gyros and reaction wheels for controlling the position. Propulsion subsystem: A hydrazine system. Power subsystem: N.A. Thermal control subsystem: N.A. Telecommand and Telemetry: Uses CCSDS standard. Data handling: Uses a 10 MIPS microprocessor T805 as onboard computer. Payload: CHADOCC, Capillarity diphasic ammonia loop heat pipe and mechanical pumped thermal technological experiments. DEBRIS, measurement of the dust environment distribution in the environment conditions. THERME, Evaluation of material degradations function of the environment conditions. MAGI, technical evaluation of an interferometric gyro. PDP, plasma diagnostics package in the case used for the ionosphere and thermosphere. CPL, Capillary pumped loop. CBEMG, confined boiling experiment under microgravity. FLUXRAD, radiometer/fluximeter for measuring the net flux from the Sun and space to the satellite. Homepage: http://smsc.cnes.fr/FBM/index.htm

MYRIADE homepage: http://smsc.cnes.fr/SAP-MYRIADE/

75 A.6 KITSAT-3 (microsat) Satellite Technology Research Center (SaTReC), Korea Advanced Institute of Science and Technology (KAIST) (KITSAT-1 Aug 1995, KITSAT-2 Jan 1996, KITSAT-4 2005)

Length: 495 mm Width: 604 mm Height: 852 mm Shape: box Weight: 110 kg Design life: Launched with PSLV C2 on May 26th 1999.

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: Sun-synchronous LEO of 720 km with an inclination of 98.37 degrees. 3-axis stabilized. Uses 3- axis magnetometer, 2-axis sun sensor, 2-axis horizon sensor, 3-axis magnetotorquer, GPS receiver, Star sensor, 3-axis fibre optic gyro and 3-axis reaction wheel. Propulsion subsystem: No propulsion onboard. Power subsystem: NiCad batteries. Thermal control subsystem: Thermo-optical properties of satellite structure and thermal coating materials. Telecommand and Telemetry: Uplink on 148 MHz and downlink on 401 MHz, 2.2 GHz and 8.2 GHz. Data handling: Main computer onboard KASCOM (80960). Payload: MEIS, Multispectral Earth Imaging System with linear pushbroom CCD camera. SENSE Space ENvironment Scientific Experiment with HEPT-High Energy Particle Telescope, REME- Radiation Effect on Micro-Electronics, ETP-Electron Temperature Probe, SMAG-Scientific MAGnetometer. Homepage: http://satrec.kaist.ac.kr/english/res_kitsat3.html http://hklee.kaist.ac.kr/publications/hyungshin.pdf

76 A.7 Leonid Meteor Satellite, LMS (microsat) University of Tohoku

Length: 50 cm Width: 50 cm Height: 50 cm Shape: cubic Weight: 50 kg Design life: 1 week Launched 2001.

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: LEO of 300 km with an inclination of 35-40 degrees. High precision in the attitude determination is not necessary, what is important is stability. 3-axis stabilized with the payload pointing to nadir. Reaction wheels and magnetotorquers onboard. GPS is needed for determining the meteor trajectory. Propulsion subsystem: Propulsion might not be necessary. Power subsystem: N.A. Thermal control subsystem: N.A. Telecommand and Telemetry: VHF uplink, 9.6 kbps and S-band downlink, 38 to 96 kbps. Data handling: N.A. Payload: At least one wide-angle camera and two spectrometers. The payload will weigh between 10 to 15 kg. Intended for observing the Leonid meteor storm from space. Homepage: http://www.sdl.usu.edu/conferences/smallsat/proceedings/14/tsiv/iv-3.pdf

77 A.8 MICRO Satellite à traînée Compensée pour l’Observation du Principe d’Equivalence, MICROSCOPE (microsat) ONERA, ESA, CNES Based on the MYRIADE platform.

Length: 800 mm Width: 700 mm Height: 600 mm Shape: box Weight: 120 kg Design life: 1 year To be launched in mid 2005 on a DNEPR rocket.

Mechanical/Structural subsystem: Solar panels on three sides of the satellite. Attitude and Orbit control subsystem: Circular LEO at 700 km. Three solar sensors, a 3-axis Magnetometer and one star sensor. Three magnetotorquers and three reaction wheels. Since the payload needs to be free from drag effects, an Attitude Control and Drag Compensation System is installed in the computer. Propulsion subsystem: Field Electric Emission Propulsion, FEEP. Four pods with two propulsion devices in each. Power subsystem: GaAs solar arrays with LiIon batteries. Uses a power regulation box. Thermal control subsystem: The temperature sensitive parts are placed on the side of the satellite that is pointing away from the Sun. Uses passive control with heaters and thermostats. Telecommand and Telemetry: A cold redundant transmitter is used for the downlink in the S-band. The maximum rate is 400 kb/s. A hot redundant system is used for the uplink, also in the S-band. The maximum rate of this link is 20 kb/s. CCSDS is used onboard. Data handling: The onboard computer is based on a transputer T805 and several microcontrollers of the type PIC 16C73 are used for interfacing the instruments onboard. Payload: Instruments to test the Equivalence Principle up to an accuracy of 10-15, using two electrostatic differential accelerometers. On ground the best accuracy achieved is in the order of 10-13. Because of disturbances on ground the instrument needs to be calibrated in space. Homepage: http://www.onera.fr/microscope/index.html http://www.zarm.uni-bremen.de/2forschung/gravi/research/microscope/microscope.htm http://www.aria.seas.wustl.edu/SSC01/papers/1-8.pdf MYRIADE homepage: http://smsc.cnes.fr/SAP-MYRIADE/

78 A.9 MightySat II (microsat) AFRL, DoD Platform.

Weight: 88 kg platform, 2.1 weighed 130 kg in total. Design life: MightySat 2.1 was launched with a Minotaur on July 19th 2000.

Mechanical/Structural subsystem: Composite primary structure with integral VME card cage. VME cards and rack-mounted components. Unobstructed upper deck for large payloads. No-shock paraffin wax mechanisms. Attitude and Orbit control subsystem: LEO at 556 km with an inclination of 97.6 degrees. 3-axis stabilized. Momentum wheels, star tracker and interferometric fibre optic gyro. Propulsion subsystem: Advanced pulsed plasma thrusters, PPT. Power subsystem: Has Si solar arrays, 330 W End of life performance. The main bus voltage is 20+/-6 V. Uses Solar Array Concentrator, SAC. Thermal control subsystem: Passive, cold-biased system using local radiators. Thermostatically controlled heaters. Contingency only. Telecommand and Telemetry: Has a Naval Research Laboratory Mini SGLS Transponder, NSX. Uplink of 2 kbps, downlink for data and telemetry of 1 Mbps and a telemetry only downlink of 20 kbps. Data handling: The onboard computer is a Quad-C40 processor, also onboard for evaluation. RAD6000, 20 MHz cpu and 128 Mbyte RAM. The payload has 256 Mbyte RAM. Payload: Has a Fourier Transform Hyperspectral Imager. A Quad-C40 processor is onboard to be tested of radiation tolerance. SMATTE, Shaped-Memory Alloy Thermal Tailoring Experiment consists of a composite that changes physical properties due to thermal conditions. SAFI, Solar Array Flexible Interconnect is a new type of wire, copper imbedded in flexible composite film. Orthogrid Substrate, a structural technology with better heat dissipation and lighter weight. Has two picosatellites onboard that it will release. SOR and Starfire Optical Reflectors. Homepage: http://www.spectrumastro.com/SAI_PressReleases/PR_details.cfm?PRID=25

79 A.10 MYRIADE (microsat) CNES Platform, five first missions: #1 DEMETER, #2 French Brazilian Microsatellite, #3 PICARD, #4 PARASOL, #5 MICROSCOPE

Mechanical/Structural subsystem: The platform uses a very rigid lower plate as an interface with the launcher. Included, optional, is a shock damper system. The architecture is modular with an independent propulsion module directly integrated on the lower plate. The general design concept allows the satellite to have one face in the shadow systematically. Attitude and Orbit control subsystem: Three coarse Sun sensors, 3-axis magnetometer, stellar sensor and three raw gyros. For controlling three reaction wheels, three magnetotorquers and a propulsion system are used. Propulsion subsystem: Hydrazine propulsion subsystem with four 1 N thrusters. Power subsystem: One steerable GaAs solar array, with two deployable panels. Uses an 11 Ah Li-Ion battery. Has a power regulation and distribution box. Thermal control subsystem: Depends on the different missions. Telecommand and Telemetry: Two S-band link transmitter and receiver chains, associated with two antennas. The TM data rate is 400 kbps in the operational modes and 25 kbps in safe mode. Scientific data are transmitted in the X-band while housekeeping is transmitted in the S-band. For ground control system MIcrosatellite Ground Segment, MIGS, is used. Data handling: Uses a central onboard computer with 1 Gbit memory, which is based on a transputer T805 and has several microcontrollers (PIC 16C73). Payload: Different payloads on different missions. Homepage: http://smsc.cnes.fr/SAP-MYRIADE/ http://www.aria.seas.wustl.edu/SSC01/papers/1-8.pdf

80 A.11 Near Earth Space Surveillance, NESS (microsat) CSA, Dynacon Same platform as the MOST satellite.

Length: 60 cm Width: 60 cm Height: 20 cm Shape: box Weight: 55 kg Design life: To be launched in 2005, or later.

Mechanical/Structural subsystem: A stack of milled-Aluminium trays with solar panels mounted on all six sides. Attitude and Orbit control subsystem: Flies in Sun-synchronous LEO at 900 km. Three Dynacon micro-sized reaction wheels, three MEMS solid-state angular rate sensors, two dual-wound rod magnetotorquers, two Sun sensors and a Star tracker. Star tracker software is developed by Dynacon. Propulsion subsystem: N.A. Power subsystem: NiCd battery at a bus voltage of 12-14 V. Uses Si photovoltaic cells on the solar panel. Peak power tracking is done independently for each panel. Thermal control subsystem: Passive. Telecommand and Telemetry: Redundant Uplink and downlink in the S-band, each unit has its own patch antenna. Data handling: A NEC-V53 processor board is used onboard. It is equipped with a 16 MByte RAM-disk. Payload: 15 cm aperture Maksutov-optics telescope, periscope mirror, to search for asteroids near Earth. Also has CCD cameras onboard, each CCD having a DSP-based CCD controller electronics board. A set of Fabry lenslets. A focal plane temperature control system. Homepage: http://www.dynacon.ca/pdf/files/newspdf_62.pdf http://www.dynacon.ca/pdf/files/newspdf_64.pdf http://www.cs.tcd.ie/Stephen.Farrell/ipn/background/ness_paper_2000.pdf

81 A.12 ORION (microsat) Stanford University

Length: 45 cm Width: 45 cm Height: 45 cm Shape: cubic Weight: 35 kg Design life: 1 year

Mechanical/Structural subsystem: 5052 Aluminium honeycomb panels. Natural frequency of 120 Hz. Operational temperature of – 20oC to 30oC. Attitude and Orbit control subsystem: The detumbling is made with the magnetometer and torquer coils, hence obtaining a GPS lock. The stabilization uses both GPS and thrusters. Propulsion subsystem: Twelve cold gas thrusters (GN2), four groups with three thrusters each. Can perform movement in all the three axis. Maximum thrust is ~60nN. Total predicted ΔV is ~25 m/s. Most of the parts are COTS. Power subsystem: The solar cells, GaAs, provide 18 W, time averaged. In the design phase Si was intended for the solar panels. The power is used to recharge the batteries. Thermal control subsystem: N.A. Telecommand and Telemetry: A SpaceQuest modem is used onboard, it has a half-duplex crosslink and a full-duplex downlink. The available baud rate is 9600 bps, giving a download data rate of 375 kBytes/day. Amateur bands are used for the radio communication, 2 m for uplink and 70 cm for downlink. The radios are Hamtronics FM TX/RX kits that has been modified for space utility. Has omnidirectional antennas. Data handling: A SpaceQuest CPU is used, it has a 10 MHz processor and 1 MB EDAC RAM. The operating system used comes from BekTek. The data bus is a COTS from Dallas, using the PIC board as controller. The I2C rate is 100 kbps. The science computer is a 200 MHz StrongARM embedded processor. Uses an ARM-Linux embedded operating system. Features low power consumption, natural radiation tolerance and ‘compact flesh’ mass storage. Payload: Carrier phase differential GPS for evaluation of formation flying. Different formations planned with the EMERALD satellites, which will be launched at the same time as ORION. Homepage: http://ssdl.stanford.edu/Emerald/meeting/review/quarter_two/0899_Experiment_Orion_Emerald.PDF http://ssdl.stanford.edu/aa/papers/SSDL9806.pdf http://www.stanford.edu/~masayosh/project.html

82 A.13 Ørsted Geomagnetic Research Satellite (microsat) Terma A/S, Danish Space Research Institute, Danish Meteorological Institute, ESA

Length: 68 cm Width: 35 cm Height: 45 cm Shape: box Weight: 60.7 kg Design life: 14 months Launched with a Delta-II rocket on February 23rd 1999. Still in contact as of October 2003.

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: LEO with an apogee altitude of 850 km and a perigee altitude of 450 km. The inclination is 96.1. The satellite is 3-axis stabilized. Uses GPS and magnetotorques for position adjustment. Propulsion subsystem: No propulsion Power subsystem: 1.1 m2 of the satellite body is covered with solar panels giving a maximum power of 60 W. The battery capacity is 6 Ah. Thermal control subsystem: N.A. Telecommand and Telemetry: Uplink on 2039.5 MHz and downlink on 2215 MHz. Has a mean communication time of 73 minutes per day. Data handling: N.A. Payload: Investigates Earth’s magnetic field with the help of a 3-axis CSC fluxgate magnetometer and a star imager. The experiments are placed on an eight meter long boom. Since the satellite lived longer than expected the next Ørsted satellite, which was launched in 2002, and the Argentinean satellite, SAC-C, with similar payloads can transmit data to Earth at the same time. This gives the mission a new perspective. Homepage: http://www.control.auc.dk/projects/satellites/orsted.html http://www.rummet.dk/2e000c

83 A.14 PICARD (microsat) CNES Built on the MYRIADE platform

Shape: box Weight: 110 kg Design life: minimum of 2 years To be launched in 2007.

Mechanical/Structural subsystem: See classification MYRIADE for details. Attitude and Orbit control subsystem: Sun-synchronous LEO at 730-750 km. Will use GPS for determination along with the MYRIADE standard (See classification MYRIADE for more details). Propulsion subsystem: Propulsion system from JPL. Power subsystem: See classification MYRIADE for details. Thermal control subsystem: Single monolithic Carbon-Carbon structure linking the SiC mirrors of the telescope to the detector. Telecommand and Telemetry: TM rate of 2.1 Gbit/day. (See classification MYRIADE for more details) Data handling: See classification MYRIADE for details. Payload: The payload mass is 40 kg. It includes: SODISM - SOlar Diameter Imager and Surface Mapper, an imaging telescope and a CCD for measuring the solar diameter and shape, and performing helioseismologic observations for further studies of the solar interior. SOVAP – SOlar VAriability Picard, a differential radiometer for measuring the total solar irradiance, PREMOS – PREcision Monitor for OScillation measurement, three UV photometers for studying the ozone formation and destruction along with helioseismologic observations. Homepage: http://smsc.cnes.fr/PICARD/

84 A.15 PRoject for On-Board Autonomy, PROBA (microsat) ESA

Length: 60 cm Width: 60 cm Height: 80 cm Shape: box Weight: 96 kg Design life: 1 year Launched with Antrix/ISRO PSLV-C3 on October 22nd 2001, still functioning as of October 2003.

Mechanical/Structural subsystem: Aluminium honeycomb structure. Attitude and Orbit control subsystem: Sun-synchronous LEO with an apogee of 681 km and a perigee of 561 km. The inclination is 97.9 degrees. 3-axis stabilized by four miniaturized reaction wheels. Has a two-headed star tracker and a GPS sensor. Propulsion subsystem: No propulsion onboard. Power subsystem: Has GaAs solar panels mounted on five sides of the structure, with a peak power of 120 W and 17 W in the safe mode. Has a Li-Ion battery of 9 Ah supplying a 28 Vdc power bus. Thermal control subsystem: Uses passive thermal control. Telecommand and Telemetry: S-band downlink with a data rate of 1 Mbps and S-band uplink with 4 kbps. Data handling: Has an ERC-32 (SPARC V7) processor onboard, >80 krad, 10 MIPS, 2 MFLOPS. Also a TCS 21020 digital signal processor, >100 krad, 10 MIPS, 45 MFLOPS and 12 other processors for the different subsystems/payloads are present. The operating system, Vx Works is COTS. The data storage capability is 1.2 GBit. Payload: Various technological systems are being tested; the SPARC, the star tracker, the Vx Works programme, the Li-Ion battery. The satellite is also made as autonomous as possible. The scientific payloads are: CHRIS – Compact High Resolution Imaging Spectrometer. HRC – High Resolution Camera, a black and white camera with a miniaturised Cassegrain telescope. WAC – Wide Angle Camera. SREM – Space Radiation Environment Monitor. DEBIE – DEBris In-orbit Evaluator. SIPs – Smart Instrument Points, measure total radiation doses and temperature around the satellite. MRM – Miniaturised Radiation Monitor, new method using quartz scintigraphy, the measurements are compared to the SREM measurements. PASS – Payload Autonomous Star Sensor. Homepage: http://www.esa.int/export/esaMI/Proba_web_site/index.html http://www.iaanet.org/symp/berlin/IAA-B4-0303.pdf

85 A.16 RØMER (microsat) Danish Space Research Institute, Terma A/S along with other Danish companies and Research Institutes.

Length: 60 cm Width: 60 cm Height: 85 cm Shape: box Weight: 85 kg Design life: To be launched with a Soyuz rocket in 2006.

Mechanical/Structural subsystem: The electronics rack includes thick Aluminium. Attitude and Orbit control subsystem: To be flown in a Molniya orbit, will be in contact with Denmark for 19 h/day. It has mini-reaction wheels in a tetrahedral configuration. Precision attitude determination is performed by the forward or aft looking Star tracker, while a vector magnetometer and solar aspect sensors provide coarse attitude determination. Three orthogonal magnetotorquers onboard, Four rate sensors based on solid gyros integrated with the reaction wheels for improving fine pointing performance. Propulsion subsystem: No propulsion onboard. Power subsystem: The solar panels, based on Advanced Triple Junction (ATJ) InGaP2/GaAs/Ge, will exceed 98 W at EOL. Li-Ion battery composed of three strings, each having seven cells of 1.5 Ah capacity. Thermal control subsystem: The radiator of the MONS telescope maintains a temperature of ~180 K. This is enough to cool the telescopes Focal Plane Electronics and to keep the temperature of this assembly stable. The Star tracker’s radiators are operating around 270 K, which is also suitable for the camera head units in the Star tracker. Telecommand and Telemetry: Single S-band transceiver connected to two antennas. The telemetry downlink has a channel data rate of 500 bps, information data rate of 219 bps giving a total data capacity of 2 Mbytes/24h. The telecommand uplink has a data rate of 500 bps in the apogee and 4000 bps when the satellite is closest to the ground station. Data handling: Input data rates: CAN, STR CHV, IO IRQ. Memory capacity: Bootstrap, Program storage, Program execution. Interfaces: CAN, STR CHV (1), STR CHV (2), Timing correlation Pulse (RS 422), External Event Input 3pcs, Debug. Radiation tolerance: TID, LET, SEL. Payload: MONS – Measuring Oscillations in Nearby Stars, 25 near stars are to be investigated, regarding interior structure and rotation. Onboard is one telescope, 1 field monitor and two smaller star cameras. It will also look for planets around these stars. Homepage: http://www.rummet.dk/2d000c

86 A.17 TechSat-21 flight experiment (microsat) AFRL Three satellites launched by AFRL to validate techniques that are to be used on the actual TechSat-21 mission.

Length: 1.12 m (7.76 m in orbit) Width: 1.08 m (2.26 m in orbit) Height: 0.79 m Shape: box Weight: 150 kg Design life: 1 year Discontinued.

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: LEO of 550 km. 3-axis stabilized. The ADAC system developed by Advanced Solutions Inc. Has one 3-axis magnetometer, three 4-head analog sun sensors, and one startracker. The 3-axis stabilization is achieved using three 1.0 Nms reaction wheels and three magnetic torque rods. GPS is used for absolute timing to an accuracy of ±100 ns and relative timing to the accuracy of ±20 ns. GPS will also provide relative position to an accuracy of ±10 cm. This information is enhanced with onboard payload signals just before data collection to ±50 ps and ±1 cm. There will also be an ultra stable oscillator onboard each satellite giving a local time precision of ±5 ps, over the maximum signal integration time of 5 s. Propulsion subsystem: Each satellite is equipped with a Hall effect thruster. Provides 5-10 Nm thrust, 1300 s Isp and 35 % efficiency. One kg of Xenon fuel provides a delta V of 65 m/s. Power subsystem: Uses thinfilm solar arrays of Copper, Indium, Gallium and diSelenide (CIGS). Gives 900 W output at BOL, 8% efficiency. Has an eight cell Li-polymer battery, 1500 Wh (48 Ah), at 60 % dod. Average power consumption of the whole satellite is 660 W, with peak usage of 2900 W for 10 minutes. Thermal control subsystem: Telecommand and Telemetry: Alternative ways of solving the communication are looked into. In one a Ku-band intersatellite link is combined with an off-the-shelf TT&C system. In an integrated system S- and L-band receive is used along with S-band transmit and GPS receive, the intersatellite communication rate would be 128 bps, uplink at 100 kbps and downlink at 1Mbps. Data handling: Developed by BroadReach Engineering. 133 MHz Rad 750 processor with 128 MByte RAM and 256 kByte EEPROM. Uses 32-bit data transfer at 33 MHz. Average operating power of 30 W. In addition a mass memory unit of 160 GBytes, requiring 80 W.

87 Payload: Three missions: - Autonomous formation maintenance and reconfiguration of three satellites in non-linear formations. - Sparse aperture sensing for multiple missions using innovative waveforms and signal processing. - Validated simulation with performance modelling for broad range of missions and satellite configurations for supporting future system architecture trades. The formation flying: Will be deployed into an along-track formation with separation distance 5 km, verifying position to 10 m accuracy. Then the sparse aperture sensing will commence along with onboard autonomy. The distance will then be decreased to 100-500 m and then the satellites will go into an elliptical 3-D Hill configuration; after a while the separation distance is increased again. At the end of the lifetime the satellites will perform more riskful task such as autonomous formation changes and separation distances less than 100 m. The AFRL’s Distributed Architecture Simulation Laboratory (DASL) will be used for modelling and simulating various manoeuvres to be performed. It may also be used during flight, since experimental data can be added. The Sparse Aperture sensing payload: Consists of an X-band antenna on each of the satellites. It is 2.0 m2 and can be electronically steered in 2-D. It transmits 175 W of effective radiated power. Each satellite transmits a distinguishable signal, and receives both its own signal and that from the other two satellites. Homepage: http://www.interfacecontrol.com/papers/TechSat21MicroSats.pdf

88 A.18 Tsinghua-1 (microsat) Tsinghua Aerospace Technology Research Center, Tsinghua University.

Length: 330 mm Width: 330 mm Height: 640 mm Shape: Box Weight: 50 kg Design life: Launched with Kosmos-3M on June 28th 2000.

Mechanical/Structural subsystem: Solar panels on four sides of the satellite. Attitude and Orbit control subsystem: 3-axis stabilized. For stabilization the satellite uses three Reaction wheels and three gravity gradient magnetotorquers for back up. There are also sun sensors and a gravity gradient boom onboard. Propulsion subsystem: N.A. Power subsystem: Uses GaAs solar cells. Each panel gives 35 W. Has 7 Ah NiCad batteries. Thermal control subsystem: N.A. Telecommand and Telemetry: Uses a 9.6 kbps VHF uplink and a 9.6 to 76.8 kbps UHF downlink. Has three single channel receivers and two synthesized receivers, as well as two synthesized transmitters. Data handling: Two onboard computers, one primary 80C186 with 16 Mbytes and a secondary 80C386 with 128 Mbytes. Also has two T805 transputers with 32 Mbytes. Three different types of buses are present onboard, 9.6 kbps serial bus, high speed CAN bus and Ethernet bus. Payload: Earth observing satellite. Has a 50 m Multispectral imaging system, Wide band range DSP/DTE, GPS and a 3-axis stable experiment. Homepage: http://www.sdl.usu.edu/conferences/smallsat/proceedings/14/tsi/i-6.pdf

89 A.19 ASUSAT1 (nanosat) Arizona State University

Diameter: 32 cm Height: 24.5 cm Shape: 14-sided cylinder Weight: 5.8 kg Design life: 2 years Launched with 1st Air Force Orbital/Suborbital Program Space Launch Vehicle on January 26th 1999. Last contact 14 hours after launch, failure in the power subsystem made charging of the batteries impossible.

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: Perigee at 750 km and apogee at 800 km, inclination 100°. Sun-Earth sensor array along with a Gravity-gradient boom and fluid damper for stabilization, also has a GPS receiver onboard. Propulsion subsystem: No propulsion onboard. Power subsystem: NiCd batteries with a GaAs solar array. Thermal control subsystem: N.A. Telecommand and Telemetry: 436.700 MHz downlink and 145.990 MHz up-link. Data handling: An Intel 80C188EC onboard. Total memory 1M. Payload: Two Dycam cameras. Homepage: http://nasa.asu.edu/asusat/ASUSat1

90 A.20 Bitsy (nanosat) AeroAstro Platform

Length: 15 cm Width: 15 cm Height: 5 cm Shape: box Weight: 1 kg Design life: 3 months to 3 years

Mechanical/Structural subsystem: Integrated electronics with integrated solar panel. Attitude and Orbit control subsystem: 3-axis stabilized; the buyer can choose the types of sensors and actuators necessary for the mission. Spin-stabilization also available. Attitude determination using Star camera: 0.5 mrad, 2 sigma. Attitude determination using Cold-gas thrusters: 50 mrad, 2 sigma. Propulsion subsystem: Can supply cold gas thrusters if needed. Power subsystem: N.A. Thermal control subsystem: N.A. Telecommand and Telemetry: N.A. Data handling: N.A. Payload: N.A. Homepage: http://sprg.ssl.berkeley.edu/ConstellationClassMissions/fleeter.pdf

91 A.21 EMERALD (nanosat) Collaboration between Santa Clara University and Stanford University. Two satellites flying in formation.

Diameter: 29 cm Height: 45 cm Shape: hexagon. Weight: 15 kg. Design life: 6 months

Mechanical/Structural subsystem: Quarter of an inch Aluminium honeycomb. Attitude and Orbit control subsystem: 2-axis stabilized. The GPS requires a spin rate of less than 1 degree per second. LEO, 350–500 km. Inclination 45-56 degrees. Magnetic stabilization with three torque coils. Drag Panels that varies the Ballistic Coefficient. For determination: Magnetometer Honeywell HMC2003, Omni-Directional Differential Sun sensor, GPS-receiver and Rate Gyroscope. Propulsion subsystem: Colloid microthruster, JPL. Size: 10x10x20 cm, weighing 0.5 kg. Uses 4 W maximum and 0 when standing by. Has a thrust of ~0.1 mN and a specific impulse of ~1000 s. Power subsystem: 24 % effective SpectroLab 3-junction GaAs solar cell with Vicor regulators to 5 V and 12 V. 2 5- cell NiCd batteries, passive charge regulation. Thermal control subsystem: Passive control through thermal paints. Telecommand and Telemetry: 9600 baud half-duplex with Circular Polarization, SpaceQuest Modem, Hamtronics Transmitters/Receiver. 437 MHz uplink/downlink/crosslink. 145 MHz backup uplink. The command and control will be conducted via a global space operations network. A number of radio communication stations will be linked via the Internet. Data handling: SpaceQuest FCV53 Main CDH Microprocessor, BekTek SCOS, Microchip PICmicro© Microcontroller, I2C Serial Data Bus, Dallas 1-Wire Serial Telemetry/Power Switching Bus. Payload: Component characterization: GPS, Colloid micro-thruster, Radiation test bed, Distributed computing. Formation flying: On-orbit precision relative position determination, closed-loop position control with drag panels, EMERALD-ORION three body flying. The satellites will be released from the launcher stacked on top of each other. Initial tests are then made. The two satellites are separated, but a tether connects them. The instruments onboard are calibrated and further check-out of the subsystems performed. In the next phase the tether is cut and the two satellites flies in formation. In the last phase the Orion satellite launched at the same time is included in the formation. More advanced formations will be tried out, where the Orion

92 satellite will make the changes in position with regard to EMERALD, since it has a greater propulsion capability. Autonomous systems: Distributed health beacon, fleet-level commanding. Lightning and ionospheric science: VLF Lighting Science. Homepage: http://ssdl.stanford.edu/Emerald/home.html http://hubbard.engr.scu.edu/docs/thesis/2003/

93 A.22 Ionospheric Observation Nanosatellite Formation, ION-F (nanosat) Utah State University, Virginia Polytechnic Institute, University of Washington. Three Satellites, (USUSat, HokieSat, Dawgstar) separated by 2 km.

Diameter: 45 cm Height: HokieSat and Dawgstar 30 cm, USUSat 15 cm Shape: hexagon Weight: 10 kg. Design life:

Mechanical/Structural subsystem: The three satellites are stackable for launch purposes. HokieSat: Aluminium 7075-T6 in isogrid panel (2.9 kg). Dawgstar: Same as HokieSat. USUSat: Aluminium 6061-T6 made in an etched isogrid design (3.7 kg). Attitude and Orbit control subsystem: LEO, at 370 km with an inclination of 51.6 degrees. USUSat relies on differential drag for manoeuvring, changing the direction of the satellite will change the drag profile. It also has a 2-axis gimbal with permanent rare Earth magnets (Nd-Fe-B) onboard. 3-axis attitude control, requiring Sun, Earth horizon sensors and geomagnetic field measurements. This will partially be done using CMOS cameras for sun and Earth horizon measurements. Propulsion subsystem: Eight micro pulsed plasma thrusters each, fuelled by Teflon bars, on Hokiesat and Dawgstar. No propulsion onboard USUSat. Power subsystem: Uses Sanyo Cadnica model KR-1400AE, 15 cells with 1.4 Ah and 16.8 nominal voltage and a DOD of 45 %. Has 13 strings of solar cells, with 12 cells in each. Thermal control subsystem: Thermal analysis was made using I-DEAS Master Series 8. Telecommand and Telemetry: The crosslink is managed in the S-band, centre frequency of 2200 to 2290 MHz, FSK. The uplink will operate at 450 MHz, FSK. The downlink will lie between 2.2 and 2.3 GHz. All three satellites share a single frequency allocation. Data handling: The C&DH system identical for all three satellites. Four modules connected to the motherboard: The Camera board, connects to four CMOS cameras. The Telemetry board, for handling the large amounts of data that the payloads deliver. The CPU board, based on the Hitachi SH7709 microprocessor with the Wind River Systems’ VxWorks Real-time Operating System (RTOS). The IO board, handles all interfacing between subsystems.

94 Payload: Three primary objectives: Investigation of the ionospheric disturbances: Plasma Impedance Probe (PIP) onboard to measure the plasma density. GPS ionospheric scintillation. Evaluate formation flying: Trying autonomous formation changes. Hardware evaluation: Micro pulsed plasma thrusters. Gimballed magnetic attitude control. Intersatellite communication and GPS. Has cameras onboard for use in the AOC system. The three partner universities will have their own ground-station linked over the internet so that the universities can control their satellite from their own station. Homepage: http://www.aa.washington.edu/research/dawgstar/docs/aux_docs/aa-22502-doc01-1.pdf http://www.aria.seas.wustl.edu/SSC02/papers/v-4.pdf Dawg Star: http://rrsl.ee.washington.edu/Projects/NanoSat/ http://www.mae.cornell.edu/campbell/pubs/IEEE99F.pdf HokieSat: http://www.aoe.vt.edu/~hokiesat/ AOCS: http://www.aoe.vt.edu/~cdhall/papers/aas01-311.pdf

95 A.23 Magnetospheric Constellation, MC (nanosat) NASA 50 to 100 small satellites orbiting Earth at various altitudes.

Length: 0.1 m Diameter: 0.3 m Weight: 10 kg. Design life: To be launched in 2010.

Mechanical/Structural subsystem: Graphite composite, cylinder with internal ribbing and composite decks, external nanosatellite bays (Honeycomb composite decks and ribbing graphite face sheet, bays of Aluminium structure). Attitude and Orbit control subsystem: Apogee altitude 63,000 km, perigee altitude 20,000 km with an inclination of 7.5 degrees. Spin stabilized, initial spin from launch vehicle. Propulsion subsystem: Cold gas micro-thrusters. Power subsystem: 4.5 Watts continuous, generated by body mounted solar-fixed solar array. A 12 Ah LiIon battery. Thermal control subsystem: Heaters, insulation and coatings. Chemical-vapour-deposited Diamond face sheet on honeycomb core provides superior heat dissipation, moderated by blankets for eclipse period. Telecommand and Telemetry: RF transmitter of 1.5 W. Downlink in the X-band, 8470 MHz with data rate of 256 kbps, and uplink also in the X-band, 7209 MHz with data rate of 1 kbps. Data handling: Uses CCSDS for uplink/downlink protocol. Payload: The satellites will fly in the magnetospheric tail, investigating how the tail stores, transports and releases matter and energy. Homepage: http://stp.gsfc.nasa.gov/missions/mc/mc.htm

96 A.24 Mothership-Daughtership Space experiment (nanosat) Hokkaido Institute of Technology, University of Tokyo, Tokyo Institute of Technology. One mothership and two daughterships.

Weight: 3 kg

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: Three small reaction wheels onboard, developed by Hokkaido Institute of Technology (HIT). The mass of each is 150 g and the torque produced is 28gcm/2W. Propulsion subsystem: Gas jet thrusters. Six gas jet thrusters are installed on the daughtership. It operates two thrusters at the same time when it moves in the front and back directions; operates one thruster when it moves in the right and left directions. HIT developed a new electrostatic thruster that can be operated at low power. The main plasma is generated by 1.5 GHz microwave discharge (possible at low power). Total power required for the thruster system is 25 W maximum. Power subsystem: LiIon battery (383 Wh/kg) manufactured by Yardney. Voltages onboard is 5 and 12 V. Thermal control subsystem: N.A. Telecommand and Telemetry: N.A. Data handling: The onboard computer is a H8/3048 manufactured by Hitachi (used onboard the mothership). The CPU has a clock frequency of 16 MHz. Payload: The mothership is to be put in orbit and then the daughters are to undock from it. They are to stay in line of sight and transmit data from their experiments to the mother, who in turn sends the data to a ground station. The daughters are also supposed to be able to dock the mother again. The mother has a camera onboard to demonstrate an optical navigation experiment using digital image processing. It is a PRO-5 manufactured by RFSYSTEM. Homepage: Proposal: http://usss.engr.scu.edu/usss00/mothership-daughtership/Mothership-Daughtershipwp.doc Docking mechanism: http://lss.mes.titech.ac.jp/usss/USSS2001_docking.pdf

97 A.25 Munin (nanosat) Swedish Institute of Space Physics, Umeå University, Luleå University of Technology, Southwest Research Institute

Length: 213 mm Width: 213 mm Height: 218 mm Weight: 6000 grams Launched with a Delta II rocket from VAFB, California on November 21 2000. Last contact on February 12 2001. Mechanical/Structural subsystem: Has an Aluminium structure. No moving parts. Has a custom- made separation system, by the Mechanical Engineering Department of Luleå University of Technology. Attitude and Orbit control subsystem: Polar elliptic orbit, perigee 698 km and apogee 1800 km. Passive magnetic attitude control. A permanent magnet fixes the satellite to Earth’s magnetic field, making the satellite perform two revolutions per orbit. A Magnetometer determines the attitude. The ground station is the same as used for Astrid and Freja. It has been upgraded and uses three LINUX computers along with a radio transmitter, a radio receiver and a custom built modem. Propulsion subsystem: No propulsion onboard. Power subsystem: Uses Siemens PowerMax Si solar cells, has six strings with 40 cells each. One string on every side of the satellite. Has Duracell (Energizer) Li-Ion batteries of 4200 mA at a nominal voltage of 10.8 V. Thermal control subsystem: N.A. Telecommand and Telemetry: Uses a TEKK KS-1000 transceiver, transmitting at 400.55 MHz and receiving at 449.95 MHz (as on Astrid and Freja). The downlink has a data rate of about 4800 to 21600 bps. The uplink is fixed to 2400 bps, both links are FSK. Data handling: Using a Texas Instrument TMS320C50 signal processor onboard, a modified spare from the Swedish microsatellite Astrid-2. It has a 40 MHz clock frequency and 2 Mbyte RAM for payload data storage. Uses a 10-bit A/D converter to monitor the satellite status. After a manual CPU reset the contact was lost. This was probably due to boot PROM failure. Payload: Studying the northern lights (student built satellite). The experiments onboard are: A combined Electron and Ion Spectrometer built by Southwest Research Institute, a Neutral Particle Detector from the Swedish Institute of Space physics. Connectix Quickcam, supplying images of the northern lights to the www. Homepage: http://munin.irf.se http://www.iaanet.org/symp/berlin/IAA-B4-0406P.pdf http://munin.irf.se/frames/technology_index.html

98 A.26 Surrey Nanosatellite Application Platform, SNAP-1 (nanosat) Surrey Satellite Technology Limited

Diameter: 330 mm Height: 330 mm Shape: prism Weight: 6.5 kg platform, 8.3 kg for SNAP-1 Design life: 1 year Launched with a COSMOS rocket on June 28th 2000.

Mechanical/Structural subsystem: Has an expandable structure, up to three platforms can be stacked on top of each other. Compatible with Cosmos-3M, Ariane-4, Delta, EELV, Athena, Dnepr, Zenit etc. Attitude and Orbit control subsystem: LEO with 400 km perigee and 1400 km apogee. 3-axis stabilization. Has momentum wheel, sun sensor, magnetotorquers in 3 axis, GPS and a 3-axis magnetometer. The GPS is a SGR-05 receiver with 25 m lateral accuracy. Uses a Kalmanfilter for attitude estimation. Propulsion subsystem: Liquefied gas propulsion system using Butane (<3ms-1); thrust 45 mN at 0oC and 120 mN at 40oC. The specific impulse is higher than 60 s. The operating voltage is between 7 to 12 Vdc and the nominal current is 500 mA. The system measures 170 mm-sided triangular base and 100 mm height. The dry mass was 422 g while 32.6 g was the weight of the propellant. Power subsystem: Has four solar panels with eight GaAs solar cells (9.1 W peak power) each. Every panel has its own charge regulator. Uses a six cell 1.4 Ah NiCd battery with nominally 7.2 V to 9 V. Has a 5.0 V regulated bus and an 8 V (from battery) unregulated. The average power is 1 W. Thermal control subsystem: Uses passive thermal control. Telecommand and Telemetry: UHF quarter-wave diplexed monopole. S-band downlink with a bit rate of 38.4 kbps and maximum 76.8 kbps, BPSK and QPSK. VHF uplink with 9600 bps FSK. Both uplink and downlink are asynchronous. There is also a programmable synchronous downlink from 2.4 kbps to 3.6Mbps and a programmable synchronous uplink from 2.4 kbps to 2.4 Mbps. 1 Mbps Controller Area Network (CAN) is used for the TT&C network. Data handling: The onboard computer is a Strong Arm SA1100 32 bit RISC processor with SSDR. The processor clock is at 220 MHz, with 2 Mbyte FLASH memory and 3 Mbyte double bit per byte correcting. Error detection and correction is used along with a watch dog timer. A PIC RISC processor is used as an interface to the payload, with a 76.8 kbps bidirectional serial link.

99 Payload: The main objectives were: - To validate a modular COTS nanosatellite bus concept. - To validate new manufacturing techniques and technologies. - To demonstrate 3-axis attitude control, precise orbit determination via GPS and orbit manoeuvres on a sub-10kg spacecraft. An ORION GPS receiver was therefore onboard for validation. - To demonstrate rendezvous and relative orbit determination with respect to another satellite (Tsinghua-1) via differential GPS. Here the ORION GPS receiver was also used. - To demonstrate technologies and techniques for formation flying. - To image the Tsinghua-1 micro-satellite both at deployment and rendezvous. For this the satellite had four CMOS APD-cameras onboard. During the release phase the other two satellites onboard the launch vehicle, Tsinghua-1 and Nadzhda were pictured with the cameras. The satellite then went into orbit and was thoroughly checked. It then increased its orbit with 3 km in one month for a rendezvous with Tsinghua-1. Formation flight was not attained due to an initial problem with the attitude control system, causing too much fuel to be spent maintaining orbit. The greater fall ratio of SNAP-1 compared to Tsinghua-1, added to the difficulties. Instead the CMOS-cameras were pointed towards nadir and Earth-imaging began. Homepage: http://centaur.sstl.co.uk/datasheets/Platform_rapid2nano_HQ.pdf http://www.isunet.edu/other_programs/Symposium2001/Symp2001Abstracts/Richardson.html

100 A.27 Space Technology 5, ST-5 (nano/microsat) NASA New millennium programme Three satellites flying in formation.

Diameter: 54.2 cm Height: 28.6 cm Shape: octagon Weight: 19.5 kg

Mechanical/Structural subsystem: The solar arrays are body mounted. Has a graphite composite structure. Attitude and Orbit control subsystem: Geostationary orbit. The rocket will release the satellites spinning, ‘flinging’ them into orbit. Equipped with magnetometer. Propulsion subsystem: A MEMS chip for the fine-tuning of the satellite position. Power subsystem: Uses LiIon batteries. Each cell has its own control circuit. Thermal control subsystem: Uses variable emittance coatings. The coating can be set to either absorbing or reflecting/emitting heat if needed, which is done by varying the power to the coating. Telecommand and Telemetry: SatTrack will be used on ground to communicate directly to the ST5 Ground data system and Ground data network. The uplink and downlink will be in the X-band at a bitrate of 750 kbps. The transponders measure 5x5x7.5 cm and weighs less than 300 g each. Data handling: N.A. Payload: Mission to study Earth’s magnetic field, for better space weather predictions. Also evaluating the new technologies onboard. This mission will validate systems that are to be used on the Magnetospheric constellation. Homepage: http://nmp.jpl.nasa.gov/st5/index.html

101 A.28 Three Corner Satellite, 3CS (nanosat) Arizona State University, University of Colorado at Boulder and New Mexico State University. Three satellites, one from each University flying in formation.

Design life: 2 to 4 months To be launched with the Space Shuttle.

Mechanical/Structural subsystem: Uses Aluminium honeycomb. Attitude and Orbit control subsystem: LEO at 380 km with an inclination of 40°. Has parallel gravity gradient booms with tip masses. GPS patch antennas. Propulsion system for reaching higher altitude, and at the end of life for deorbiting the satellites. Propulsion subsystem: Uses micropropulsion. Power subsystem: Body mounted GaAs solar cells. Uses an integrated battery pack/release mechanism. Thermal control subsystem: N.A. Telecommand and Telemetry: Two transceivers (TH-D7A) onboard each satellite, redundant system. Uses 135 to 148 MHz and 438 to 450 MHz, GMSK/FM. Maximum bitrate is 9600 bps. The bandwidth is about 20 kHz. On the ground IC-821H is used as transceiver, one for each University. Uses 144 to 148 MHz and 430 to 450 MHz, GMSK/FM, for the uplink. The maximum bitrate is 9600 bps here as well. Data handling: The onboard computers are Power PC 750 flight processors. Onboard communication will be made using Spacecraft Command Language (SCL). The satellites will use CASPER onboard planning system (NASA-JPL). Payload: Stereoscopic imaging: Has a CMOS camera onboard each satellite. Pictures are to be taken of clouds, sandstorms etc with a narrow beam and short duration, yielding dynamic photographs. Component validation: A micropropulsion experiment, a MEMS Heater Chip. The satellite is built and managed by students. Homepage: http://threecs.colorado.edu/ http://telemetry.nmsu.edu/~shoran/nanosat/documents.htm

102 A.29 Artemis (picosat) Santa Clara University

Length: 8 +/- 0.003 inches Width: 1 +/- 0.003 inches Height: 3 +/- 0.003 inches Weight: 611.87 grams Launched with OPAL 26th January 2000.

Mechanical/Structural subsystem: Structure in Al6061-T6. Antenna in tempered steel tape measure, 0.5” wide and 2-8”long. Attitude and Orbit control subsystem: Spin axis stabilization using rubber ferrite magnets. Attitude determination using four IR/visible phototransistors. Propulsion subsystem: No propulsion onboard. Power subsystem: GaAs solar cells with two secondary AA NiCd batteries. Thermal control subsystem: N.A. Telecommand and Telemetry: N.A. Data handling: N.A. Payload: VLF receivers, in conjunction with the STARLab at Stanford University. For studying occurrence and amplitudes of both vertical and horizontal lightning. Homepage: http://screem.engr.scu.edu/artemis/

103 A.30 Can-Sat (picosat) Tokyo Institute of Technology, University of Tokyo, Stanford University, University of Texas, Univeristy of Hawaii.

Shape: Soft-drink can. Weight: Less than a soft-drink can.

Mechanical/Structural subsystem: Aluminum structure made of two parts, an inner structure with the satellite components and an outer shell with a protective covering. Attitude and Orbit control subsystem: N.A. Propulsion subsystem: Turbojet propulsion (Jet propulsion Laboratory, JPL) Power subsystem: N.A. Thermal control subsystem: N.A. Telecommand and Telemetry: N.A. Data handling: N.A. Payload: N.A. Homepage: http://horse.mes.titech.ac.jp/srtlssp/arliss/index.html http://ssdl.stanford.edu/arliss/

104 A.31 The Canadian Advanced Nanospace eXperiment, CanX 1 (picosat) University of Toronto Based on the CubeSat program.

Length: 10 cm Width: 10 cm Height: 10cm Shape: Cubic Weight: 1 kg Design life: Launched with Rockot on June 30th 2003.

Mechanical/Structural subsystem: Aluminium 6061 was chosen over Aluminium 7075 because of the cost issue. Attitude and Orbit control subsystem: N.A. Propulsion subsystem: No propulsion. Power subsystem: N.A. Thermal control subsystem: N.A. Telecommand and Telemetry: Transmitter with 330 mW DC power and a 925.286 MHz carrier frequency along with an intermediate frequency of 166.287 MHz. Receiver with a DC power of 33 mW and a carrier frequency of 910.7 MHz and the intermediate frequencies of 49.3 MHz and 10.7 MHz. Data handling: A custom-built onboard computer was built on the base of an ARM7 core. Payload: The four part payload is subject to validation. A CMOS Imager, An ARM7-based On-Board computer, a GPS Receiver and an Active Magnetic Attitude Control System. Homepage: http://cubesat.calpoly.edu/reference/canx_paper.pdf http://www.utias-sfl.net/code/cubesats/

105 A.32 Constellation Pathfinder (picosat) Boston University

Shape: hockey-puck. Weight: less than 1 kg. Design life:

Mechanical/Structural subsystem: Stackable. Attitude and Orbit control subsystem: Magnetometer, Sun sensor, Satellite spin. Propulsion subsystem: N.A. Power subsystem: GaAs solar cells. Thermal control subsystem: N.A. Telecommand and Telemetry: N.A. Data handling: N.A. Payload: QUATRO: QUantitative Assessment of magnetospheric TranspOrt. Multiple satellites for measurements in the magnetosphere; assesing general space physics issues. Homepage: http://www.bu.edu/csp/mmm/index-flash.htm

106 A.33 CubeSat (picosat) Stanford University, Tokyo Institute of Technology LSS among others. Platform. At least 18 satellites from different organizations.

Length:10 cm Width: 10cm Height: 10 cm Shape: Cubic Weight: less than 1 kg. Design life: Depends on the mission

Mechanical/Structural subsystem: Satellite platform made of Aluminium. Using a special deployment system called P-POD. Attitude and Orbit control subsystem: Made for LEO. Propulsion subsystem: Some satellites without thrusters, some have thrusters from JPL. Power subsystem: GaAs solar cells, with LiIon batteries. Thermal control subsystem: N.A. Telecommand and Telemetry: Varies with the different satellites. Data handling: Varies with the different satellites. Payload: Varies with the different satellites. Homepage: http://cubesat.calpoly.edu/ http://www.cubesat.info/

107 A.34 MEMS Picosat (picosat) DARPA (developed by Artemis) Two satellites connected with a 30 m long tether.

Shape: Box. Weight: less than 280 g, each. Design life: Launched with a Minotaur on January 26th 2000.

Mechanical/Structural subsystem: Aluminium 6061-T6. Attitude and Orbit control subsystem: LEO of 796 km, with an inclination of 100.2 degrees. Has six IR/visible phototransistors, the data read from these photo sensors are fed into an A/D converter in the microprocessor onboard. Propulsion subsystem: N.A. Power subsystem: 2 AA alkaline batteries, rated at 1.5 V and 800 mAh. Regulation is done with a LM262 Step-up DC-DC converter. Has GaAs solar cells and a LiCl primary battery. Thermal control subsystem: Telecommand and Telemetry: TCM 3105 FSK modem IC. The transmitter circuit is a Motorola MC 13176 UHF FM/AM transmitter chip. The receiver is an RF Mono Lithium Rx1000. BSIT is used as communication system. Data handling: Using a BASIC Stamp II microprocessor, with 2048 bytes of EEPROM and 16 word registers of R4. Payload: N.A. Homepage: http://www.skyrocket.de/space/index_frame.htm?http://www.skyrocket.de/space/doc_sdat/mems- picosat.htm http://ssdl.stanford.edu/opal/Subsystems/Picosats/Aerospace/PicoReview/sld001.htm

108 A.35 MEms-based PicoSat Inspector, MEPSI (picosat) DARPA, AFRL Two satellites attached to each other with a 15.2 m long tether.

Length: 10 cm Width: 10 cm Height: 12.5 cm Shape: box Weight: 1 kg. Design life: 3 days. Launched with the Endeavour shuttle on November 24th 2002 and deployed December 2nd 2002.

Mechanical/Structural subsystem: N.A. Attitude and Orbit control subsystem: 3-axis inertial sensor, magnetometer. Propulsion subsystem: Cold gas micro propulsion system, JPL. Power subsystem: Average power usage is 2 W. Thermal control subsystem: N.A. Telecommand and Telemetry: RF data receiver. Data handling: N.A. Payload: N.A. Homepage: http://www.skyrocket.de/space/index_frame.htm?http://www.skyrocket.de/space/doc_sdat/mepsi.htm http://accesstospace.gsfc.nasa.gov/ats3/admintools/msnSpacecraftDetails.asp?mid=336&ms_type=1&proxy id=guest&xsection=0&subxsection=0&linkback=<,>ats3<,>missionquery<,>Report.asp<.>ProxyId=guest <->xsection=0<->subxsection=0<->MenuRequest=5<->Sort=1

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110

Appendix B Structure

111 B.1 The Design Criteria from the point of the launching company

1. Stiffness criteria. The fundamental frequency of the satellite mounted on the separation plate should not be less than • 20 Hz in the longitudinal axis, and • 10 Hz in the lateral axis.

2. Quasi-static and dynamic loads. The dimensioning factors should not be less than • 2.0 for ground handling, • 1.5 during launch when the LV is inside the silo, • 1.3 when the LV exits the silo, and • 1.3 during LV flight. The acceleration of the satellite during the transportation is shown in table B.1-1, and during the launch in table B.1-2. Included in the values is the gravity force component; dynamic accelerations given with limits. The lateral acceleration in any of the two directions may occur at the same time as the longitudinal.

Table B.1-1. Acceleration on the satellite (and launch vehicle) during transportation.

Table B.1-2. The acceleration experienced by the satellite during the different stages of the launch. 3. Vibrational loads. There are two types of vibrations acting on the satellite attachment points during the launch, Harmonic oscillations and Random vibrations. The Harmonic oscillations are represented by their amplitude, frequency and duration in tables B.1-3 and B.1-4. The random vibrations are represented by their spectral density and their duration in table B.1-5. It should be noted that the random vibrations are equally distributed in all directions of the satellite’s axis.

Table B.1-3. Amplitude and duration of the Harmonic oscillations along the longitudinal axis (X) of the satellite.

112

Table B.1-4. Amplitude and duration of the harmonic oscillations in the lateral plane (Y,Z) of the satellite.

Table B.1-5. The spectral density and duration of the Random vibrations during launch. 4. Shock loads. The separation of the satellite from the LV, the release of the fairings from the LV, the burn of the third stage and the release of neighbouring satellites will impose shock loads on the satellite. The frequency spectrum of this is shown in table B.1-6. The numbers are accurate for Q=10, and in all three directions of the satellite. The duration of the shock processes can be up to 0.1 s.

Table B.1-6. The shock spectrum at the satellite’s attachment points; * denotes the number of satellites that are in the same compartment. 5. Acoustic loads. Two causes of acoustic loads are the first stage burn of the LV and the frame surface pressure fluctuations in the turbulent boundary layer. The level of sound pressure for the octave frequency band is shown in table B.1-7.

Table B.1-7. The acoustic loads on the satellite during launch.

113

6. Pressure inside the LV fairing. The maximum rate of pressure drop inside the LV fairing envelope during flight will not exceed 0.035 kgf/(cm2/s). This data can be specified by the launch company for each mission. 7. Gas-dynamic effect on the satellite. When the SHM is separated it will be exposed to the exhaust plume of the third stage for several seconds. All combustion products are in the gaseous state, so there will be no contamination of the surfaces of the satellite. The impact on the satellite is shown in table B.1-8.

Table B.1-8. Third stage motor plume parameters affecting the satellite, maximum values. x – distance (along X-axis) from attachment plate inside the SHM

Po – gas stagnation pressure P – Pressure of undisturbed gas flow T – Temperature of undisturbed gas flow V – Velocity of undisturbed gas flow The satellite might experience some changes in motion while passing through the plume. Some torque may be added, depending on the satellite’s inertia and position regarding the LV X-axis. Previous satellites that have flown with this launch vehicle have not been affected in their operation by the plume.

114 B.2 Required documents from the launching company

- Line and dimensional drawings of spacecraft (including its adapter); - Spacecraft envelope drawing (The envelope where the spacecraft and adapter are placed, taking into account all protruding elements and possible deviations from the nominal position due to errors during its manufacturing and balancing as well as deformations during its joint operation with the LV with respect to the plane of the adapter interface with the LV. The axis of the spacecraft envelope will be perpendicular to the plane of the adapter interface with the LV drawn from the centre of the circumference on which the attachment holes are located); - Detailed drawing of the spacecraft (adapter) interface with the LV; 4) Detailed drawing of the spacecraft interface with adapter denoting the elements of the separation system (separation mechanisms, guiding pins, attachment elements, etc.) and their characteristics with tolerances and deviations). The drawing that shows the area of spacecraft structural elements penetration into the adapter denoting structural gaps and “dangerous” points; - The list of connection lines to the adapter describing their characteristics (the number and type of connection lines, their location, disconnection force and travel with tolerances and deviations); - The diagram showing the location of the separation telemetry sensors at the spacecraft/adapter interface and their characteristics (disconnection force and travel with tolerances and deviations); - Mass, Centre of Gravity and inertia characteristics of the spacecraft, the adapter as well as the spacecraft/adapter assembly with tolerances and deviations for all variants and modifications of the spacecraft, and also the distribution of weight and moment of inertia along the length of the spacecraft/adapter assembly; - Stiffness characteristics of the spacecraft (bending rigidity, longitudinal rigidity, and torsion rigidity along the length of the spacecraft/adapter assembly); - Data on spacecraft structural elements separated in flight; requirements and constraints regarding the separation time; - Spacecraft longitudinal load constraints; - Constraints for dynamic pressure at the moment of fairing separation; - Number, type and electric characteristics of the spacecraft separation system pyros; - Documents confirming the completion of the spacecraft tests for static and dynamic loads with the level of loading exceeding the actual loads acting on the spacecraft during flight with LV.

115 B.3 Separation System

B.3.1 Drawing

Figure B.3.1-1. Standard Adapter to Spacecraft attachment points.

B.3.2 Required documents from the launching company

The number, type and electric characteristics of the spacecraft separation system pyros.

116

Appendix C Short summaries of important articles on orbit control

117 Hanspeter Schaub & Kyle T. Alfriend, “J2-invariant relative orbits for spacecraft formations”

Possibility discussed for choosing orbits that relative to each other are J2-invariant. This will lower the fuel consumption since less orbit rectifications needs to be done in the out-of-plane direction. The article gives the constraints that need to be imposed on the orbits for J2-invariance. The article is interesting in the sense that the choice of suitable orbits will decrease the need for corrections due to the significant J2-disturbance.

Hanspeter Schaub & Kyle T. Alfriend, “Impulsive spacecraft formation flying control to establish specific mean orbit elements” The mean orbital elements makes it easy to see the long-term response from orbital disturbances on the satellite motion. The short-term effects are oscillatory and counteracting them with the control system is a waste of fuel. The authors use Gauss’ variational equations of motion for developing a thruster firing sequence that gives corrections in one orbital element, and poses only minor or no effects on the rest of the orbital elements. This article does not deal with the control system in the sense that it offers a control algorithm. Rather it describes the thrusting sequences that the control system needs for orbital corrections.

S. R. Vadali, H. Schaub & K. T. Alfriend, “Initial conditions and fuel-optimal control for formation flying of satellites.” Requirements for the formation are summarized as: a certain inclination change between the orbits should still yield the same drift in the ascending node, and the sum of the drift in the argument of perigee and mean anomaly should be the same for the satellites. Further, the relative motion is described in a rotating coordinate system and periodic boundary constraints are posed on the relative motion. Propulsion schemes are proposed for orbital changes with minimal fuel consumption that the control system can use for orbital corrections. The thrust schemes developed in the article are suited for plasma or ion propulsion since they require low-thrust and variable Isp. The authors give many references in the text to previously presented solutions.

Hanspeter Schaub & Kyle T. Alfriend, “Hybrid Cartesian and orbit element feedback law for formation flying spacecraft” The authors show how to map the orbital elements in the LVLH (Local Vehicle Local Horizon) representation. Then they use the relative constraints from the former articles for deriving a feedback control law. The article also includes some simulation results, stating that the solution is fuel-efficient.

118 S. R. Vadali, S. S. Vaddi, K. Naik & K. T. Alfriend, “Control of satellite formations” The mass and aerodynamic properties need to be kept at equal levels for the satellites in the formation in order for the differential drag to be disregarded. This can only be achieved if they all use equal amounts of fuel. The amount of control needed for formation keeping is directly dependent on the inclination difference between the satellites. Hill’s equations are used, but modified to suit the needs. The controller is an LQR, based on the linear Hill’s equations, but not taking into account the short-term periodic oscillations. It penalizes radial manoeuvres hard, in order to keep the fuel consumption down. Non-linear simulation is presented in the article in order to test the results. A plot for delta-V cost per year for an orbit with an inclination of 70° is presented. Both the cost of traditional brute force, and the refined method of the authors are shown in the article.

Dong-Woo Gim & Kyle T. Alfriend, “The state transition matrix of relative motion for the perturbed non-circular reference orbit” Equations are presented for determining if the satellites are in formation, using a geometric method for elliptic orbits. The equations, taking the J2-term into account, are expressed in a curvilinear coordinate frame in order to deal with the eccentricity. It appears that the equations presented draw on previous articles that now include the fact that the orbits will never be exactly circular, but indeed eccentric. Uses high inclinations, therefore the plots are quite interesting.

S. R. Vadali, S. S. Vaddi & K. T. Alfriend, “An intelligent control concept for formation flying satellite constellations” The authors discuss different coordinate frames and methods for deducing the equations that determine if the satellites are actually flying in formation, and give suggestions for initial conditions. The reference orbit is not circular. The non-linear equations that include the perturbations into Hill’s equations are presented, resulting in a rate matching constraint. Then they introduce a continuous feedback controller using pole placement and Hill’s equations, and in addition the same type of controller but including the perturbations in the Hill’s equations. The proposed controller strives to be fuel-efficient and use an equal amount of fuel for all satellites in the formation. A fair amount of background theory is included in the paper.

Kyle T. Alfriend, Hanspeter Schaub & Dong-Woo Gim, “Gravitational perturbations, non- linearity and circular orbit assumptions on formation flying control strategies” In the article a geometrical model for describing the relative motion of the formation is derived. Simulations of the model against the unperturbed Hill’s equations are made, which show that the error in position is much less. Further improvements on the model are suggested using Hamiltonian mechanics and Lie series The article presents substantial background material, and is used as a reference in some of the other articles. No control is discussed, just how to determine the initial conditions and the equations for relative motion.

119 Kyle T. Alfriend & Hanspeter Schaub, “Dynamics and control of spacecraft formations: challenges and some solutions”

J2-invariant relative orbits are derived in the paper. The authors discusses the problem of near- polar orbits, since the change needed in eccentricity is too large for making the desired orbits feasible. Further, the problem of near circular ‘chief’ orbits is addressed since it becomes hard to compensate for the inclination difference. The authors look at the delta-V cost for making the suggested changes and maintain the orbits. This article also serves as reference to some of the other articles. It also deals with the compensation of the J2-invariance in the equations, and the manoeuvres that have to be performed in order to maintain the orbits.

Hanspeter Schaub, Srinvas R. Vadali, John L. Junkins & Kyle T. Alfriend, ”Spacecraft formation flying control using mean orbit elements” Two non-linear controllers that use the mean orbital elements are presented. The first feeds the errors back using mean orbital elements. The model is simulated and the results are presented. By changing some parameters the controller can shift between a fuel saving mode and a time saving mode. The second controller feeds back the values using Cartesian elements. This method is more suitable to use for shorter periods of time. Finally the authors state that further work is needed in order to best determine the matrices for the control system.

Lyon B. King, Gordon G. Parker, Satwik Deshmukh & Jer-Hong Chong, “A Study of Inter- Spacecraft Coulomb Forces and Implications for Formation Flying” 2002 Since the thruster plumes might become a problem for tight formations, a new type of propulsion is proposed. It uses the coulomb forces attained from spacecraft charging caused by the surrounding plasma. Valid for formations with separation distances of 10 up to 50 m, in high Earth orbit. The authors use Hill’s equations for validation, and calculate a thrust of 100 μN for 10 m separation distance and down to a few μN for separation distances of 50 m. The specific impulse is high, up to 1013 s. An interesting idea, and very innovative. It will take time to develop it into flight readiness.

Pini Gurfil, “Control-Theoretic Analysis of Low-Thrust Orbital Transfers Using Orbital Elements” 2003 The author uses Gauss’ variational equations (GVE) as a dynamical model, thus creating a framework for design and analysis of low-thrust orbital transfers with orbital element feedback (nonlinear continuous-time orbital transfer feedback controllers). This has been done before, but here the authors include parabolic trajectories and take into account the controllability.

120 P. K. C. Wang, E. G. Sayegh & F. Y. Hadaegh, “Rule-Based Cooperative Control of Optically Linked Model Spacecraft: Experimental Study” 2004 An experiment is presented with three model spacecraft, magnetically levitated and with rotation possible around one axis. The experiment simulates an interferometric mission with two receivers and a combiner linked by optical sensors. Uses laser beams in order to simulate the starlight. A rule-based cooperative control resulting in a hybrid continuous-time and discrete-event system is used. Works well with few sensors under the condition that the relative drift in angular motion is small. Very task specific control, does not take into account disturbances in all dimensions. It seems like the article is focusing on the test set-up more than the actual control.

Yoonsoo Kim, Mehran Mesbahi & Fred Y. Hadaegh, “Dual-Spacecraft Formation Flying in Deep Space: Optimal Collision-Free Reconfigurations” 2003 The authors use the Hill’s equations of motion in the Hill’s frame, for deriving optimal control of a reconfiguration manoeuvre for two formation-flying satellites. The manoeuvre is performed in deep space so no J2-effect is considered. All other disturbances are also neglected. The optimization equations with the satellites in error boxes are defined as well. The next step is to involve more satellites in the manoeuvre, but that will make the control parameters complex. The authors instead propose that the solution presented should be used for manoeuvres with two satellites at a time until the desired formation is acquired.

Roy S. Smith & Fred Y. Hadaegh, “Control Topologies for Deep Space Formation Flying Spacecraft” 2002 The control discussed is intended for interferometric missions in deep space with heliocentric orbits. The satellites are assumed only to measure relative position, not absolute. Uses centralized control, with local parameters only, that is, no communication of parameters between the satellites. This makes the scheme suitable for constellations of 3 to 6 satellites. Theorems are provided for stability and performance. The idea is that a global controller is used, but that it is modified on each satellite so that it only requires local measurements. The case of failure of a measurement unit, or the case where a satellite cannot see all the other satellites in the formation is discussed using nestled topology, i.e. with some communication introduced. Very high-level control, which does not consider propulsion limitations, among other things.

Fred Y. Hadaegh, Ali R. Ghavimi, Gurkirpal Singh & Marco Quadrelli, “A Centralized Optimal Controller for Formation Flying Spacecraft” 2000 The article discusses the control for a Terrestrial Planet Finder, an interferometric mission with an Earth trailing heliocentric orbit. Solar pressure and third-body effects are included in the model, but the third-body effects are assumed to be much smaller than the solar pressure and are therefore not included in the model. Hill’s equations are used for the relative motion, since the distance to Earth is much greater than the relative distances. Five spacecraft are included in the formation, four collectors (treated as followers) and one combiner (treated as leader). Optimal control is developed, first an LQR in continuous-time and then an LQR in discrete-time. An interesting article with an actual mission in mind. Not discussed were the propulsion system limitations.

121 Randal W. Beard, Timothy W. McLain & Fred Y. Hadaegh, “Fuel Optimization for Constrained Rotation of Spacecraft Formations” 2000 This article seems to be a follow-up of “Fuel Optimized Rotation for Satellite Formations in Free Space”. It discusses interferometric missions in deep space. The authors use N +2 coordinate systems for N satellites. They use the same assumptions regarding thrusters and free space as before. The trajectory is assumed to be bang-off-bang, but the theory could be used for other motion schemes as well. The time for the manoeuvre is a parameter to be chosen, large if fuel needs to be optimized but always according to the mission objective. A cost function is developed (as in the former article), J, for the fuel consumption. The Nelder-Mead Simplex method is used for optimization of the cost function and by using that the open-loop control law is attained. The fuel spent for one and 15 rotations are shown, with slightly different results than the previous article.

Randal W. Beard & Fred Y. Hadaegh, “Fuel Optimized Rotation for Satellite Formations in Free Space” 1999 The control is intended for interferometric missions in deep space. The authors derive an algorithm for rotation of the formation, equalizing the fuel used for each satellite. Uses N + 3 coordinate systems for N satellites. The algorithm can be altered tin order to take minimization of fuel or time into account; these are competing with the fuel optimization. The authors develop an open-loop control from the constraints for fuel optimization on the satellite motion. No perturbations are included, and the satellites are assumed to move in free space. The thrusters have limited thrust, but can fire in any direction and perfect absolute and relative positions of the satellites are assumed to be known. Calculates the fuel used for making 15 rotations. Future work will include more rotations. This is an early article. It deals with the reconfiguration in free space in a basic way.

Randal W. Beard & Fred Y. Hadaegh, “Finite Thrust Control for Satellite Formation Flying with State Constraints” 1999 Discusses interferometric missions in deep space; thrust is restricted but not in direction. The authors use Newton’s laws for calculating motion, and the relative motion for the constraints. The constraints in the end give the control law. First, the case of impulsive thrust is discussed, which then is converted to finite thrust by a look-ahead operator. An algorithm is given for the feedback control. The scenario to be controlled is a rotation of the formation while keeping the separation distances constant. A closed-loop control is produced. The authors conclude that future work will include rotational dynamics, formation spin-up and spin-down modes and the ability to track arbitrary trajectories.

122 Wei Ren & Randal W. Beard, “Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach“ 2004 The article deals with interferometric missions. The authors use three reference frames, one inertial, one tied to the formation centre and one for each satellite in the formation. The idea is to combine a virtual structure (VS) approach with a decentralized approach. This is done using the VS restrictions in the controllers of the decentralized satellites, and by having bi-directional ring architecture. A negative effect is the increase in communication as compared to VS. Future work will include time delays in the communication. A simulation example is included, three cases are considered; 1) without actuator saturation and formation feedback, 2) with actuator saturation but without formation feedback and 3) both actuator feedback and formation feedback. The article discusses very high-level control and it does not discuss perturbations,

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124 References

Books

Wigbert Fehse, (2003). Automated Rendezvous and Docking of Spacecraft. 1st Edition, The Press Syndicate of the University of Cambridge, Cambridge, UK.

David A. Vallado, (2001). Fundamentals of Astrodynamics and Applications. 2nd Edition, Microcosm Press, California, USA.

Web pages

AML - APPLIED MICROENGINEERING LTD (2003), Design, Fabrication and Evaluation of a MEMS Sun Sensor, http://www.aml.co.uk/PDF/sunsensor.pdf

BEI Systron Donner Inertial Division, BEI Technologies Inc, (2003). QDARS MEMS Quartz Dual Axis Rate Sensor, http://www.systron.com/pro_QDARS.asp

Paul Zetocha, (2001). Satellite Cluster Command and Control, http://www.interfacecontrol.com/papers/z2_0106.pdf

U. S. Department of Energy, (2004). Photovoltaics, http://www.eere.energy.gov/solar/photovoltaics.html

Dr. Xunming Deng, (2003).High-efficiency Amorphous Silicon Thin Film Solar Cells, http://www.physics.utoledo.edu/~dengx/highefficiency.pdf

Science Beat, (2004). A Step Closer to the Optimum Solar Cell, http://www.lbl.gov/Science-Articles/Archive/sb-MSD-multibandsolar-panels.html

BUSEK, (2003). Micro-propulsion Colloid Thruster, http://www.busek.com/colloid.htm

Centro Spazio, (1998). The FEEP Principle, http://www.centrospazio.cpr.it/FEEPPrinciple.html

R. Joseph Cassady, W. Andrew Hoskins, Mark Campbell and Christopher Rayburn, (2002). A Micro Pulsed Plasma Thruster (PPT) for the “Dawgstar” Spacecraft, http://www.mae.cornell.edu/campbell/pubs/IEEE002.pdf

Surrey Satellite technology Ltd, (2003). SNAP-1: Propulsion System, http://centaur.sstl.co.uk/datasheets/SNAP-1%20Propulsion.pdf

C Rossi, T Do Conto, D Estève and B Larangot, (2001). Design, fabrication and modelling of MEMS-based microthrusters for space application, http://stacks.iop.org/SMS/10/1156

125 SPENVIS, (2004), http://www.spenvis.oma.be/spenvis/

Kosmotras, (2001). Dnepr Space Launch System. User’s Guide. Issue 2, http://www.kosmotras.ru/archive2.htm

Conference proceedings

J.H. Hales and M. Pedersen, (2002). Two-Axis MOEMS Sun Sensor for Pico Satellites, 16th Annual AIAA/USU Conference on Small Satellites, Utah State University, Logan, UT, USA,

Marcello Buonocore, Michele Grassi and Giancarlo Rufino, (2003). APS-Based miniature sun sensor for Earth observation nanosatellites, 4th IAA Symposium on Small Satellites for Earth Observation, Berlin, Germany,

John L. Jørgensen, Troelz Denver, Maurizio Betto, Peter S. Jørgensen, (2003). MICROASC a miniature star tracker, 4th IAA Symposium on Small Satellites for Earth Observation, Berlin, Germany,

Freddy Mathias Pranajaya, (1999). Progress on Colloid Micro-Thruster Research and Flight Testing", 13th Annual AIAA/USU Conference on Small Satellites, Logan, Utah, USA,

Alexei Golikov, (2003). Evolution of Formation Flying Satellite Relative Motion: Analysis based on the THEONA Satellite Theory, 17th International Symposium on Space Flight Dynamics, Moscow, Russia.

Hanspeter Schaub & Kyle T. Alfriend, (2000). Impulsive spacecraft formation flying control to establish specific mean orbit elements, AAS/AIAA Spaceflight Mechanics Conference, Clearwater, Florida, USA.

S. R. Vadali, H. Schaub & K. T. Alfriend, (1999). Initial conditions and fuel-optimal control for formation flying of satellites, AIAA GN&C Conference, Portland, Oregon, USA. Paper No. AIAA-99-4265.

Hanspeter Schaub & Kyle T. Alfriend, (2000). Hybrid Cartesian and orbit element feedback law for formation flying spacecraft, AIAA/AAS Guidance, Navigation and Control Conference, Denver, Colorado, USA.

Dong-Woo Gim & Kyle T. Alfriend, (2001). The state transition matrix of relative motion for the perturbed non-circular reference orbit, AAS/AIAA Space Flight Mechanics Meeting, Santa Barbara, California, USA.

Kyle T. Alfriend, Hanspeter Schaub & Dong-Woo Gim, (2000). Gravitational perturbations, non- linearity and circular orbit assumptions on formation flying control strategies, AAS Rocky Mountain Guidance & Control Conference, Breckenridge, Colorado, USA.

Roy S. Smith & Fred Y. Hadaegh, (2002). Control topologies for deep space formation flying spacecraft, American Control Conference, Anchorage, Alaska, USA. pp. 2836--2841.

126 Fred Y. Hadaegh, Ali R. Ghavimi, Gurkirpal Singh & Marco Quadrelli, (2000). A Centralized Optimal Controller for Formation Flying Spacecraft, Internal Conference on Intelligence and Technology, JPL California Institute of Technology, California, USA.

Randal W. Beard (Brigham Young University) & Fred Y. Hadaegh, (1999). Fuel Optimized Rotation for Satellite Formations in Free Space, American Control Conference, San Diego, California, USA.

Randal W. Beard (Brigham Young University) & Fred Y. Hadaegh, (1999). Finite Thrust Control for Satellite Formation Flying with State Constraints, American Control Conference, San Diego, California, USA.

S. R. Vadali, S. S. Vaddi, K. Naik & K. T. Alfriend, (2001). Control of satellite formations, AIAA Guidance, Navigation and Control Conference and Exhibit, Montreal, Canada.

Journal Articles

Hanspeter Schaub & Kyle T. Alfriend, (2001). J2-invariant relative orbits for spacecraft formations, Celestial Mechanics and Dynamical Astronomy, Vol. 79, pp. 77–95.

S. R. Vadali, S. S. Vaddi & K. T. Alfriend, (2002). An intelligent control concept for formation flying satellite constellations, International journal of robust and nonlinear control , Vol. 12, No. 2-3, pp. 97–115.

Kyle T. Alfriend & Hanspeter Schaub, (2000). Dynamics and control of spacecraft formations: challenges and some solutions, AAS The Richard H. Battin Astrodynamics Symposium 2000, Volume 106, pp. 205-225.

Hanspeter Schaub, Srinvas R. Vadali, John L. Junkins & Kyle T. Alfriend, (1999). Spacecraft formation flying control using mean orbit elements, AAS Astrodynamics 1999, Volume 103, pp.163-183.

Pini Gurfil, (2003). Control-Theoretic Analysis of Low-Thrust Orbital Transfer using Orbital Elements, AIAA Journal of Guidance, Control and Dynamics, Vol. 26, No. 6, pp. 979-982.

P. K. C. Wang, E. G. Sayegh & F. Y. Hadaegh, (2004). Rule-Based Cooperative Control of Optically Linked Model Spacecraft: Experimental Study, AIAA Journal of Guidance, Control and Dynamics, Volume 27, Issue 1, pp. 83-90.

Yoonsoo Kim (University of Washington), Mehran Mesbahi (University of Washington) & Fred Y. Hadaegh, (2003). Dual-Spacecraft Formation Flying in Deep Space: Optimal Collision-Free Reconfigurations, AIAA Journal of Guidance, Control and Dynamics, Volume 26, Issue 2, pp. 375-379.

Randal W. Beard (Brigham Young University), Timothy W. McLain (Brigham Young University) & Fred Y. Hadaegh, (1999). Fuel Optimization for Constrained Rotation of Spacecraft Formations, AIAA Journal of Guidance, Control and Dynamics, Volume 23, Issue 2, pp. 339-346.

127 Wei Ren & Randal W. Beard, (2004). Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach, AIAA Journal of Guidance, Control and Dynamics, Volume 27, Issue 1, January 2004, pp. 73-82

Lyon B. King, Gordon G. Parker, Satwik Deshmukh & Jer-Hong Chong, (2003). A Study of Inter-Spacecraft Coulomb Forces and Implications for Formation Flying, Journal of Propulsion and Power, Volume 19, Issue 3, pp. 497-505.

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