specs: submillimeter probe of the evolution of the cosmic structure...

SPECS: Submillimeter Probe of the Evolution

of the Cosmic Structure

AOE 4065 - Space Design

Karen Amores Mir Arash Ghaderi Amanda Hibbert

Michael Shoemaker Brian Verna Sarah Hefter Theissam Kilani

Frances Durham

May 10, 2004

Contents

1 Introduction 1

1.1 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 Tethers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.3 Lagrange Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Relevant Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Value System Design 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Analytical Hierarchy Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 System Synthesis 17

3.1 Mission Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 Launch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.2 Transfer Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.3 Parking Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.4 Orbit at L2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.5 Mission Geometry Summary . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Tether Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

ii

CONTENTS iii

3.2.1 Tether Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.2 Hex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.3 Tetra-Star . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.4 Triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.5 Radial Tethers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.6 Triangle+Radial Tethers . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.7 Tether Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Attitude Determination Control System . . . . . . . . . . . . . . . . . . . . 26

3.3.1 Control Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.2 ADCS Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3.3 ADCS Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Ground Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4.1 Dedicated Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4.2 Existing Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4.3 Ground Station Summary . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5 Retirement Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5.1 Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5.2 Retirement Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.6 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.6.1 Cryogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.6.2 Secondary Components . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.6.3 Previous Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.6.4 Thermal Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.7 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7.1 Solar Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7.2 Solar Cell Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7.3 Battery Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.7.4 Primary Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.7.5 Secondary Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.7.6 Power Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

iv CONTENTS

3.8 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.8.1 Chemical Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.8.2 Electrical Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.9 Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.9.1 Overall Subsystem Design . . . . . . . . . . . . . . . . . . . . . . . . 47

3.9.2 Telemetry, Tracking and Command System . . . . . . . . . . . . . . . 47

3.9.3 Command and Data Handling System . . . . . . . . . . . . . . . . . 48

3.9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.10 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4 System Analysis 50

4.1 Configuration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 Mission Geometry Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3 Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3.1 Initial Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4 Contamination Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4.1 Light Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.4.2 Outgassing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.4.3 Electric Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.4.4 Chemical Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.4.5 Allowable Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5 Propulsion Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5.1 CSC and MSC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5.2 Propulsion System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.6 Communication Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.6.1 Computer System Analysis . . . . . . . . . . . . . . . . . . . . . . . . 75

CONTENTS v

4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5 Optimization 78

5.1 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.1.1 Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.1.2 Tether Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.1.3 Boom Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.2 Orbit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.2.1 Direct Transfer Method . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.2.2 HEO and Lunar Swingby Method . . . . . . . . . . . . . . . . . . . . 106

5.3 Attitude Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.3.1 Attitude Control System Model . . . . . . . . . . . . . . . . . . . . . 109

5.3.2 L2 Mission Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.3.3 Near-Earth Mission Phase . . . . . . . . . . . . . . . . . . . . . . . . 121

5.4 Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.4.1 Uplink and Downlink . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.4.2 Crosslinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.4.3 Data Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.5 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.5.1 Cryogenic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5.5.2 Radiant Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.5.3 Thermal Struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.5.4 Space Radiators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.6 Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.6.1 Outgassing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.6.2 Mirror Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.7 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.7.1 Propulsion Technology Selection . . . . . . . . . . . . . . . . . . . . . 145

5.7.2 Monopropellant Selection . . . . . . . . . . . . . . . . . . . . . . . . 146

vi CONTENTS

5.7.3 CSC Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.7.4 MSC Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5.7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

6 Design Selection 150

6.1 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6.1.1 Structural Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6.1.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

6.1.3 Tethers and Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 156

6.1.4 Truss Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6.2 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.2.1 Cryogenic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.2.2 Passive Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.3 Orbit Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6.4 Attitude Determination and Control Subsystem . . . . . . . . . . . . . . . . 176

6.4.1 Attitude Determination Hardware . . . . . . . . . . . . . . . . . . . . 176

6.4.2 Attitude Control Hardware . . . . . . . . . . . . . . . . . . . . . . . . 177

6.5 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

6.5.1 CSC and MSC Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . 177

6.5.2 CSC and MSC Propellant Tanks . . . . . . . . . . . . . . . . . . . . 178

6.6 Communication System Decisions . . . . . . . . . . . . . . . . . . . . . . . . 180

6.6.1 Uplink and Downlink . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

6.6.2 Crosslink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

6.6.3 Data Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

6.6.4 Computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

6.7 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

6.7.1 Solar Array Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

6.7.2 Battery Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

6.8 Ground Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

6.9 Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

CONTENTS vii

6.10 Launch Vehicle Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

6.10.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

6.10.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

6.10.3 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

6.10.4 Launch Vehicle Selection . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

7 Summary 198

7.1 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

7.1.1 Formation Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

7.1.2 Structural Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

7.1.3 Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

7.1.4 Future Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

7.2 ADCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

7.3 Thermal Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

7.4 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

7.5 Communication and Data Handling . . . . . . . . . . . . . . . . . . . . . . . 201

List of Figures

2.1 Objective hierarchy for value system design . . . . . . . . . . . . . . . . . . . 13

2.2 Analytical hierarchy for value system design . . . . . . . . . . . . . . . . . . 16

3.1 “Hex” configuration option for SPECS formation . . . . . . . . . . . . . . . 22

3.2 “Tetra-Star” configuration option for SPECS formation . . . . . . . . . . . . 23

3.3 “Triangle” and ”Triangle+Radial” configuration options . . . . . . . . . . . 24

3.4 Radial configuration option for SPECS . . . . . . . . . . . . . . . . . . . . . 25

3.5 Illustration of boresight attitude control using precession . . . . . . . . . . . 28

4.1 Simple thermal model of MSC . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 Computer - Star Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.3 Computer - Bus Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.1 Sample observation during mission . . . . . . . . . . . . . . . . . . . . . . . 80

5.2 Deployment rate required for Radial configuration . . . . . . . . . . . . . . . 82

5.3 Required angular momentum for Radial configuration . . . . . . . . . . . . . 83

5.4 Thrust required for Radial configuration . . . . . . . . . . . . . . . . . . . . 84

5.5 Instantaneous linear speed for Triangle configuration . . . . . . . . . . . . . 86

5.6 Radial, angular, and out-of-plane displacements for Triangle configuration . 87

5.7 Elongation over time for steady-state model . . . . . . . . . . . . . . . . . . 89

5.8 Elongation over time for dynamic model . . . . . . . . . . . . . . . . . . . . 90

5.9 Instantaneous Linear Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.10 Potential Truss Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.11 Specific stiffness of Triangular and Square Truss Configuration . . . . . . . . 94

viii

LIST OF FIGURES ix

5.12 Shape memory behavior of thermoplastics . . . . . . . . . . . . . . . . . . . 96

5.13 Formation and Deployment using a Thermoplastic Matrix . . . . . . . . . . 97

5.14 Truss deployment scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.15 Typical Composite Laminate cross-section . . . . . . . . . . . . . . . . . . . 100

5.16 Typical Aluminum Laminate cross-section . . . . . . . . . . . . . . . . . . . 101

5.17 Columnation Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.18 Internal compartmentalization . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.19 Candidate HEO trajectory leading to lunar swingby . . . . . . . . . . . . . . 108

5.20 Solar radiation force at L2 as a function of spacecraft surface area . . . . . . 112

5.21 Diagram of simplified MSC showing solar radiation force . . . . . . . . . . . 114

5.22 Diagram of the initial and final tether lengths in the Triangle formation . . . 116

5.23 Illustration of how CG offsets in MSC can cause disturbance torques from

tether forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.24 Illustration of spool mechanism to adjust tether line of action on MSC . . . 119

5.25 MSC layout of major mass components causing CG offsets . . . . . . . . . . 120

5.26 Atmospheric drag force at perigee for different highly elliptic transfer orbits

as a function of spacecraft surface area . . . . . . . . . . . . . . . . . . . . . 122

5.27 Altitude of HEO during one orbital period . . . . . . . . . . . . . . . . . . . 123

5.28 Estimated gravity gradient torque during single HEO peroid . . . . . . . . . 124

5.29 Uplink S-band Receiving Diameter vs. Margin . . . . . . . . . . . . . . . . . 129

5.30 Uplink X-band Receiving Diameter vs. Margin . . . . . . . . . . . . . . . . . 130

5.31 Downlink S-band Data Rate vs. Margin . . . . . . . . . . . . . . . . . . . . 131

5.32 Downlink S-band Transmitting Diameter vs. Margin . . . . . . . . . . . . . 132

5.33 Downlink X-band Data Rate vs. Margin . . . . . . . . . . . . . . . . . . . . 133

5.34 Downlink X-band Transmitting Diameter vs. Margin . . . . . . . . . . . . . 134

5.35 Crosslink Diameter vs. Margin . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.1 Final CAD drawing of Triangle formation . . . . . . . . . . . . . . . . . . . 157

6.2 Schematic of Docking Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 159

6.3 Diagram of docking mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 160

x LIST OF FIGURES

6.4 Spool Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

6.5 ISF structure concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

6.6 Truss deployment scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

6.7 Truss on SPECS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

6.8 Rigid Components in Truss design . . . . . . . . . . . . . . . . . . . . . . . . 167

6.9 Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.10 Maximum Load Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

6.11 Strut Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

6.12 Strut Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

6.13 Final CAD drawing of MSC and CSC ADCS layout . . . . . . . . . . . . . . 178

6.14 CSC thruster configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

6.15 MSC thruster configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

6.16 Chart of average power requirement for each MSC at L2 . . . . . . . . . . . 186

6.17 Chart of average power requirement for CSC at L2 . . . . . . . . . . . . . . 187

6.18 Illustration showing stack height available in payload fairing . . . . . . . . . 194

6.19 Illustration showing stack configuration inside the Ariane 4 fairing . . . . . . 197

List of Tables

1.1 Needs for the proposed SPECS mission . . . . . . . . . . . . . . . . . . . . . 8

1.2 Alterables for the proposed SPECS mission . . . . . . . . . . . . . . . . . . . 8

1.3 Constraints for the proposed SPECS mission . . . . . . . . . . . . . . . . . . 9

2.1 List of performance and cost objectives . . . . . . . . . . . . . . . . . . . . . 12

3.1 Summary of ISEE-3 direct transfer trajectory to L1. . . . . . . . . . . . . . . 18

3.2 Excluded ADCS system-synthesis options . . . . . . . . . . . . . . . . . . . . 29

3.3 Included ADCS system-synthesis options . . . . . . . . . . . . . . . . . . . . 30

3.4 Photovoltaic solar cells and efficiencies . . . . . . . . . . . . . . . . . . . . . 41

3.5 Primary batteries and their characteristics . . . . . . . . . . . . . . . . . . . 42

3.6 Secondary batteries and their characteristics . . . . . . . . . . . . . . . . . . 42

4.1 Radiation properties and equilibrium temperatures . . . . . . . . . . . . . . 56

4.2 Thermal conductivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3 Cryogenic fluid parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4 Comparison of current backflow produced by electric propulsion systems . . 67

4.5 Normalized contamination produced by Hydrazine . . . . . . . . . . . . . . . 68

4.6 Normalized contamination produced by F2H2 . . . . . . . . . . . . . . . . . 69

4.7 Normalized contamination produced by Hydrazine . . . . . . . . . . . . . . . 69

4.8 Comparison of normalized contamination amounts for some common mono-

propellants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.9 Allowable particle contamination . . . . . . . . . . . . . . . . . . . . . . . . 70

xi

xii LIST OF TABLES

5.1 Direct transfer ∆V budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.2 Candidate HEO orbit parameters . . . . . . . . . . . . . . . . . . . . . . . . 108

5.3 Lunar swingby ∆V budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.4 Frequencies of the transponders and the DSN . . . . . . . . . . . . . . . . . 126

5.5 Thermal conductivity of various Multilayer Insulations . . . . . . . . . . . . 138

5.6 Organic mass contributing to outgassing . . . . . . . . . . . . . . . . . . . . 142

5.7 Byproducts of monomethyl hydrazine . . . . . . . . . . . . . . . . . . . . . . 143

5.8 MSC Propellant Mass vs. Mission Geometry . . . . . . . . . . . . . . . . . . 145

6.1 Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.2 Tether Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

6.3 Truss Element Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.4 Finalized mass and power of attitude sensors . . . . . . . . . . . . . . . . . . 176

6.5 Uplink Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

6.6 Downlink Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

6.7 Crosslink Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

6.8 MSC average and peak power requirements at L2 . . . . . . . . . . . . . . . 186

6.9 CSC average and peak power requirements at L2 . . . . . . . . . . . . . . . 187

6.10 MSC+CSC stack average and peak power requirements in HEO . . . . . . . 187

6.11 Cost estimates of the CSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

6.12 Cost estimates of the MSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

List of Acronyms

ADCS Attitude Determination and Control System

AHP Analytical Hierarchy Process

BER Bit Error Probability

BPSK Binary phase shift keying

C&DH Command and Data Handling System

C/L Crosslink

CMB Cosmic Microwave Background

COSMIC Constellation Observing System for Meteorology

CR Compression Ratio

CTA Cryogenic Telescope Assembly

D/L Downlink

DSN Deep Space Network

EIRP Equivalent Isotropic Radiated Power

FIR Far Infrared

FIRST Far Infra-Red Submillimeter Telescope

GaAr Gallium-Arsenide

GALEX Galaxy Evolution Explorer

GEO Geostationary Earth Orbit

GN&C Guidance, Navigation, and Control

GSFC Goddard Space Flight Center

GTO Geostationary Transfer Orbit

HEO Highly Elliptic Orbit

xiii

xiv LIST OF TABLES

HST Hubble Space Telescope

InP2 Indium-Phosphide

IOC In-Orbit Checkout

IR Infrared

IRAS Infrared Astronomical Satellite

ISEE International Sun-Earth Explorer

ISF Inflatable Space Frame

L1,L2 Lagrange Point 1,2

LEO Low Earth Orbit

LSS Laboratory Space Systems

MEO Medium-Orbit

MLI Multi-Layer Insulation

MOE Measures of Effectiveness

MS Margin of Safety

NAC Needs Alterables and Constraints

NASA National Aeronautics and Space Administration

NiCd Nickel-Cadmium

NiH2 Nickel-Hydrogen

OSG outer shell group

OSR Optical Solar Reflectors

R3BP Restricted Three Body Problem

RFP Request For Proposal

SDST Small Deep Space Transponder

SE-L1 Sun-Earth L1 (Lagrange Point)

SfHe Superfluid Helium

SGLS Space Ground Link Station

Si Silicon

SIRTF Space Infrared Telescope Facility

SMM Submillimeter

SNECMA Societe Nationale d’Etude et de Constructions de Moteurs d’Avions

LIST OF TABLES xv

SOHO Solar Heliospheric Observatory

SOI Sphere of Influence

SOME NASA’s Space Operations Management Office

SPECS The Submillimeter Probe of Evolution of Cosmic Structure

SSRM Srap-on Solid Rocket Motor

SUSI Sydney University Stellar Interferometer

TDRS Tracking and Data Relay Satellites

TPF Terrestrial Plane Finder

TSS Tethered Satellite System

TT&C Telemetry, Tracking, and Command System

U/L Uplink

USN Universal Space Network

UV Ultraviolet

VLTI Very Large Telescope Interferometer

VSD Value System Design

WMAP Wilkinson Microwave Anisotropic Probe

Nomenclature

αn neutral divergence angle

αa materials absorptivity

γ Material strain

γc proportional constant between the beam ion and neutral flux

γred reduction factor

∆he Momentum buildup from external disturbances

∆hsp Momentum buildup from solar radiation pressure

∆hsp Momentum change from solar pressure disturbance

∆Lavg Average change in tether length from spool

∆V Change in velocity

δ deflection

δs Lunar swingby orbit turning angle

δ(Tstruts) difference of the temperatures between the two bodies connected

�i infrared emissivity

ηp propulsion efficiency

η Efficiency of DSN antenna

ηP Power efficiency

ηProp Propulsive efficiency

ηth Thermal efficiency

θ angular distance of mirror spacecraft

θp angle from the central axis of the exhaust

thetat Transmitting Antenna Beamwidth

νcex frequency of collisions between the beam ions and the neutrals

xvi

LIST OF TABLES xvii

nui ion divergence angle

νs Lunar swingby orbit true anomaly

ρ radius of gyration

σ Material stress

σcex(vi) velocity-dependent charge-exchange cross-section

σcr elastic buckling stress

σh hoop stress

σm meridional stress

σt Stephan-Boltzmann constant

ψ cylinder geometric parameter

ωB Body frame angular velocity

ωs Matrix containing axial angular velocities of reaction wheels

ω angular rate of MSC

ωspool Spool spin rate

A cross–sectional area of tether

A Matrix of reaction wheel unit vectors in body frame

A1 cross–sectional area of longerons

AB cross–sectional area of the backflow

Ai cross–sectional area of the ion beam

An cross–sectional area of the neutrals

As Area exposed to Sun

Astruts cross-sectional area of the struts

Aw aperture weighing

as Lunar swingby orbit semi-major axis

bitso Number of bits in an observation

bitsc Number of bits after compressed

c Speed of light

cef end fixity coefficient

D diameter of mirror

Dplume distance from the thruster

xviii LIST OF TABLES

Dr Receiving Antenna Diameter

Dt Transmitting Antenna Diameter

dae accelerator-emitter distance

E modulus of elasticity

Eb/No Energy-to-Noise Ratio

es Lunar swingby orbit eccentricity

et Transmitting Antenna Pointing Offset

F required thrust for radial configuration

FC number of station contacts per week

Fcr critical load

Fs Solar constant

Fsl Lunar swingby orbit hyperbolic anomaly

Fsp Solar radiation force magnitude

Fsp Solar radiation force vector

fGHz Bandwidth Frequency in GHz

fnat natural frequency

G Modulus of rigidity

Gpt Peak Transmitting Antenna Gain

Gr Receiving Antenna Gain

Grp Peak Receiving Antenna Gain

Gs radiation of the sun at L2

Gt Transmitting Antenna Gain

g acceleration due to gravity

ge External torque acting on system

h angular momentum

ha Axial angular momenta of reaction wheels

hB System angular momentum in body frame

hspool Spool angular momentum

I Moment of inertia of system

IB current of the backflow charge-exchange particles

LIST OF TABLES xix

Icsc Moment of inertia of CSC

Ii current of the ion beam

Im Moment of inertia of MSC

Is Matrix containing axial momenta of reaction wheels

Isp specific impulse

Ispool Axial moment of inertia of spool

Itotal Total moment of inertia

i Sun incidence angle

J Inertia-like matrix relating system and wheel inertia matrices

k Boltzman’s Constant

k1, k2 material-dependent constants

kt thermal conductivity of the material used in the struts

L stretched length when tether is loaded

Lo unstretched length of the tether

La Propagation & Polarization Loss

Limp Implementation Loss

Ll Antenna Line Loss

Lpt Transmitting Antenna Pointing Loss

Lpr Receiving Antenna Pointing Loss

Ls Space Loss

Lstruts is the length of the struts

Lteth Initial tether length for Triangle

L′teth Final tether length for Triangle

le length of the emitter

M Moment to be applied by thrusters

mb beam mass

˙mloss mass loss rate

mm mass of MSC

mn mass of one neutral atom

mpcscd propellant mass for direct transfer

xx LIST OF TABLES

mpcscl propellant mass for elliptic phasing loops with a lunar swing–by

mpdus propellant mass for Upper Stage

mpmsc MSC propellant mass

mspool Mass of spool

˙Ncex number of particles in the backflow

˙Nsp number of sputter particles per second

nB number density of the backflow charge-exchange particles

nn number density of neutrals

npropellant moles of propellant used

P Power in dBW

Paxial axial load

Pcr critical buckling load

Peq equivalent axial load

Pw Power in Watts

p(t) forcing function

p(θ,Dplume) plume density profile

q Reflectance factor

R radius of longeron

RB contact dependent hourly rate

r radial distance of mirror spacecraft from central spacecraft

rspool Radius of spool

St sticking coefficient

§ Propagation Path Length

sf shielding factor

T Tether tension

Ta temperature of the anode

Tg glass transition temperature

Ts System Noise Temperature

TOF Lunar swingby orbit time of flight

t time

LIST OF TABLES xxi

tdl Time to download

Vcex volume of charge-exchange ions depending on the dimensions of the accelerator

vB velocity of the backflow charge-exchange particles

vn velocity of the neutrals

vi velocity of the ion beam

we width or diameter of the emitter

Y sputter yield

z out-of-plane distance

Chapter 1

Introduction

The Submillimeter Probe of the Evolution of the Cosmic Structure (SPECS) mission will

enable a comprehensive study of the origins of the modern universe. Data obtained from

SPECS will address the formation of stars from primordial matter and galaxies from pre-

galactic structures, the evolution of galaxies and cosmic structures, the history of energy

release, nucleosynthesis, and dust formation. To achieve these goals, SPECS will make ob-

servations in the far infrared and submillimeter (FIR/SMM) spectral regions. The FIR/SMM

region represents a wealth of astrophysical information. Half of the luminosity of the universe

and 98% of the photons released after the Big Bang are now observable at far IR wavelengths

(40 - 500 µm).1

The remainder of this chapter includes background information related to SPECS, defi-

nition of the problems to be addressed by the design, separation of the problem into relevant

elements, and a summary of the overall mission and remaining steps in the design process.

1.1 Background Information

SPECS is intended to be a rotating interferometer located in an orbit about the second

Lagrange point, L2. The interferometer formation consists of individual mirrors controlled

by tethers rotating about a central beam combiner. An observation is made by deploying

the tethered mirrors as the formation rotates, such that the resulting spiral pattern partially

or entirely covers the focal plane. The tethered mirrors must then be retracted, and the

1

2 CHAPTER 1. INTRODUCTION

process repeated for successive observations. The attitude of the entire constellation will

also be controlled to study numerous targets of scientific interest.2

1.1.1 Interferometry

Interferometry enables greater angular resolution without increasing the diameter of the

telescope lenses by using two or more telescopes in close proximity to one another. The

telescopes use the interference of the light waves emitted from the target to superimpose

multiple images from each telescope, and the image is resolved to produce one image of high

resolution. The radiation from the target reaches each telescope at different times because

the telescopes are different distances from the radiation source. When the waves reach two

telescopes in opposite phases at the same time, interference occurs and the target disappears.

Thus, dark fringes appear each time destructive interference occurs. Placing the telescopes

farther apart reduces the size of these fringes. Using spatial Fourier transform algorithms,

astronomers can understand the observed cosmic structure by examining the contrast and

visibility of the fringes. One disadvantage of all interferometers is their narrow field of view.

In 1801, Thomas Young demonstrated that light passing through apertures would form

interference patterns in dark fringes, which is the basic principle underlying the method of

interferometry. Albert Michelson and Francis Pease first applied interferometry to astronomy

at Mount Wilson in 1920 and 1921. Their purpose was to measure stellar diameters. Instead

of two telescopes, they placed two apertures on the Mount Wilson telescope, the largest

telescope at that time. This method enabled Michelson and Pease to measure the apparent

diameter of Betelgeuse because the star was larger than the fringe.3

Interferometry was initially used to improve ground-based observations. The resolution

of ground-based optical telescopes is limited to approximately one arcsecond despite the size

of the lens, due to blurring caused by the turbulent nature of Earth’s atmosphere.4 The best

ground-based observations today are available at Mauna Kea Observatory in Hawaii, where

the resolution is 0.5 to 0.6 arcseconds. This observatory consists of two 10-meter diameter

telescopes located 85 meters apart. Another operating interferometer is the Very Large

Telescope Interferometer (VLTI) in Chile, which consists of four 8-meter diameter telescopes.

The longest baseline now in existence is the Sydney University Stellar Interferometer (SUSI),

1.1. BACKGROUND INFORMATION 3

which has a resolution better than the Hubble Space Telescope (HST) by more than two

orders of magnitude. However, such long-baseline interferometers are extremely limited in

sensitivity.3

The next step in improving image quality is to use interferometry in space. This step is

analogous to constructing space-based optical telescopes, like the HST, which operate in orbit

to mitigate the blurring effects of the atmosphere. However, the observation of submillimeter

wavelengths requires even greater resolution to achieve the same quality of images as would

be obtained in optical wavelengths. The Space Interferometry Mission (SIM) is designed as

a space-based 10-meter baseline interferometer to be launched in 2009. SIM will observe

wavelengths in the visible region for the purpose of the detection of planets orbiting nearby

stars.5 SPECS will develop space interferometry further by increasing the baseline.

1.1.2 Tethers

Clusters of small spacecraft flying in formation may provide revolutionary capabilities for

a wide range of applications, including interferometric astronomy for investigation of the

structure of the cosmos, synthetic aperture radar for environmental studies, and military

surveillance missions. However, a group of satellites in orbit will tend to drift apart due to

various perturbing forces. Consequently, to hold the spacecraft in formation requires some

form of propulsion. For some applications, rockets or electric thrusters for formation flying

is an acceptable solution, but for many applications the propellant requirements would be

prohibitive. Tethers Unlimited Incorporated is currently working with a team of engineers

and scientists led by NASA-Goddard to develop small, lightweight tether systems that will

enable satellite clusters to fly in formation for long durations without expending excessive

propellant.6

Space tethers are long cables in space that are used to couple spacecraft to each other

or to other masses and that allow the transfer of energy and momentum from one object to

another. In a momentum-exchange tether system, a long high-strength tether is deployed

from a facility in orbit and set into rotation around a central body. The tether system

is placed in an elliptical, equatorial orbit and its rotation is timed so that the tether is

oriented vertically below the central facility and swinging backwards when the system reaches


perigee.7 At that point, a grapple mechanism located at the tether tip can rendezvous with

and capture a payload moving in a lower orbit. Half a rotation later, the tether can release

the payload, tossing it into a higher energy orbit. This concept is termed a momentum-

exchange tether because when the tether picks up and tosses the payload, it transfers some

of its orbital energy and momentum to the payload, lowering the tether system’s apogee.7

The first mission of the Tethered Satellite System (TSS-1), launched 31 July 1992 aboard

the space shuttle Atlantis, deployed an electrically conductive 1.6 m diameter satellite that

was tethered to the Orbiter by a conductive tether.6 The goals of the TSS-1 mission were to

demonstrate the feasibility of deploying and controlling long tethers in space, and to evaluate

some of the unique applications of the TSS as a tool for research by conducting exploratory

experiments in space plasma physics. The TSS hardware has several major elements: the

deployer system, that raises the satellite for release, reels out (and in) the tether cable, and

nestles the satellite back in the payload bay for return to Earth; the tether that connects the

satellite to the Shuttle and acts as a conductor and an antenna; the satellite that contains

science instruments; and the carriers that hold the TSS in the Shuttle’s cargo bay.8

The deployer system raises the satellite for release, reels the tether cable in and out, and

safely nestles the satellite back in the cargo bay for return to Earth. With a mass of 2,027 kg

(∼ 4,470 lb), the system includes a deployment boom, the satellite support, the tether reel,

and a system that powers the satellite before deployment, motor controls, and equipment to

acquire data.9

The tether reel mechanism controls the length, speed, and tension of the tether. The

tether reel carries 22 km (∼14 miles) of conducting tether, the level wind mechanism, and

the reel motor.8 The motor control assembly and a data acquisition assembly control the

tether reel mechanism. The reel can deploy the tether at 16 km (∼ 5 mi) per hour.8

1.1.3 Lagrange Points

Orbit design using Lagrange points is typically described in the literature using the Restricted

Three Body Problem (R3BP).10 The R3BP concerns two massive bodies revolving in circular

orbits around their center of mass under the influence of their mutual gravitational attraction,

and the resulting orbital motion of a third, much smaller body. The libration or Lagrange

1.1. BACKGROUND INFORMATION 5

points are five equilibrium points in the gravitational field that are apparent when the system

is analyzed from a rotating reference frame fixed to the line joining the two massive bodies.

In the vicinity of the Earth, the systems of interest are the Sun-Earth and the Earth-Moon

systems, giving a total of 9 possible Lagrange points, excluding the L3 point on the far side

of the Sun.11

The first basic formulation of the R3BP appears in Euler’s memoirs on his second lu-

nar theory, which was written nearly 200 years ago.11 In 1772, the French mathematician

Lagrange identified the five equilibrium points that now bear his name.12 Two Lagrange

points in the Sun-Earth system, the so-called “L1” and “L2” points, have unique astronau-

tical characteristics. Both lie on the line joining the two massive bodies, with L1 located

between the Earth and the Sun, and L2 located on the far side of the Earth. These points

have gathered the interest of space mission designers since the late 1960’s, with numerous

missions planned or currently operating.10

The L1 point is ideal for solar observations or taking measurements of the interplanetary

environment upstream from the Earth. The first spacecraft to orbit around a Lagrange point,

International Sun-Earth Explorer 3 (ISEE-3), had such a mission. ISEE-3 was launched on

August 12, 1978, and was injected into a “Halo orbit” around L1 on November 20, 1978. A

Halo orbit belongs to a special class of unstable periodic orbits in the vicinity of libration

points. Occasional stationkeeping maneuvers are required to maintain this orbit, due to the

inherent instability. In the case of ISEE-3, the Halo orbit had a period of approximately

6 months, and passed slightly above and below the ecliptic plane. The term “Halo” comes

from the shape of the orbit when viewed from the Sun-Earth line. In other words, when

viewed from this rotating reference frame, the spacecraft appears to orbit in a halo around

the libration point. ISEE-3 made fifteen stationkeeping maneuvers during its halo-orbit

phase from November 1978 to September 1982.12

The Solar Heliospheric Observatory (SOHO) is another spacecraft to use an L1 orbit to

make measurements of the Sun. SOHO was launched on December 2, 1995, injected into

a Halo orbit similar to that of ISEE-3 on February 14, 1996, and is currently operating.

One motivation for SOHO’s placement is that measurements of the solar wind can be made

about an hour before it reaches Earth, allowing for solar “weather predictions.” Conversely,


one downside of the L1 point is that unless the Halo orbit is large enough, solar noise would

interfere with communication transmissions from the spacecraft.12

The L2 point has characteristics favorable to certain missions as well. The viewing

constraints placed on sensitive instruments can be lessened since the Earth, Moon, and Sun

all lie in the same general direction. This nearly constant geometry can also assist in the

design of the communication subsystems. Additionally, the 1.5 million kilometer distance

from the Earth creates a relatively benign radiation and thermal environment.12

The first spacecraft to be positioned around L2, the Wilkinson Microwave Anisotropic

Probe (WMAP), was launched on June 30, 2001 on a Delta-II launch vehicle and is currently

operating. WMAP is a differential microwave radiometer designed to make high fidelity

maps of the cosmic microwave background (CMB). The Lagrange point L2 is a suitable

operating location for such a mission due to the low microwave emission, magnetic fields,

and other disturbances associated with geocentric orbits that would reduce the quality of

scientific observations.13 WMAP is in a Lissajous orbit, a member of the general class of

unstable orbits along with Halo orbits,12 which in this case requires about four stationkeeping

maneuvers per year. The transfer trajectory from Earth to L2 took advantage of a Lunar-

swingby maneuver, which reduced onboard propellant requirements.14

Another spacecraft slated to orbit around L2 is the Terrestrial Planet Finder (TPF)

Mission. TPF is part of NASA’s Origins Program and will seek to identify terrestrial plan-

ets around neighboring stars. One TPF design candidate is similar to SPECS, namely a

formation-flying infrared interferometer. TPF will take advantage of the low cost to deliver

mass to an L2 orbit as compared with a comparable heliocentric orbit. Another benefit is

that repair or servicing missions to L2 are more feasible than heliocentric orbits, should the

need arise. TPF is currently in the design phase, with a projected launch sometime within

the next decade.15

1.2 Problem Definition

The entire SPECS mission will involve many disciplines, such as aerospace, electrical, and

mechanical engineering, each to be incorporated in the development of the subsystems of

1.2. PROBLEM DEFINITION 7

SPECS. Orbital trajectories, orbit stationkeeping, spacecraft attitude control, and spacecraft

formation flying are a few of the astronautical factors of the mission. Electrical engineering

will be used in the design for the communications and data handling, propulsion, and power

subsystems. Power system specialists will be needed to assure adequate power generation

at L2. The thermal control subsystem will require special attention from thermodynami-

cists and mechanical engineers. The structural mechanics of SPECS, including the complex

dynamics of the tether system will require a mechanical engineering approach. Mission plan-

ners and managers must allocate available funds, assure successful mission operation, and

incorporate the astronomy base that will ultimately make use of acquired data. All of these

professions must interact during the entire design process, and optimize the spacecraft design

given available funds.

The design of the SPECS constellation is the primary scope of this project. The space-

craft constellation consists of the central beam combiner spacecraft, the individual mirror-

spacecraft, and the tether system. The scope does not include design of the optical systems;

however they must be properly sized to meet overall design criteria. Also, the scope does

not include the design of a dedicated launch vehicle. Rather a pre-existing launch system

will be chosen that best meets the design requirements. In order for the SPECS mission

to be successful, the spacecraft constellation and subsystems must act to fully support the

operation of the optics payload.

Numerous societal sectors will be involved in the design and operation of SPECS, as well

as the consumption of acquired astronomical data. SPECS is the collaborative project of

a number of government and academic institutions, but primarily falls under the direction

of NASA Goddard Space Flight Center (GSFC) in Greenbelt, Maryland. The management

and operation of the mission will likely involve both NASA and the Department and Defense

(DoD) for various mission segments. The international astronomy community will be integral

in determining targets of scientific interest, and must work closely with mission operators

to assure SPECS resources are used in an optimal manner. Additionally, educators and the

general population will benefit by whatever discoveries SPECS may find.

The needs, alterables, and constraints of the SPECS mission are summarized in Tables

1.1,1.2, and 1.3.


Table 1.1: Needs for the proposed SPECS mission

Need Short Description

5-year lifetime Must operate reliably for 5 years

Observations of wavelength

40 ≤ λ ≤ 500µm

Range of the observations in the FIR/SMM

Variable interferometer

baseline

Retractable tethers must cover a circular area of 10 m to

1 km in diameter

Boresight attitude control Able to change line-of-sight to different targets

Thermal protection IR instruments need shielding from external and internal

thermal sources

Table 1.2: Alterables for the proposed SPECS mission

Alterables Short Description

Numbers of mirrors Minimum of three, but subject to change

Tether mechanisms Deployment and retraction methods can vary

Launch vehicle Depends on payload mass and constellation deployment

method

Orbit design Variable transfer trajectory and Halo orbit design

All subsystem level designs Individual subsystems are subject to change due to in-

terdependencies

Material selection Will vary depending on available technology

Propulsion method Will vary depending on orbit design and attitude control

requirements

1.3. RELEVANT ELEMENTS 9

Table 1.3: Constraints for the proposed SPECS mission

Constraints Short Description

Tether-controlled formation Constellation must use tethers

L2 location Constellation must operate in orbit about L2

Radial distance from center

to mirrors

Change in distance must be held to within 10 cm

Mirror position with respect

to center

Must be measurable at all times to within 0.5 µm

Mirror position with respect

to observation plane

Must not exceed 10 cm in direction normal to plane

Observation period Time to conduct observation must not exceed 3 × 105

seconds

Dimensions of observation

spiral pattern

Must be annulus of inner radius ≈ 10 m and outer radius

1 km, with gaps no bigger than the equivalent of 1 mirror

radius

Instantaneous linear speed

of spacecraft

Must not exceed 1 m/s at all times

Payload Sun-angle Angle between anti-sun direction and boresight axis must

never exceed 20◦

Payload pointing range Observation plane must be capable of reorientations up

to 40◦ from initial attitude

Payload slew maneuver Must be accomplished within 105 seconds, including set-

tling time

1.3 Relevant Elements

The main elements of the SPECS mission design consist of launch, transfer trajectory, inser-

tion into an L2 orbit, initial deployment, regular operation, and retirement. Each of these

stages will influence subsystem design.

The spacecraft design will depend on available launch vehicle limitations, which in turn


will affect the characteristics of the launch trajectory. Different methods of orbit insertion

such as LEO parking orbit, transfer trajectories, and lunar-swingby methods must all be

considered. Once at L2 the propulsion system must insert SPECS into an orbit that meets

the observation and stationkeeping requirements.

After achieving orbit about L2 and performing any necessary checkout procedures, SPECS

will begin its regular operation. Tasks will include collection and storage of scientific data,

transmitting data and receiving commands from Earth through the communication subsys-

tem, and normal operation of all subsystems.

Of primary concern is the operation of the tether system, which determines the dynam-

ics of the formations used for observations. Each observation will include deployment and

retraction of the tethers, resulting in a spiral pattern to sweep out the focal plane. This pro-

cess must be repeated in a reliable manner for successive observations during the operational

lifetime. The issues associated with retirement of the spacecraft at L2 will be considered.

1.4 Summary

The proposed SPECS mission will lead to scientific breakthroughs in the field of FIR/SMM

astronomy. Information obtained from this mission will aid in answering some of the re-

maining questions regarding the formation of the universe.

Interferometry with cryogenically cooled Michelson mirrors and photon counters allows

for the investigation of the FIR wavelengths, the least explored in the electromagnetic spec-

trum. SPECS also takes advantage of the L2 environmental conditions. Unique to SPECS

is the use of a tether system in conjunction with formation flying and observations. SPECS

utilizes a thermal subsystem capable of handling the strict thermal requirements of the

payload.

Chapter 2

Value System Design

2.1 Introduction

The purpose of this chapter is to describe a Value System Design (VSD) that is used to eval-

uate the overall quality of the SPECS mission design. The VSD is based on the requirements

established by the needs, alterables and constraints (NAC) previously discussed in Chapter 1.

The measures of effectiveness (MOEs), defined in the objective hierarchy, specify the quanti-

ties to be maximized or minimized. The MOEs can be grouped into two primary categories:

cost and performance. Different combinations of the design alterables are evaluated using

the VSD, with interactions existing between each subsystem. Also, an analytical hierarchy

is developed to further aid in evaluating design alternatives in a systematic manner.

2.2 Objectives

The mission objectives are listed in Table 2.1, with a separation between performance and

cost objectives. The performance objectives consist of criteria to ensure optimal subsystem

operation while meeting mission requirements. Also shown in Table 2.1 are the subsystem

or subsystems that are most affected by these objectives.

Maximizing the power and thermal efficiency reduces power subsystem mass, and im-

proves payload performance by lowering the mirror operating temperature. Data handling

performance is maximized by improving computer processing rate, computer storage capabil-

11

12 CHAPTER 2. VALUE SYSTEM DESIGN

ity, and communication efficiency. Material selection involves maximum thermal efficiency,

material strength, and structural integrity. The performance of the attitude and orbit con-

trol subsystem is optimized through maximizing position accuracy, pointing precision, and

minimizing stationkeeping, slew time, response time. Finally, mission lifetime is maximized,

which is affected by all the spacecraft subsystems.

Table 2.1: List of performance and cost objectives and

related subsystems

Objective Related Subsystem(s)

Performance

Maximize power efficiency Power

Maximize thermal efficiency Thermal, Payload

Maximize computer capability C&DH

Maximize material strength Structures and Mechanisms

Maximize position accuracy ADCS, Structures and Mechanisms

Minimize stationkeeping ∆V Propulsion, GN&C

Minimize slew time ADCS

Minimize response time ADCS

Maximize propulsive efficiency Propulsion

Maximize pointing accuracy ADCS, GN&C

Maximize lifetime All

Cost

Minimize mass All

Minimize mission operation costs Management, C&DH

Minimize production costs All

The remaining objectives consist entirely of minimizing cost. Decreasing spacecraft mass

results in decreasing costs, primarily because the launch costs are reduced. The overall

spacecraft mass will obviously be dependant on the combined mass of all the subsystems.

Minimizing production cost is a straightforward method of reducing cost, and is achieved by

2.2. OBJECTIVES 13

using off-the-shelf technology and reducing research costs, which are assumed to be affected

by all subsystems. The cost of mission operation, including the cost to operate ground

facilities, conduct scientific observations, collect and manage data, and overall maintenance

and program management, is also minimized.

The performance and cost objectives and their associated MOEs can be seen in the

objective hierarchy in Figure 2.1. The objective hierarchy gives a graphical representation

of the separation between performance and cost, with the MOE for each objective contained

in a box on a lower level of the hierarchy. The border style of objective-level boxes is used

to indicate which objectives are either maximized or minimized.

Figure 2.1: Objective hierarchy for value system design

Interactions between subsystems show competing mission objectives. Structural integrity,

thermal subsystem efficiency, and propulsive efficiency are all maximized, which increases

mass due to extra hardware. However, one objective states that spacecraft mass is minimized


to reduce launch costs. Minimizing stationkeeping and time to perform attitude maneuvers

requires increased command authority from the attitude determination and control system

(ADCS), which corresponds to increased propulsion, guidance, navigation, and control hard-

ware and associated mass increase. Mission lifetime is maximized, which competes with the

goal of reducing mission operation costs. Contradicting mission objectives are expected, and

show that a systematic approach to evaluating designs is preferred for such situations. One

method, the Analytical Hierarchy Process, is described in the following section.

2.3 Analytical Hierarchy Process

An Analytical Hierarchy Process (AHP) is a systematic method for comparing predefined

lists of alternatives. The result of creating an AHP is a list of weights, which can be directly

multiplied to normalized values for the MOEs to obtain a numeric measure for the quality

of a given design.

The AHP is given as a chart in Figure 2.2. The center of the chart consists of a matrix,

with mission objectives from the objective hierarchy contained in the rows and columns along

the edges. The numbers in the center of the matrix form a pairwise comparison matrix, where

the number in the ith row and jth column represents the relative importance of objective i,

Oi, compared with objective j , Oj. A scale ranging from 1 to 9 is used for the comparisions,

where the members of the matrix, aij, are defined as

aij = 1if the two objectives are equal in importance

aij = 3 if Oi is weakly more important than Oj

aij = 5 if Oi is strongly more important than Oj

aij = 7 if Oi is very strongly more important than Oj

aij = 9 if Oi is absolutely more important than Oj

Likewise, the reciprocals of the above values are used for comparing Oj with Oi. Next, the

weights are obtained by calculating the sum of each column, then dividing each column by

the corresponding sum. Lastly, the sum of each row in the normalized matrix is found, which

becomes the final AHP weights to be applied to the MOEs.

2.4. SUMMARY 15

The method of selecting the values of aij in the above matrix is somewhat subjective. The

decisions were based on the available information on SPECS, such as the NACs in Tables

1.1 through 1.3 and the information presented in Chapter 1. Even without the AHP, it is

assumed that each requirement will be met by the final design. However, the values of aij

represent the group’s collective intuition on the level of added importance each objective

should receive in order to assure the best design. The highest weight was chosen to be 20%

for the maximization of position accuracy. Since a successful mission relies on the correct

control of the mirrors during the observation periods, this result is intuitive. That is, even

if the all the spacecraft are functioning and in “good health,” the formation is useless if the

mirrors cannot be commanded to sweep out the desired area for an observation. Also, the

thermal efficiency receives a high weight of 18%. The rationale for this weight is that the

mirrors and optics must be operate at the correct temperature in order to collect useful data.

If the photon measurements are contaminated by waste heat from the spacecraft, again the

formation would be rendered useless. Overall, the other objectives receive lower weights.

The next highest group – material strength, stationkeeping, propulsive efficiency, and mass

– each receive weights of 9%. These objectives are not necessarily critical to the operation of

SPECS, but cost effectiveness and performance would increase substantially if they receive

more attention in the final design.

2.4 Summary

Defining performance and cost objectives allows SPECS to accomplish its mission with the

optimal design. The realization of these objectives depends on a thorough understanding of

the interactions between subsystems. Additionally, trade-offs will be made considering the

contrasting nature of the relationships between performance and cost. Once numeric values

for the MOEs are calculated in later Chapters, the AHP is useful to systematically evaluate

different design options.


Figure 2.2: Analytical hierarchy for value system design

Chapter 3

System Synthesis

This chapter describes alternatives for the subsystems and major aspects of the SPECS

mission. Options are given for the mission geometry, tether configuration, ADCS, com-

munication system, ground systems, retirement, and the thermal, power, and propulsion

subsystems. The advantages and disadvantages of each option and application to SPECS is

discussed. This chapter is used as a basis for analysis that occurs in the following chapter.

3.1 Mission Geometry

The first step in the orbit design process is to divide the spacecraft’s mission into different

phases based on their overall function. These phases include launch, parking orbit, transfer

orbit, and operational orbit. This step is done here in Chapter 3, which results in different

options for the mission geometry. Chapter 4 includes a comparison of the orbit-related

mission requirements and the system synthesis options for the orbit segments, after which a

design review of the best orbit choices is discussed.

3.1.1 Launch

As mentioned in section 1.2, the scope of the SPECS design does not include the design of a

new launch vehicle. Therefore, the most suitable launch vehicle for the mission will be chosen

from the existing pool of launch vehicles on the market. Important factors when considering

17

18 CHAPTER 3. SYSTEM SYNTHESIS

a launch vehicle include cost, payload accommodation (mass, volume, launch loads, etc.),

destination (LEO, GEO, interplanetary, etc.), and the launch vehicle’s success rate. The

geographic location of the launch system, including the launch pads and support facilities,

determines the allowable launch inclinations, and affects the initial orbit into which the

spacecraft is inserted. Additional launches may be necessary if SPECS components (MSC

and CSC) are launched separately and not as a single unit.

3.1.2 Transfer Orbits

Two options for transfer trajectories to L2 are direct transfer and lunar gravity-assist swingby

trajectories. The ISEE-3 spacecraft used a direct transfer to L1, and serves as an illustrative

example since L1 and L2 are collinear libration points and are approximately equal distance

from Earth. A summary of the ∆V maneuvers for this transfer is given in Table 3.1. The

first midcourse correction accounted for launch vehicle errors, whereas the second was a

scheduled trajectory-shaping burn. The NGST is also considering a direct transfer to L2

instead of using a lunar swingby.16

Table 3.1: Summary of ISEE-3 direct transfer trajectory

to L1.

Mid-course

#1

Mid-course

#2

Halo orbit

insertion

Total

∆V (m/sec) 17.7 24.3 12.0 54.0

Days from launch 1 26 100 100

The lunar gravity-assist swingby method is another option for a transfer trajectory to

L2, which decreases the overall propellant needed to conduct the transfer maneuver. The

Moon’s gravitational field is relatively weak, but has been proved to be effective at changing

spacecraft trajectories as early as 1959 when the Soviet space probe Luna-1 used a lunar

flyby to transfer into a heliocentric orbit. The ISEE-3 spacecraft used a double lunar swingy

to study the Earth’s magnetotail after spending time at L1.12 A single lunar swingby method

was used successfully by the WMAP spacecraft to assist in its transfer to L2.17 One disad-

3.1. MISSION GEOMETRY 19

vantage of the lunar swingby method is a potentially more restrictive launch window, since

the timing for the rendezvous between the spacecraft and the Moon must be more carefully

controlled than a simple direct transfer. Options to reduce these restrictions are described

in the section on parking orbits.

3.1.3 Parking Orbits

A parking orbit is a temporary orbit that provides a stable and safe location for the spacecraft

to perform checkout tasks, as storage between mission phases, and for end-of-life disposal.

A parking orbit can be used to match conditions between mission phases, such as between

launch and transfer orbits.18

A typical parking orbit used by many kinds of spacecraft is a simple low earth orbit

(LEO) with low eccentricity. These orbits are well known, simple to control, and provide

good communication links with ground stations. Another parking orbit option is a series of

highly elliptic phasing orbits leading to a lunar swingby. The WMAP spacecraft was the

first spacecraft to use such a parking and transfer orbit combination, and the procedure used

by WMAP was as follows. The last stage of the launch vehicle performed the burn needed

to inject the spacecraft into the high eccentricity orbit. This orbit had a perigee altitude

extending nearly to the Moon’s orbit height of 400,000 km. The launch vehicle upper stage

then de-spun and separated from the spacecraft. The WMAP spacecraft performed three

orbits in this manner, and then used a ”trailing swingby” of the moon to begin its transfer

to L2.17 Instead of making corrections during a direct transfer from LEO, like NGST,16

WMAP corrected launch vehicle errors in the parking orbit before the lunar flyby.12

A parking orbit might also be used for combining the SPECS formation if its components

are launched separately. While this option is heavily dependent on the final mass of SPECS

and the launch vehicle selection, there still exists the possibility that the individual spacecraft

will be launched separately and docked while in orbit. One option is to join the spacecraft

while in parking orbits early in the mission, such as in LEO or in elliptic phasing loops.

Another option is to send each element to L2 individually, then attempt to join the spacecraft

while in the Halo orbit. In either case, a complicated docking procedure would warrant

good communication links and knowledge of spacecraft telemetry, whether it is performed


autonomously or manually.

3.1.4 Orbit at L2

The SPECS mission calls for an operational orbit at L2. Options for orbits around libration

points, such as Halo orbits, were discussed briefly in Chapter 1. General descriptions are

given here, followed by comparisons in Chapter 4.

There exists a family of unstable orbits about L2, such as Halo, Lissajous, and Lyapunov

orbits. Lissajous orbits typically have a shape that changes over time, but not in a periodic

manner. The ratio of the in-plane and out-of-plane amplitudes are independent and arbitrary.

A special kind of Lissajous trajectory is a Halo orbit, which is characterized by only one

amplitude that depends on both the in-plane and out-of-plane directions. When modelling

perturbing effects, “near-Halo” or “Halo-type” orbits are obtainable using numerical patching

techniques.19 Lyapunov orbits are another type of planar periodic orbit.10 However, the

actual type of “Halo orbit” used for SPECS will be analyzed in following chapters. Thus,

the Halo orbit characteristics that are discussed here are more general in nature, and relate

to the overall mission geometry and subsystem interactions.

One important parameter of the Halo orbit is the amplitude, which describes the size of

the orbit when viewed along the x-direction in the R3BP (from the primary to the secondary

bodies). Typical Halo orbit amplitudes range from approximately 200,000 to 600,000 km.

Another halo orbit parameter, which is closely related to the amplitude, is the ∆V needed

to inject into the orbit. For planar halo orbits about collinear libration points (L1 and L2),

the ∆V for injection approaches zero as the amplitude is increased.12 Other work has been

done on finding “stable manifolds,” which describe ranges of optimal transfer trajectories to

L1 and L2 from Earth parking orbits.19 Lastly, the amplitude of the Halo orbit also directly

affects how much stationkeeping ∆V is required to maintain the unstable orbit.

3.1.5 Mission Geometry Summary

Options for the mission geometry are given for the launch, transfer orbits, parking orbits, and

Halo orbits that could possibly describe the SPECS mission. The launch type depends on the

3.2. TETHER CONFIGURATION 21

capabilities of the selected launch vehicle. The transfer orbit options include direct transfer

or lunar-swingby trajectories. The parking orbit options depend largely on the combination

of launch and transfer orbits selected, as well as spacecraft launch configuration. Types

of parking orbits include LEO and highly elliptical phasing orbits. Many specific Halo

orbit types exist, but one must be chosen based on orbit amplitude, insertion costs, and

stationkeeping costs. The amplitude of the Halo orbit must also extend beyond the Earth’s

magnetotail to avoid unwanted effects of operating in such a harsh environment.

3.2 Tether Configuration

The structures and deployment method of SPECS must work together as one unit and

operate without problems in order to gather the sharpest images. Maintaining the constant

angular momentum of SPECS minimizes the need for propulsion, but one problem with

tethered arrangements having only subaperture masses, is the ”ballerina” effect.20 As the

masses move radially closer to the center, the spin rate increases by one over the square

of the radius, moving the subapertures faster than the sampling time required to minimize

image blur. This section discusses options for the overall tether configuration of SPECS,

some of which were gathered from the literature, as well as original ideas.

3.2.1 Tether Options

SPECS can have counter masses to disable the increase in spin rate or alternate the tether

configuration to control the spin rate. Without the use of counter masses, to control the

increase in spin rate, the structures of the mission would be too complex and difficult to

control. The tethers would have to be designed with an extra mechanism to be able to

control the spin rate by reeling in/out at predetermined periods of time to slow the spacecraft

down. There would also have to be excess amounts of propellant used during the lifetime

of the mission (5 years) to keep SPECS steady enough to accomplish the mission and stay

within its constraints. To control the spin rate without propellant, countermasses are used

in the tethered arrangement. Each subaperture would have its own counter mass to disable

the“ballerina” effect. The following are two possible configurations that would allow SPECS


to complete its main objectives using counter masses.

3.2.2 Hex

Figure 3.1: “Hex” configuration.20

Figure 3.1 shows a pendulum-type arrangement. As the pendulum-connected subaperture

reels out, the counter mass reels in with a 1:1 ratio. The radial reel-in speed required to

sample the aperture plane in 105 seconds, is 2.5 mm/s with an initial rotational speed of

0.0165 RPM(revolutions per minute).20 It produces a Coriolis acceleration in which the

reeled-in element leads the hub attachment point by an angle, and the reeled-out element

lags by that same angle. That way, the subaperture and counter-mass tethered elements

approach each other by twice the angle in the spin plane. The central hub radius (17

meters) is chosen to keep the total approach angle (lead + lag) no greater than 20 degrees.

The initial radial length of the tethers is 577 m from the hub center, which provides a baseline


of 1000 m (1 km).

3.2.3 Tetra-Star

Figure 3.2: “Tetra-Star” configuration.20

Another possible arrangement of SPECS is the configuration in Figure 3.2. Triangles

are used as the basic shape to give the tethered arrangement in-plane shape rigidity. The

three counter masses are located at the apex of the outer three triangles, in which the two

legs of each outer triangle are of a constant length tether.20 The base of the outer triangles

forms the inner triangle, where the subapertures are located in each corner. The length of

this tether constitutes the interferometer baseline. The three tethers, which change length

to spiral in and out, fully sample the u-v plane. Each of the three inner tethers has a tether-

winch on one end, and a passive in-line spring/damper suspension system on the other end.

For a standard observation, the reel-in rate of the inner tethers is 4.28 mm/s, with an initial


rotational speed of 0.0165 RPM.20

3.2.4 Triangle

Some possible SPECS configurations do not use countermasses, such as the Triangle con-

figuration illustrated in the top of Figure 3.3. In this configuration, three variable-length

tethers attach the mirrors while the central spacecraft rotates in the middle of the config-

uration gathering the photon data. The tethers connecting the mirrors retract and deploy

to sweep out the focal plane. Previous work has focused on modelling the dynamics and

controllability of this formation.21

Figure 3.3: “Triangle” and ”Triangle+Radial” configuration options


3.2.5 Radial Tethers

Another configuration that does not utilize countermasses is the radial tethers method (Fig.

3.4). In this formation, three identical variable length tethers are deployed and retracted

from the central spacecraft with the use of a spooling mechanism for each individual tether.

Each tether is approximately 600 meters in length to allow the maximum baseline of one

kilometer to occur once the tethers have been fully deployed. By performing simple dynamics

analysis on this configuration, it will need some work since the central spacecraft will not

be spinning at the same rate as the mirror spacecrafts, which causes a problem in the data

collection process and therefore the sharpness of the images.

Figure 3.4: Radial configuration option for SPECS


3.2.6 Triangle+Radial Tethers

The last configuration option is the triangle with the use of additional tethers to attach the

central spacecraft to the rest of the formation. This formation is illustrated in the bottom

of Figure 3.3. The addition of tethers allows for the central spacecraft to spin at the same

rate as the rest of the components. Also since the central spacecraft is connected to the

rest of the structure, it does not allow it to drift from the formation during deployment or

retraction when comparing it to the previous configuration, where there were no additional

tethers connecting the mirrors to the central spacecraft.

3.2.7 Tether Summary

SPECS must be configured such that all of the constraints to be met. Three configurations,

which do not use counter masses, are presented. A configuration without the use of coun-

termasses is complex and increases the complexity of the structure subsystem. Two other

configurations using counter masses as an option are discussed. All five configurations allow

SPECS to achieve its mission objectives, but each has advantages and disadvantages, which

are analyzed in Chapter 4.

3.3 Attitude Determination Control System

The ADCS is responsible for attitude determination and control of both the individual

SPECS spacecraft and the formation as a whole. Thus, the subsystem must be capable of

controlling the relative attitude of the mirror spacecraft with respect to the beam combiner,

as well as the attitude of the focal plane with respect to an inertial target. Therefore,

this section on the ADCS is closely related to options for the overall tether configuration

of SPECS. First, the control-mode options are discussed. Then, the actuator and sensor

options for these different control modes are given.

3.3. ATTITUDE DETERMINATION CONTROL SYSTEM 27

3.3.1 Control Modes

The first step in the design of the ADCS is to define the control modes used by the spacecraft

throughout the mission lifetime. These modes are determined by the mission requirements,

the mission geometry, and the type of insertion used by the launch vehicle.18 The mis-

sion requirements are described in detail in Tables 1.1-1.3, along the mission geometry was

described above in Section 3.1.

The first control mode is during the orbit insertion, which is the period during and after

boost when the spacecraft must be brought to a particular orbit, either an initial parking

orbit or its final orbit. Here, the attitude control options include spin stabilization or 3-axis

stabilization.18

Acquisition is the initial determination of the attitude and the stabilization of the space-

craft. This mode is typically used after orbit insertion, or after some emergency situation

when the spacecraft is returning from a safe mode condition.18 Possible candidates for safe

mode control schemes should 1) maintain communication links with ground stations 2) pre-

vent sensitive subsystems (such as the payload) from pointing at the Sun 3) allow other

subsystems that are intended to point at the Sun (such as solar panels) to continue doing

so. This mode essentially allows for the minimum control needed to assure the spacecraft

will not damage itself while ground controllers (or on-board systems) attempt to solve any

problems. Thus, the control mode here would likely also use spin stabilization or 3-axis

control.

The normal, on-station control mode shares some characteristics with the safe modes,

with added requirements related to the interferometry observations. The same pointing

constraints listed in the safe mode still apply. The added portion concerns the orientation of

the boresight axis during actual observations. The boresight axis is the axis perpendicular to

the focal plane, which corresponds to the centerline of the virtual telescope made up by the

interferometer formation. This axis must be reoriented to acquire new astronomy targets,

and is constrained from pointing towards the Sun.

Two options exist for the reorientation of the formation’s boresight axis. The first option

is to retract all the mirrors and/or counter-masses that might be deployed and secure them


Figure 3.5: Illustration of boresight attitude control using precession

physically using a latching or docking mechanism of some kind. Once the entire formation

is combined as a unit, a central collection of attitude actuators will reorient the formation.

Once the reorientation occurs, the mirrors and/or counter-masses can be re-deployed, and the

process repeated. The second option is to reorient the entire formation while the separate

spacecraft are still deployed and spinning about the boresight axis. This process can be

accomplished in a manner similar to the precession of an ordinary rigid body, such as a

spinning disk after applying a lateral moment to the axle. An illustration of this principle

is given in Figure 3.5. Since the formation as a whole is obviously non-rigid, the separate

elements in the formation must somehow “feel” a perturbing force perpendicular to the

“disk” (focal plane). This idea has been discussed in previous research, and it has been

argued that this precession can be accomplished by using thrusters located on each separate

body, firing perpendicular to the focal plane.20 Thus, the boresight attitude can be reoriented


by causing the formation to precess to a new direction in a controlled manner, then stopping

the precession.

The first option has the benefit that potentially fewer components of ADCS hardware

need to be located on each element in the formation. If all elements are retracted and secured

to the beam combiner, then only the beam combiner needs to have the control authority

to slew the boresight axis. A disadvantage of this approach is that there will likely be

many complicated mechanisms and procedures needed to perform these repeated docks over

the course of the operational lifetime. An advantage of the precession approach is that the

tethers need not be retracted as often, but conversely, more ADCS hardware must be located

on each element.

3.3.2 ADCS Options

The two types of hardware used by the ADCS consist of sensors to determine the current

attitude of the spacecraft, and actuators to control the attitude. Some kinds of ADCS

hardware or methods can be excluded immediately from consideration on SPECS, such as

gravity gradient stabilization or magnetic torque coils, since they are designed to function

only near the Earth. These excluded options, as well as remaining options typically used by

spacecraft ADCS can be seen in Tables 3.2 and 3.3.

Table 3.2: Excluded ADCS system-synthesis options

ADCS Component or Method Description

Actuators

Gravity gradient stabilization Too far from Earth gravity field

Magnetic torque coils/rods Too far from Earth magnetic field

Sensors

Earth horizon sensor Too far from Earth

Magnetometer Too far from known Earth magnetic field


Table 3.3: Included ADCS system-synthesis options

ADCS Component or Method Description

Actuators

Thrusters Different fuels available, rapid control pos-

sible

Spin stabilized Mainly applicable for formation as a whole

Momentum/reaction wheels Fine-tuned control possible

Control moment gyro (CMG) High rates possible

Sensors

Star trackers Accurate inertial-sensing possible

Sun sensors Not accurate, but simple and cheap

Rate gyros Numerous types, accurate relative-sensing

possible

Sun sensors provide a cheap and reliable means to determine the direction to the Sun,

and numerous sensors can be placed around the spacecraft at various locations. Besides

being used by the ADCS to determine the attitude, the Sun direction will likely be needed

by the power, thermal, and overall fail-safe subsystems to ensure safe and efficient operation.

Star trackers are typically larger than other types of sensors and require more power and

computing capability. However, they provide accurate inertial attitude knowledge, and would

be a necessity for this kind of astronomical observatory. Rate gyros come in many different

varieties (optical, mechanical, resonating, etc.) and are useful for determining the relative

attitude of the spacecraft.18 Since each kind of sensor mentioned here has individual pros

and cons, and attitude determination algorithms are typically used that take advantage of

numerous sensors, SPECS will likely use a combination of these sensors.

Different options exist for ADCS actuator selection and placement as well. The included

actuator options in Table 3.3 are all well known and have been used extensively in the

past. Fine-tuned attitude control, as would be needed during observations, might be best

accomplished using momentum wheels. Coarse attitude control, as would be needed during

stationkeeping maneuvers or during transfer to L2, might be best accomplished using gas


thrusters. Also, if momentum wheels are used during normal operation, thrusters would

be necessary to provide external torque to allow for momentum dumping. This momentum

build-up is a result of persistent perturbing torques acting on the spacecraft, and the resulting

spinning-up of the momentum wheel to compensate. In the case of SPECS, solar radiation

pressure acting on a large solar shield/power array might cause considerable disturban

specs: submillimeter probe of the evolution of the cosmic structure...

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