HYPER Industrial Feasibility Study

Transcription

1 HYPER Industrial Feasibility Study Executive Summary / Final Report Document Number HYP-9-04 Authors: Dr. Walter Fichter, Dr. Ulrich Johann Date: 25 June 2003

2 Astrium GmbH Page 2 Distribution List Name Company Giorgio Bagnasco Phil Airey Ruediger Reinhard ESA/ESTEC ESA/ESTEC ESA/ESTEC Ernst Maria Rasel Philippe Bouyer Arnaud Landragin IQO, Uni Hannover IOTA, Paris SYRTE, Paris Ulrich Johann Walter Fichter Steve Kemble Astrium GmbH Astrium GmbH Astrium Ltd Giovanni Cherubini Galileo Avionica Stephan Theil ZARM

3 Astrium GmbH Page 3 Change Record Issue Date Change Description

4 Astrium GmbH Page 4 Table of Contents 1. INTRODUCTION SCOPE AND BACKGROUND SCIENTIFIC OBJECTIVE AND MEASUREMENT PROCESS OBJECTIVE MEASUREMENT PROCESS 7 2. SYSTEM REQUIREMENTS PERFORMANCE BREAKDOWN CRITICAL REQUIREMENTS AND FUNCTIONAL INTERCONNECTION ORBIT SELECTION PAYLOAD MODULE OPTICAL BENCH REQUIREMENTS DESIGN AND ANALYSIS RESULTS PRECISION STAR TRACKER REQUIREMENTS PST DESIGN FEATURES MEASUREMENT ERROR ANALYSIS GUIDE STAR SELECTION PAYLOAD-PLATFORM INTERFACE THERMAL INTERFACE MECHANICAL INTERFACE SECONDARY AOCS REQUIREMENTS AND PHASE DISTURBANCE REJECTION DESIGN CONCEPT DISTURBANCE FORCES AND TORQUE, AND CONTROL BANDWIDTH SECONDARY AOCS ARCHITECTURE SIMULATION RESULTS SIMULATION PROCEDURE OUTLINE STEADY STATE PERFORMANCE RESULTS FURTHER RESULTS AND IMPLICATIONS COMPONENT TECHNOLOGY DRAG-FREE SENSOR MICRO-PROPULSION CONFIGURATION, MASS, AND POWER CONFIGURATION BUDGETS 34

5 Astrium GmbH Page MASS POWER ON-GROUND TESTING PROGRAMMATICS 37

6 Astrium GmbH Page 6 1. Introduction 1.1 Scope and Background Cold Atom Interferometry is an emerging field with great interest in the physics community. It can be applied for extremely precise measurements of angular rates and linear accelerations. In order to fully exploit its potential it was recently proposed to apply this technique in space, where the limitations due to the 1-g environment are eliminated. Therefore, the European Space Technology Center (ESTEC) together with a science team led by the Institut für Quantenoptik (University of Hannover) started a project for hyper-precision cold atom interferometry in space (HYPER). The first industrial feasibility study was carried out by a consortium led by Astrium GmbH. The major results are reported in this executive summary. The HYPER mission aims primarily at the test of General Relativity by mapping the spatial structure of the gravitomagnetic (Lense-Thirring) effect of the Earth, i.e. the latitude dependent frame dragging in the vicinity of a rotating mass, with a precision of 10%. This requires the (differential) measurement of miniscule (integrated) angular rates and attitudes. The local angular rates and attitudes are measured by cold atom interferometers and referenced to a distant inertial frame by a precision star tracker, respectively. This is shown in Figure 1-1. Besides a superior measurement accuracy, the two devices have to be extremely stable aligned to each other and therefore, are integrated on an optical bench. In order to keep the measurement devices within their operational envelope, a dedicated drag-free and attitude control system has to provide a quite environment in terms of residual rates, accelerations, and pointing accuracy. These concepts lead to stringent performance requirements for the spacecraft and payload design. Equatorial plane frame dragging measured by HYPER Local inertial frame: probed by ASU rotation rate Global reference: distant guide star pointing with star sensor (PST) Accuracy Requirement rad/sec one year interval Global reference: guide star position Local reference: ASU rotation rate PST line of sight Figure 1-1: Principle of measuring the Lense-Thirring effect. 1.2 Scientific Objective and Measurement Process Objective The scientific objective of the HYPER mission is the verification of the Lense-Thirring effect in a near

7 Astrium GmbH Page 7 Earth orbit by means of an atomic Sagnac unit (ASU) and a precision star tracker (PST). The 3accuracy of the differential measurement between the precision star sensor and the atomic Sagnac unit over lifetime (i.e. after one year of signal integration) shall be at least 10 percent of the peak value over one orbit. The LT effect occurs at double orbit frequency. For the presently selected 1000 km orbit, the peak value is rad/sec. Therefore, for this altitude the 3 measurement accuracy shall be less than rad/sec Measurement Process The a simplified way the verification of the LT effect can be explained by 4 steps as follows: Step 1: The rates transverse to the presicion star tracker line of sight are measured with the ASU and then integrated numerically. This signal contains the LT effect (rate or integrated rate, respectively) ASU t ( t) ( LT )d n ASUd ASU (t) 0 n ASU is the ASU noise, ASU (t) denotes mechanical misalignment that affects the ASU measurements. is the inertial rate, the index LT denotes the additional rate contribution due to the Lense-Thirring effect. Step 2: The attitude / angles transverse to the precision star tracker line of sight are measured by the PST PST t ( t) d n PST PST (t) 0 n PST is the PST noise, PST (t) denotes mechanical misalignment that affects the PST measurements. Step 3: The two measurements are subtracted. The resulting signal contains the LT effect (integrated) and disturbances. t 0 ( t) : ASU (t) PST (t) LT (t) n ASUd n PST t 0 (t) Here, (t) is the difference between the angle measured by the ASU and the PST. It can be seen that this signal represents the Lense-Thirring effect, under the condition of negligible errors and the elimination of other differential effects. (t) is the alignment angle between ASU and PST. It is t) (t) (t). ( ASU PST Step 4: The difference signal (t) is filtered in order to obtain the LT contribution (at LT frequency). The filter function is given by the actual data processing algorithms that will be applied to flight data. These algorithms are not yet completely defined at this stage. However, the filter characteristics has a significant effect on the requirements specifications. Therefore, a conservative and feasible filter behaviour was assumed for the subsequent requirements breakdown and design of the spacecraft.

8 Astrium GmbH Page 8 The frequency response is shown in Figure 1-2. Figure 1-2: Filter behaviour of the data processing algorithms.

9 Astrium GmbH Page 9 2. System Requirements 2.1 Performance Breakdown Starting with the scientific objective of the HYPER mission, a thorough performance requirements breakdown was performed. This is shown in Figure 2-1. On a top level ( level-0 ), the requirements can be divided into 4 groups. The numerical values for the top-level requirements are listed in Table 2-1. LT measurement accuracy 2.2e-15 rad/sec ASU measurement accuracy ASU-PST alignment & stability PST measurement accuracy ASU operational envelope Level-0 gravity gradient knowledge PST/OB alignment PST internal high frequency linear acceleration dynamic range Level-1 geopotential model geopotential pos. knowledge geopotential att. knowledge self gravity OB/RRM alignment PST/OB alignment stability OB/RRM alignment stability External high frequency PST internal low frequency External low frequency timing/jitter drag-free point acceleration from angular motion acceleration from thermo-elastic motion rate dynamic range Level-2 magnetic environment rotation of rigid body timing/jitter rotation from thermo-elastic motion radiation grav. grad. knowledge (for compensation) alignment (set of reqs.) alignment RRM/FI and RRM/AA Figure 2-1: Performance requirement breakdown. Req. # Requirement Value (3) R0-ASU Rate measurement accuracy rad/s R0-PST PST measurement accuracy rad R0-ALN Alignment between ASU-frame and PST-frame rad R0-ENL Provide functional envelope for ASU and PST n/a Table 2-1: Values for Level-0 requirements

10 Astrium GmbH Page Discussion of Requirements and Functional Interconnection The Level-0 requirements are briefly discussed in the following and the most critical lower level requirements are addressed. ASU measurement requirements. The rate measurement accuracy of the ASU is not directly part of the study, but represents a constraint to the rest of the performance requirements breakdown. However, in order to obtain accurate measurements, precise knowledge of the gravity gradient is required. This leads to stringent requirements for the modelling precision of the geo-potential and to self gravity gradient requirements. Precision Star Tracker measurement requirements. The required star tracker accuracy requirement is extremely stringent. There are two main contributors to the error budget: the centroiding error and the noise equivalent angle. This leads to a challenging start tracker design ASU-PST Alignment requirement. Any alignment variation between the ASU and the PST that occurs with LT frequency mimics a LT effect. Therefore, the alignment has to be extremely stable at double orbit frequency. This requirement leads to a challenging design of theoptical bench, together with a thermal control system. ASU Operational envelope requirements. In order to obtain unambiguous interferometric measurement (i.e. remain in the central fringe), the residual accelerations and rates must be kept within a range that corresponds to about 1/10 of the central fringe. This leads to a challenging drag-free and attitude control system. In Figure 2-2 the main components of the HYPER spacecraft are shown and their interdependence in terms of function and performance is outlined.

11 Astrium GmbH Page 11 Configuration, Mass, and Power (6) Payload/Platform Interface (5) thermal/mechanical Thermal Subsystem (5) thermal interface mass/power mech. design alignment stability launcher Optical Bench (2) sensor configuration phase disturbance rejection ASU Secondary AOCS (4) gravity gradient model measurement accuracy Precision Star Tracker (3) Orbit (1) measurement and control accuracy force, torque disturbances technology Micro-Propulsion & Drag-Free Sensor (4) Figure 2-2: Performance interconnection between components.

12 Astrium GmbH Page Orbit Selection 3.1 Orbit Altitude Trades and Requirements The orbit shape and orientation of the orbit is basically determined by the mission: In order to obtain a signature of the Lense-Thirring effect, the orbit is required to be near-polar. A stable thermal environment requires a Sun-synchronous orbit. Thus, the only free parameter to be selected is the orbit altitude. The following effects drive the orbit altitude selection: Higher altitude leads to degradation of Lense-Thirring effect increased radiation smaller launch mass Lower altitude leads to increased aerodynamic disturbances for drag-free control increased gravity gradient model error Moreover, the launch cost impose a constraint on the orbit altitude. Assuming an affordable Rockot launch, the limitation for a 1000 kg satellite is an altitude of about 1000 km. Of all the above effects, the gravity gradient model error is most driving. Investigations have shown that for an altitude of 1000 km the gravity gradient error requirements of /s 2 on ground, /s 2 on board can be fulfilled with a gravity gradient model of order 20 on ground and of order 2 on board. This is still a reasonable effort. Even a second order gravity gradient model provides an accuracy in the range of /s 2, see Figure E E E-10 8E-11 6E-11 4E-11 2E-11 0 Longitude (deg) Lat Figure 3-1: Error of a second order geo-potential model with respect to a 10 th order model (truth).

13 Astrium GmbH Page Implications of the Increased Orbit Altitude In summary, the baseline altitude of 1000 km has the following impact. Positive implications The gravity gradient can be modelled accurately enough with reasonable complexity, as explained above. The aerodynamic disturbance become relatively small. High frequency aerodynamic noise disturbances need not to be actively controlled. The observation time increases by 10 percent, due to less observation day with eclipses. This is good. Negative implications The magnitude of the Lense-Thirring effect degrades by about 12 percent. This is still acceptable. The radiation is still within acceptable limits, i.e. no exceptional electronics has to be used. The launch mass limitation is 1000 kg, which is a number that can be met, see mass budget below. In order to obtain a Sun-synchronous orbit at altitude 1000 km, the inclination has to be 99.5 deg.

14 Astrium GmbH Page Payload Module 4.1 Optical Bench Requirements The optical bench is one of the most challenging components of the HYPER spacecraft. The major requirements for the optical bench can be summarised as follows. ASU-PST alignment stability An alignment stability between the ASU and the PST of rad (3) is required, in the frequency range from Hz to 0.15 Hz. This corresponds to a spectral density of rad/sqrt(hz) in this frequency range. At lower frequencies, the stability is relaxed according to a 4 th order filter. The constant misalignment (zero frequency) shall be better than 1 arcsec. This is the crucial requirement. It is verified by detailed thermo-elastic analysis based on a finite element (FE) model Minimise mass The optical bench is one of the major mass contributions. The mass minimisation is in contradiction to the alignment stability. Accommodation of drag-free sensors Accommodate two drag-free sensors with its connection line ( DFS axis ) coincident with the intersection line of the two ASU planes. In this case any angular acceleration around the PST boresight (which is controlled by a conventional star tracker) leads to linear accelerations perpendicular to the ASU planes, see Figure 4-1. These do not have any impact on the ASU operational envelope and thus, the system is robust with respect to the control system around the PST boresight. Drag-Free Point ASU plane 1 ASU Plane 1 r z =0 TZ DFS2 TX TY d x /dt acceleration due to angular X motion not critical DFS1 PY PX ASU Plane 2 r y =0 DFS1/2 ASU plane 2 PZ Figure 4-1: Accommodation of drag-free sensors.

15 Astrium GmbH Page Design and Analysis Results Baseline Design The baseline configuration of the optical bench is shown in Figure 4-3. The bench itself consists basically of 4 modular elements plus the precision star tracker, see Figure 4-2. The following elements are connected to the optical bench: Atom preparation benches Drag-free sensors Precision star tracker Fiber injectors Retro-reflecting mirrors Bench Modular Architecture Figure 4-2: Modules of optical bench. Three mounting points (interface pads) are foreseen for the mechanical support interface. The length of the optical bench is about 700 mm. The dimensions of the whole assembly are shown in Figure 4-4. The optical bench structure itself is the vacuum enclosure for the ASU drift tube. This eliminates the implementation of mirrors. For high alignment stability the need for extremely low CTE values are required. Moreover, the mass minimisation requirement leads to the need of a low density of the optical bench material. This led to the selection of ULE material as a baseline.

16 Astrium GmbH Page 16 Figure 4-3: Optical bench configuration. Figure 4-4: Optical bench dimensions. Mass The total mass of the optical bench and precision star tracker including a margin of 10 % is 275 kg. This value excludes the mass of atomic assemblies (denoted ASU in Figure 4-3), drag-free sensors ( DFS ), and laser benches.

17 Astrium GmbH Page 17 Alignment Stability The alignment stability was analysed with a detailed FE model. The following thermal interfaces were used for this analysis: Radiation: The optical bench is considered de-coupled with respect to radiation from the environment. De-coupled means a temperature variation of less than 1 mk. Conduction: A temperature variation of 0.1 K with orbit frequency is assumed at the mechanical interfaces (mounting pads) of the optical bench. The validity of these interface assumptions is verified in a separate analysis of the thermal control system, which is outlined further below. With the above assumptions, the alignment analysis results in a maximum misalignment angle of rad over one orbit which is a factor of 2 larger than the requirement ( rad). Since there is a linear relation between temperature variation and misalignment, the interface temperature variation has to be about half of the above value in order to meet alignment requirement. This means the thermal control system has to guarantee a temperature variation of 0.05 K. Then the alignment requirement is met. 4.2 Precision Star Tracker Requirements Besides the optical bench also the precision star tracker has to meet stringent performance requirements. The most severe performance requirement is the following: The measurement accuracy within the frequency range of Hz and 5 Hz shall be < rad = 2.5 marcsec 10 Hz sampling frequency. This requirement can be further divided according to the following major contributors: Errors originated by the PST Centroiding error, requirement: arcsec (3) Noise Equivalent Angle, requirement: arcsec (3) Errors originated externally Aberration, approximately v/c [rad], where v [m/sec] is the spacecraft s velocity and c [m/sec] is the speed of light. The aberration will not be treated within the error budget as explained below PST Design Features The PST design features are summarised in Table 4-1.

18 Astrium GmbH Page 18 Optical configuration: Ritchey-Chretien telescope Focal length 36 m F number 190 FOV ±25 arcsec CCD number of pixels 1024x1024 CCD pixel size 13 micron IFOV arcsec Integration time 100 ms, jitter < 1 ms magnitude range 2 V 4 Centroid algorithm Based on a 17x17 pixels tracking window Table 4-1: Summary of PST baseline configuration Measurement Error Analysis Noise Equivalent Angle and Centroiding Error A detailed error analysis was carried out for the assessment of the PST measurement performance. The results for the major error contributions. the centroiding error and the noise equivalent angle error, are plotted over one pixel in Figure 4-5 and Figure 4-6, respectively, for different start colours. It can be seen that the requirements are fulfilled and that the major contributor, the centroiding error, is linear over one pixel. Linearity is very important since in this case a Gaussian error distribution, which is the basis for the overall performance breakdown, is not destroyed by any non-linearity. This leads to the requirement for the attitude control system to keep the star spot always within the central pixel of the CCD. Figure 4-5: Centroiding error over one pixel.

19 Astrium GmbH Page 19 Figure 4-6: Noise equivalent angle over one pixel. 1 pixel Figure 4-7: Non-linearity of centroiding error over several pixels. Aberration The angular measurement error due to the orbit velocity of the spacecraft ( aberration ) is in the order of v/c, where v is the spacecraft velocity and c is the speed of light. This yields a measurement error with an amplitude of about 4.5 arcsec, at orbit frequency. Clearly, this value is much larger than one pixel size and therefore, aberration must not be considered for spacecraft control purposes. Instead, the star spot is always centred in the central pixel, as it is required from the consideration given above. This introduces rate oscillations which are measured by the ASU. However, the rate oscillations are still within the limits tolerable by the ASU Guide Star Selection A guide star catalogue was composed of 48 stars with magnitude between 2 and 4. In Figure 4-8, the direction of the guide stars are plotted. The declination range correspond to the orbit geometry and the smallest angular separation in right ascension is 26.4 deg (requirement: < 30 deg). The latter is the maximum slew angle that has to be performed when changing the guide star.

20 Astrium GmbH Page 20 Figure 4-8: Guide stars as a function of right ascension and declination. 4.3 Payload-Platform Interface Thermal Interface Thermal Concept The thermal concept is based on a de-coupling of payload and platform as far as possible: the side walls are MLI covered and the anti-sun side is used as radiator. The central cylinder is actively controlled by heaters and in addition a inner shield is implemented to further de-couple the payload from temperature variations at the central cylinder. Optionally, coolong straps could be added to remove dissipated heat from the atom preparation boxes (denoted ASU in the figure) however, analysis showed that this is not necessary. In fact, the thermal system is feasible and simpler when this option is dropped.

21 Astrium GmbH Page 21 Figure 4-9: Thermal control concept. Analysis Approach and Results Two steps were carried out for the thermal analysis. 1. Thermal balancing of radiator to find design drivers. 2. Analysis based on a simple thermal model of the payload (several nodes) in order to assess damping effects and thus, verify the thermal interface assumption that were used for the thermo-elastic FE analysis, and to assess box temperatures. Using the nominal area of the anti-sun side as radiator results in a radiator temperature of about 20 degc. With an extended are as large as the solar array, the resulting radiator temperature is about 8 degc. For the second analysis step a mean radiator temperature of 15 deg C was selected.

22 Astrium GmbH Page 22 Figure 4-10: Temperature levels and temperature variations. The results of the second analysis step are shown in Figure 4-10, for a temperature variation input of 0.5 K from thermal control A realistically achievable performance of the temperature control of 0.05 K at the central cylinder leads to the following results: A temperature variation of 0.73 mk at the optical bench. This is compliant with the assumption of radiation de-coupled that was used for thermp-elastic analysis. A temperature variation of 0.67 mk at the drag-free sensor. This is complaint with the drag-free sensor specification. A temperature variation of 0.05 K at the mechanical support interfaces of the optical bench (as assumed for the optical bench thermo-elastic analysis) does not require any thermal damping from the mounts itself. Therefore, this is a conservative result. Temperature levels of the ASU and DFS of about 30 deg C and 27 deg C, respectively, see Figure This is still within reasonable and feasible limits. An important point for the ASU design is that sufficient radiation area is kept in future design modifications. Any changes will lead to different temperature levels Mechanical Interface The optical bench is supported on the central cylinder with isostatic mounts. One of the interfaces is shown in Figure It supports two translation degrees of freedom and is flexible along the third degree of freedom. Thus, three mounts are required for a 6 degree of freedom support, which is depicted in Figure 4-12.

23 Astrium GmbH Page 23 Figure 4-11: One mechanical interface between optical bench and central cylinder. Figure 4-12: Optical bench, central cylinder and three isostatic mounts.

24 Astrium GmbH Page Secondary AOCS 5.1 Requirements and Phase Disturbance Rejection In order to obtain unambiguous phase measurements from the ASU, an operational envelope in terms of rotational rate, and linear and angular acceleration has to be maintained. This envelope is defined by the following performance requirements for residual rates and accelerations (3): Linear acceleration < m/sec 2 Angular acceleration < rad/sec 2 Rotation rate < rad/sec Rotation around boresight < 10-6 rad/sec The requirements are comparable to the requirements of the GOCE spacecraft. The phase measurement scheme, the disturbance sources, and the rejection mechanisms are sketched in Figure 5-1. There are 3 major mechanisms that attenuate and/or reject phase measurement disturbances: 1. The ASU itself acts as a low pass, since it is operated as a sampled device with a sampling ( corner ) frequency of 0.3 Hz. 2. The ASU has to have a built-in phase correction mechanism that rejects low frequency disturbances. Here, low frequency means time constants of 8 h or more. This is actually the same mechanisms that is required to acquire the central fringe of the measurement. 3. There is a drag-free control loop that rejects phase disturbances in the range between 8 hours and 0.3 Hz in order to meet the above requirements. The three mechanisms are shown in Figure 5-2, together with the frequency ranges where they are effective.

25 Astrium GmbH Page 25 low frequency servo loop a GG estimate Internal ASU phase correction GG estimate r C,A estimate GG r C,A compensation of gravity gradient acceleration gravity gradient acceleration a GG laser frequency phase Drag-free and attitude control disturbance (drag, etc.) spacecraft a, ddt Other effects (magnetic, self gravity, thermo-elastic motion) Atom Interferometer Figure 5-1: Functional measurement diagram. DFS Noise FEEP Noise acceleration Drag-Free Control ASU Sampling acc@asu ASU Phase Control Equivalent ASU Disturbance frequencies < control bandwidth Disturbance very low frequencies < typically 3.5e-5 Hz (8 hours) Disturbance frequencies > 0.3 Hz (sampling frequency) Figure 5-2: Phase disturbance rejection mechanisms. 5.2 Design Concept Disturbance Forces and Torque, and Control Bandwidth Deterministic Disturbances The major contributors to the disturbance forces and torque are listed in Table 5-1. The frequency of these disturbances is in the order of the orbit rate and below. In order to achieve the required acceleration level, a rejection of typically 60 db is needed. For this, a relatively moderate closed loop control bandwidth is sufficient.

26 Astrium GmbH Page 26 In conclusion deterministic disturbances are not a driver for controller design however, they drive the sizing of the propulsion system. The required thrust level is significantly higher than the one for SMART-2. Source Forces Torque Gravity gradient < 150 micro-n < 80 micro-nm Aerodynamic 34 micro-n, < 120 micro-n < 100 micro-nm Magnetic n/a < 50 micro-nm Solar pressure < 20 micro-nm negligible Table 5-1: Disturbance forces and torque. Stochastic Disturbances The major random disturbance contributors for the linear acceleration are the micro-propulsion thrusters and the aerodynamic disturbance. Their effect in terms of acceleration is shown in Figure 5-3, together with the requirement specification. For this computation, the ASU sampling effcet and the closed drag-free control loop with a bandwidth of 0.01 Hz is assumed. Also from Figure 5-3 it can be seen that also for stochastic disturbances drag-free control is required only at frequencies below about Hz, for micro-propulsion noise rejection. Spectral Densities m/sec 2 /sqrt(hz) Linear Acceleration: Requirement and Disturbance Rejection Requirement FEEPs AeroDistMax Accel@ASU Frequency [Hz] Figure 5-3: Linear acceleration requirement and disturbance rejection.

27 Astrium GmbH Page Secondary AOCS Architecture Functional Diagram The functional block diagram of the Secondary AOCS is shown in Figure 5-4. This diagram also includes components that are used for both, Primary and Secondary AOCS tasks (GPS receiver, 3- axis star tracker). GPS Receiver inertial position Gravity Gradient Estimate Estimated gravity gradient To ASU for compensation purposes 3-axis attitude Star Tracker x-axis attitude X-Axis Attitude Controller PST DFS 1 DFS 2 y/z-attitude 3-axis linear accelerations Y,Z-Axis Attitude Controller X,Y,Z-Axis Linear Acceleration Controller Thruster Selection FEEPs 4 sets of 4 thrusters each Actuation signal for each FEEP thruster Figure 5-4: Secondary AOCS architecture. Drag-Free Sensor and Thruster Arrangement In Figure 5-5 the configuration of the drag-free sensors with respect to the ASU planes and the PST boresight is shown. The connecting line between the drag-free sensors is coincident with the ASU plane intersection line. The PST boresight is parallel. This results is a configuration that is insensitive to angular accelerations around the boresight. Drag-Free Point PST boresight ASU Plane 1 DFS2 ASU Plane 2 DFS1 Figure 5-5: Drag-free sensor configuration. The thruster configuration is shown in Figure 5-6. It is relatively simple and results in a simple thruster actuation logic. Furthermore provides redundancy and a maximum clearance with respect to the solar arrays.

28 Astrium GmbH Page Y Z X Solar Array Figure 5-6: Thruster arrangement. Modes, Sensor Acquisition, and Re-Orientation Duration The following Secondary AOCS modes are foreseen: Inertial Pointing Mode. In this mode the DFS and PST have to be initialised. The DFS acquisition is driven by the gravity gradient and the maximum range is in the order of 10-6 m/sec 2. The misalignent between 3-axis star tracker and PST is about 50 arcsec. The PST field of view is 25 arcsec. Thus, a scan strategy for the guide star is necessary. The inertial pointing mode includes also re-orientation manoeuvres. Science Mode. In this modes science measurements are taken. Hold Mode. Control with respect to star spot at initialisation. Control Mode. Control star spot at zero position and keep it there. The duration of a re-orientation manoeuvre is composed of 1. time needed for the slew manoeuvre itself and 2. settling time to achieve steady state conditions. The time for the slew manoeuvre itself is plotted in Figure 5-7. A typical 30 deg slew takes about 0.37h. As a conservative estimation, the total manoeuvre including settling takes typically less than one hour. The maximum rate and acceleration during the manoeuvre is rad/sec and rad/sec 2, respectively. This means, that both, drag-free sensor and 3-axis star tracker can remain switched on/ operational during the slew.

29 Astrium GmbH Page Time [h] Slew Angle [deg] Figure 5-7: Slew time as a function of slew angle. 5.3 Simulation Results Simulation Procedure Outline A detailed simulation campaign of the closed loop drag-free and attitude control system was carried out. About 20 different sets of test cases were executed. The purpose of the simulation campaign was two-fold: Tuning, evaluation and validation of drag-free and attitude control Confirmation of the PST measurement error distribution In order to take into account the filtering effect of the ASU phase control mechanism (< LTfrequency/10) and the ASU sampling effect (> 0.3 Hz), the simulated data was post processed with a bandpass with a frequency characteristics as shown in Figure 5-8. For the nominal simulations a small drag-free sensor bias of 10-9 m/sec 2 was assumed. The conclusions for realistic drag-free sensor biases is given below. Simulation runs were performed for the baseline control system that relies on two drag-free sensors, and an optional control system that is based on only one of the nominally accommodated drag-free sensors.

30 Astrium GmbH Page ASU velocity attenuation characteristic Bode Magnitude Diagram -40 Magnitude (db) ASU acceleration attenuation characteristic Frequency (Hz) Figure 5-8: Filter effect of the ASU. Two test scenarios were considered: 1. Acquisition of the PST, i.e. the Hold (Sub-) Mode of the Science Mode. These simulations take about several hundred seconds. 2. Steady state performance behaviour, i.e. the Control (Sub-) Mode of the Science Mode These simulations take typically 1.5 orbits Steady State Performance Results The results of the steady state performance for the baseline design (two DFS) and the optional design (one DFS) are summarised in Table 5-2, together with the performance requirements. It can be seen that most requirements are met with the following exceptions: Optional control system with one DFS: The acceleration exceeds slightly the requirement however, at this stage this is not considered to be problematic. The angular rate around the Y and Z axis exceeds the requirement. The reason is the angular motion that is caused by controlling the guide star in the centre of the PST central pixel, i.e. not considering / compensating any aberration effect caused by the spacecraft orbital motion. Remember that this strategy is necessary for sufficient accurate PST measurements (error distribution). A time history is shown in Figure 5-9, which shows nicely the deterministic effect in the Y and Z rates. Since the original rate requirement specification is derived such that it corresponds to 1/10 of the central fringe, it might be possible to re-specify this parameter with a somewhat relaxed number say, 30 % more, without affecting the operational environment of the ASU.

31 Astrium GmbH Page 31 Table 5-2: Drag-free and attitude control simulation results. Figure 5-9: Simulation time histories.

32 Astrium GmbH Page Further Results and Implications Transitions from Primary to Secondary AOCS With initial conditions of 1 arcsec/sec and 15 arcsec in rate and attitude, the transition from the Primary AOCS to the Secondary AOCS was demonstrated. The initial rate is a factor of 5 larger than typical steady state rates of the Primary AOCS, based on a 3-axis star tracker. The PST field of view is 25 arcsec. Drag-Free Sensor Usage It is shown that attitude control can be implemented based on PST attitude information only. Drag-free sensor information is not required for attitude control (angular acceleration). Number of Drag-Free Sensors Simulations demonstrated that the drag-free control is possible with only one drag-free sensor, using a gravity gradient model to place the drag-free point. This gives a potential for either mass savings or redundancy. Normal PST Measurement Distribution Evaluation of the simulation time histories shows that the PST error remains approximately normally distributed (with guide star controlled to the centre of the CCD). This validates the assumption applied for the overall performance breakdown. Rate Error due to Aberration The orbital motion creates an inertial rate that exceeds the requirement specification. The latter has to adapted in the future. This change of the operational envelope should have no impact on the ASU function and performance. Robustness The control system shown insensitive behaviour to parameter uncertainties such as: mass properties, including products of inertia 10 % thruster mismatch, which leads to coupling between linear and angular motion environment disturbances and spacecraft magnetic dipole directions variation of the distance between spacecraft CoM and drag-free point (5 10 cm) maximum PST centroiding error Drag-Free Sensor Bias The drag-free control with a bias of 10-5 m/sec 2 is not feasible, since thruster saturation weakens the attitude control in the Y and Z axes. A bias of 10-7 m/sec 2 is feasible technologically and from a control point of view. It adds another 50 micro-n force demand per thruster (in one axis only, since the bias is caused by the gold wire necessary for discharge). Optionally, in order to avoid additional force demand (maximum thrust), low frequency acceleration biases can be filtered out in the closed loop control system. This means that low frequencies will not be controlled by drag-free control, but by the ASU phase correction mechanism. However, this leads

33 Astrium GmbH Page 33 to an initialisation problem of the drag-free control filters and long transients. 5.4 Component Technology Two elements of the Secondary AOCS that are most demanding from a technological point of view: the drag-free sensor and the micro-propulsion system. The requirements for these components with respect to the HYPER specific application are compared with the requirement specifications for missions currently under development (GOCE and SMART-2) Drag-Free Sensor The GRADIO sensor to be flown on the GOCE mission meets all requirements with the following two exceptions: No data for launch load data was available The constant bias part must be improved in order to minimise the maximum thrust demand. A value in the range of 10-7 m/sec 2 seems to be achievable. It is limited by the gold wire necessary for the test mass discharging Micro-Propulsion Both, Indium and Caesium FEEPs could be applied for the HYPER mission considering specifications of these systems. Minor modifications with respect to GOCE and SMART-2 are necessary, such as different thruster arrangement and slight increase of thruster actuation frequency. However, this is not considered to be an issue. In order to assess the performance results rather than dealing with specifications, lifetime tests and qualification programs of the FEEP options have to be monitored at suitable intervals.

34 Astrium GmbH Page Configuration, Mass, and Power 6.1 Configuration The complete spacecraft configuration is sketched Figure 6-1. Moreover, it can be seen that it is compliant with a Rockot fairing. Figure 6-1: Spacecraft configuration and Rockot fairing. 6.2 Budgets Mass A condensed mass budget is shown in Table 6-1. Margins are applied to the different elements as well as an additional system margin of 20 % is used. The total mass of 1061 kg represents a slightly negative margin. However, considering the uncertainty of the data at this stage and the safety factors applied for the compilation of the mass budget, it can be concluded that total mass is not a show stopper for the mission.

35 Astrium GmbH Page 35 Mass Budget Element Unit Raw Mass (kg) Maturity Margin to be applied (%) Predicted Mass (kg) CDF Mass Budget (kg) Optical Bench % Atomic Assy % Atomic Assy % Laser Bench % Drag Free Sensor % Structure % Thermal % Solar Array % Power % Harness % Propulsion % AOCS % OBDH % TT&C % Satellite Dry Mass 515 Satellite Dry Mass including Maturity Margin 883 Satellite Dry Mass 595 System Margin 20% 177 System Margin 119 Dry Mass 1060 Adapter 50 Propellant Cold Gas 1.0 Propellant 3.2 Total Launch Mass Table 6-1: Mass budget Power The power budget results is a total solar array power of 714 W (compared to 499 W of the CDF report). This is still feasible but marginal. There are further measures to improve the power situation: As an alternative concept a decrease of the required power can be obtained by a different operational procedure: during eclipse periods the instrument shall be shut down. This safes about 240 W, which is almost half of the power demand excluding battery loading. The estimate for the payload power demand is quite conservative. The original number of 203 W already contains margin and is itself a conservative estimate. In addition to that a 20 % unit margin was added. Not considering the (additional) 20 % unit margin and taking 100 W as a baseline for the payload power (instead of 203 W) would result in a power demand reduction of 140 W. It can be concluded that also the total power demand is not a show stopper for the mission, due to the availability of additional potential measures for power reduction

36 Astrium GmbH Page On-Ground Testing For HYPER the following items are considered critical with respect to verification and testing: Secondary AOCS validation PST performance validation ASU-PST internal alignment stability validation A possible approach for the alignment determination is to route a fraction of the Raman laser light to the CCD of the PST. Such a built-in system could be maintained to be operated during flight in order to monitor alignment changes. ASU functional verification Under a 1 g environment the ASU shows a completely different behaviour than in space. A fast drift mode has to be implemented / considered in the ASU design in order to allow functional testing on ground. ASU initialisation and calibration mode The initialisation and calibration mode is virtually the same mechanism that has to be used for ASU internal phase correction at low frequencies (time constants > 8h). The first two items can draw heritage from drag-free space missions under advanced preparation (Gravity Probe B, GOCE), while the latter three items are HYPER payload specifics, which shall be tackled in the frame of a payload development program.

37 Astrium GmbH Page Programmatics The schedule for further technology and system development is shown in Table 8-1. Under the assumption that the instrument and system implementation programme could start earliest in 2007, a three years TRP programme is envisaged covering both the research programme for the key instrument technologies and the advanced study of crucial system design aspects. The staggered TRP of the instrument is more or less arbitrary, while the system aspects should be analysed later in order to be based on the most actual instrument technology. Task Name Instrument TRP (AO&I) 1-Cold Atoms Source 2-Laser Source for Cold Atoms 3-Ultra-Stable Raman Lasers 4-Best-form / Space-flight optics 5-Ultra-Stable Microwave Sources 6-Atom Interferometer Simulations System Studies 7- Mass Reduction Investigations 8- ASU acquisition / phase control 9- Science Data processing 10- System / Mission Improvements Instrument Development System PHASE B System PHASE C/D Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Table 8-1: Schedule.