Development of models for high precision simulation of the space mission MICROSCOPE Stefanie Bremer Meike List Hanns Selig Claus Lämmerzahl
Outline The space mission MICROSCOPE High Performance Satellite Dynamics Simulator Surface force modelling by means of finite elements Payload modelling EP violation: Results for simplified ansatz Conclusion 2
The space mission MICROSCOPE French mission proposed by ONERA and OCA with the participation of CNES, ESA, ZARM and PTB Mission goal: Test of Equivalence Principle with an accuracy of η = 10-15 Mission overview Micro-satellite of the CNES Myriade series Payload: Two differential accelerometers (T-SAGE) Sun-synchronous Altitude about 790 km Lifetime of 1 year 3
High Performance Satellite Dynamics Simulator Cooperation project of ZARM and DLR Institute of Space Systems since July 2008 Simulation tool to support mission modelling and data analysis Source code development in Fortran, C, C++, Matlab and Simulink User Interface: Matlab/Simulink Modular design; Adaptation to user requirements possible Developer and User version 4
HPS Structure Environment Disturbance Models Sensor Models Control Algorithm Actuator Models Satellite and Test Mass Dynamics 5
HPS Structure Environment Disturbance Models Sensor Models Satellite and Test Mass Dynamics Control Algorithm Actuator Models - Earth gravity model - Gravity gradient torque Satellite and Test Mass Dynamics 5
HPS Structure Environment Disturbance Models Sensor Models Satellite and Environment Test Mass Dynamics Control Algorithm Actuator Models - Atmospheric model Earth gravity model - Magnetic field model Gravity gradient torque - Position of planets Satellite and Test Mass Dynamics 5
HPS Structure Environment Disturbance Models Sensor Models Satellite and Environment Test Mass Disturbance Models Dynamics Control Algorithm Actuator Models - Atmospheric Aerodynamic model drag Earth gravity model - Magnetic field moment model Gravity gradient torque - Position Solar pressure of planets Satellite and Test Mass Dynamics 5
HPS Structure Environment Disturbance Models Sensor Models Sensor Models Control Algorithm Control Algorithm Actuator Models Actuator Models Satellite and Test Mass Dynamics 5
Coordinate Systems 6
Satellite dynamics Satellite acceleration in inertial frame && ( ) i i i i r + a + a a i i r i, b = g i b i, b control dist +, coupl, sat Attitude motion of satellite (body frame w.r.t inertial frame) ( ) [ ( )] b 1 b b b b b T + T T ω I & ω b i, b = I b control dist coupl, sat i, b ω b i, b b 1 b q & ˆ i = ω i, b q 2 b i 7
Test mass dynamics Desription of test mass motion in sensitive-axis frame && r sens sens, tm ( ) sens sens sens sens sens sens r + a a + a a a sens = g b, tm sens, tm coupl, tm coupl, sat rotation control dist Test mass attitude motion (test mass w.r.t senitive-axis frame) & ω ( ) ( ) ( ) ( ( ) tm 1 tm tm 1 tm tm tm tm tm tm I T I ω + ω I ω + ω & tm sens, tm = tm tm i, b sens, tm tm i, b sens, tm ω i, b tm 1 tm q & ˆ sens = ω sens, tm q 2 tm sens 8
Simulink Implementation of HPS Core 9
Simulink Implementation of HPS Core Simulation of satellite and test mass dynamics in six degrees of freedom by numerical integration of the equations of motion. 9
Simulink Implementation of HPS Core Satellite specific timedepending inputs. 9
Simulink Implementation of HPS Core External forces and torques in orbital, inertial or body coordinates. 9
Simulink Implementation of HPS Core Input of environmental models. 9
Modelling of surface forces by means of finite elements The disturbance force depends on several factors: Incident angle of sunlight α Affected area A Surface properties (coefficient of specular / diffuse reflexion c s / c d ) Value of solar pressure (P = S/c) General Idea: Fragmentation of the satellite surface into several elements Check illumination conditions Calculation of normalized surface force due to radiation pressure for each element f i 1 = Ai 1 si sun si di N 3 ( c ) e + 2 c cosα + c e cosα F sp = P n i= 1 f i 10
Illumination conditions Backside elements are identified first by comparing the element unit vector and the unit vector to the sun Each element is classified as visible and invisible respectively Sun light e Normal e Normal e Normal e Normal 11
Illumination conditions Backside elements are identified first by comparing the element unit vector and the unit vector to the sun Each element is classified as visible and invisible respectively e Normal e Normal e Normal e Normal 11
Illumination conditions Backside elements are identified first by comparing the element unit vector and the unit vector to the sun Each element is classified as visible and invisible respectively e Normal e Normal e Normal e Normal A shadow algorithm is applied to all visible elements, starting from the element that is nearest to the sun The relative position of the centre point coordinates indicates if an element is shaded or not 11
Preprocessing FE model must be set up first Calculation process must be executed for all possible directions 12
Preprocessing FE model must be set up first Calculation process must be executed for all possible directions Values become available in Simulink via look-up tables 12
Payload modelling 13
Payload modelling ONERA contoller and actuator 13
Payload modelling ONERA sensor 13
Payload modelling ZARM sensor 13
Payload modelling 14
Payload modelling 14
Modelling of EP violation A weak equivalence principle (EP) violation is quantified by the difference in acceleration of two test bodies exposed in the same gravitational field (given by the Eötvös-factor ) η = 2 a ( a a ) tm1 tm1 + a tm2 tm2 In HPS the EP violation is modelled via the gravity gradient acceleration: = m m tm1, g tm1, i m m tm2, g tm2, i a i gg i = g + η i i ( 1+ ) g g gg, tm i, b gg 15
Simplified Ansatz Satellite moves on a circular orbit Satellite rotates with constant angular velocity w.r.t. inertial frame Test mass motion is constrained to x-axis Spherical Earth potential Satellite and test masses are coupled by springs: F coupl = F s ( i ) = K ( i ) r r r ( i ) link trans link ( ) j i offset link 16
Test orbit for MICROSCOPE Semi-major axis a = 7159 km Inclination i = 98.566 Orbit frequency ω orbit = 1.0410-3 rad/s 17
Results for simplified ansatz Spin frequency of satellite ω spin = 3.6ω orbit = π + Effect due to gravity gradient ωgg =9. 2ω orbit 1 2 ω orbit 18
Results for simplified ansatz Spin frequency of satellite ω spin = 3.6ω orbit = π + Effect due to gravity gradient ωgg =9. 2ω orbit 1 2 ω orbit EP violation frequency ω = 4. 6ω = ω + ω EP orbit spin orbit 18
Conclusion HPS is used to model the satellite and test mass dynamics of MICROSCOPE High effort is made to model the disturbances due to surface forces Sensor model is implemented and tested against ONERA approach Simplified ansatz is introduced to investigate the EP violation Further development of the simulation tool is necessary 19