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H. Sünkel Institut für Geodäsie Technische Universität Graz und Institut für Weltraumforschung

Die Satellitenmission GOCE der ESA Eine Herausforderung an Mathematik, Numerik und Informatik. H. Sünkel Institut für Geodäsie Technische Universität Graz und Institut für Weltraumforschung Österreichische Akademie der Wissenschaften. Galilei - Newton - Einstein. Space- time.

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H. Sünkel Institut für Geodäsie Technische Universität Graz und Institut für Weltraumforschung

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  1. Die Satellitenmission GOCE der ESA Eine Herausforderung an Mathematik, Numerik und Informatik H. Sünkel Institut für Geodäsie Technische Universität Graz und Institut für Weltraumforschung Österreichische Akademie der Wissenschaften

  2. Galilei - Newton - Einstein Space-time Gravitation „Mass tells space-time how to curve and space-time tells mass how to move“. Mass Gravity = Gravitation + Rotation

  3. Gravity in control of our daily life • Shape of the Earth‘s surface • Distribution of land and water on Earth • Speed of processes inside, on and outside the Earth • Density and constitution of the Earth‘s atmosphere • Biological processes • Growth of plants • Anatomy and physiology of men and animals • Motion of living organism • Architecture of buildings • Mechanical design and structure of machines and vehicles Gravity scales life in space and time

  4. A primitive Earth model Radial-symmetric, not rotating, static mass distribution Crust Upper mantle Lower mantle Core Radial-symmetric, static gravity field

  5. Gravity anomalies due to mass anomalies Tectonic processes(Lithosphere) CouplingMantle - Core Rheology Mantle convection

  6. The dual role of the gravity field 108 - 106 yr Time Scales 102 - 100 yr Volcanicactivities Ice SheetMelting Ocean circulation& heat transport Post-glacialrebound Sea level change

  7. Turning inside out mass Gravitational potential shape ? Geoid

  8. The gravitational potential Properties of the gravitational potential: 1. is harmonic outside the Earth: 2. decreases to zero towards infinity 3. belongs to an infinite dimensional space Consequence: is represented by a linear combination of harmonic functions (= solutions of )

  9. The gravity potential Gravitational potential ( ) Rotational potential ( ) Gravity potential ( ) Unique „global horizontal“ surface of constant gravity potential ( ) at „mean“ sea level: geoid Global reference surface for „orthometric height“ Unique „local vertical“ Reference direction for „local-horizontal reference system“

  10. gravdensBGI.gif Surface gravity: incomplete data coverage

  11. POD for gravity field recovery Satellite orbit The idea: ? Mass distribution Gravitational field

  12. POD for gravity field recovery Equation of motion, defined in a space-fixed geocentric reference system free fall (around the Earth) = Satellite motion due to surface forces Satellite orbit as a function of gravitational field parameters Reference gravitational field controlled by parameters Reference satellite orbit as a function of gravitational field parameters

  13. POD for gravity field recovery Principle: Real orbit from satellite tracking Reference orbit based on a priori gravitational field Residual harmonic coefficients unknowns Functional relation

  14. POD for gravity field recovery Pseudo-observations Design matrix from partials LSA Observation residuals Harmonic coefficient (parameter) residuals

  15. lmax l m 0 0 0. 0.1 0 0. 0.1 1 0. 0.2 0 -0.48417e-03 0.2 1 0.85718e-12 0.28961e-112 2 0.24382e-05 -0.13999e-053 0 0.95714e-06 0.3 1 0.20297e-05 0.24943e-063 2 0.90465e-06 -0.62044e-063 3 0.72030e-06 0.14147e-05... ... ... ... The Earth’s gravitational field: models • JGM3 lmax = 70 • OSU91a lmax = 360 • EGM96 lmax = 360

  16. Open problems • Solid Earth Physicsanomalous density structure of lithosphere and upper mantle • Oceanography quasi-stationary dynamic ocean topography • Sea Level Change • Glaciology ice sheet balance • Geodesyunification of height systems, levelling by GPS, inertial navigation, • orbit prediction

  17. Gravity field: current knowledge The geoid: a surface of constant gravity potential at zero level Offset from reference ellipsoid: Accuracy + 100 m Now: Required: 0 m - 100 m

  18. Gravity field exploration from space • 3 Mission scenarios: • 1. Satellite-to-Satellite Tracking in high-low mode • SST - hl • 2. Satellite-to-Satellite Tracking in low-low mode • SST - ll • 3. Satellite Gravity Gradiometry • SGG

  19. Gravity Field Satellite Missions

  20. Love affairs with body Earth(... “move your body close to mine”) CHAMP (2000) GRACE (2002) GOCE (2006)

  21. The CHAMP mission: spacecraft CHAllenging Minisatellite Payload

  22. sst_hl.eps The CHAMP Mission: SST - hl GPS - satellites SST - hl CHAMP 2000 3-D accelerometer Earth mass anomaly

  23. The CHAMP mission: objectives Earth‘s gravity field and its temporal variations Gravity Field Model „Eigen 1S“ Geostrophic currents

  24. The CHAMP mission: objectives Earth‘s magnetic field and its temporal variations

  25. The CHAMP mission: objectives Earth‘s atmosphere and ionosphere and temporal variations

  26. The CHAMP mission: payload STAR accelerometer • Electrostatic STAR Accelerometer • GPS Receiver TRSR-2 • Laser Retro Reflector • Fluxgate Magnetometer • Overhauser Magnetometer • Advanced Stellar Compass • Digital Ion Drift Meter Laser retro-reflector FluxgateMagnetometer OverhauserMagnetometer

  27. The CHAMP mission:spacecraft front side view rear side view

  28. The CHAMP mission: launch & orbit • Launch: July 15, 2000, Cosmodrome Plesetsk • almost circular orbit: e = 0.004 • near polar orbit: i = 87° • initial altitude: 454 km • satellite lifetime: 5 years COSMOS launch vehicle

  29. The CHAMP mission: altitude

  30. The GRACE Mission

  31. sst_ll.eps The GRACE Mission: SST-hl and SST-ll combined GPS - satellites SST - hl SST - ll GRACE 2002 Earth mass anomaly

  32. The GRACE Mission: constellation • Two satellites following each other on the same orbital track • Position and velocity of the satellites are measured using onboard GPS antennae • Interconnected by a K-band microwave link • S-band radio frequencies used for communication with ground stations

  33. The GRACE Mission: constellation

  34. The GRACE Mission: payload • K-Band Ranging System (KBR) • Accelerometer (ACC) • GPS Space Receiver (GPS) • Laser Retro-Reflector (LRR) • Star Camera Assembly (SCA) • Coarse Earth and Sun Sensor (CES) • Ultra Stable Oscillator (USO) • Center of Mass Trim Assembly (CMT)

  35. The GRACE Mission: spacecraft structure

  36. The GRACE Mission: launch & orbit • Launch: March 17, 2002, Cosmodrome Plesetsk • almost circular orbit: e < 0.005 • near polar orbit: i = 89° • initial altitude: 485 - 500 km • satellite system lifetime: 5 years

  37. The CHAMP mission: altitude

  38. The GOCE Mission Gravity Field and Steady-state Ocean Circulation Explorer

  39. The GOCE mission: team structure GOCE Industry Team GOCE Project Team GOCE - MAG Project scientist (ESA) and members European GOCE Gravity Consortium (EGG-C) Team leader and Task leaders Science Data Use: Solid Earth Science Data Use: Oceanography Science Data Use: Ice Science Data Use: Geodesy Science Data Use: Sea Level

  40. gradiometry.eps The GOCE Mission: SST-hl and SGG combined GPS - satellites SST - hl GOCE 2006 SGG Earth mass anomaly

  41. Launch: Feb. 2006, Cosmodrome Plesetsk (62.7° N, 40.3° E) Total satellite mass: 800 kg Orbit inclination: i = 97° Injection altitude: 270 km Passive descent from 270 km to 250 km Altitude controlled by ion thrusters Satellite lifetime: 2 years The GOCE mission: launch & orbit

  42. Mission duration: 20 months Commission phase: 3 months Phase 1: 6 months Hibernation phase: 5 months Phase 2: 6 months Design orbit altitude: Phase 1: 250 km Phase 2: 240 km Orbit characteristics: Dawn-dusk sun-synchronous, Inclination: 96.5° Injection eccentricity: 0.000 phase 1: two months repeat, phase 2: eventually drifting ground track Maximum air drag during gradiometer operation: 0.3 mGal / in mbw GOCE: mission parameters

  43. The GOCE mission: timeline

  44. The GOCE mission: spacecraft design • Scientific payload: • 3-axis gravity gradiometer • GPS receiver • SLR retroreflector • Star tracker center of mass • Auxiliary equipment: • Ion thrusters • FEEPS • Solar panels (8 m²) • On board computer • Telemetry S 44

  45. The GOCE mission: gravity gradiometer Z • Gravity gradiometer: • 3-axis • mbw: 5 - 100 mHz • Precision: < 1 mE Y X 1 mE: curvature radius of equipotential surface of 10 Mill. km !

  46. The GOCE mission: gradiometer noise 3 mE / Hz specified (Predicted per- formance curve derived from a combination of analysis and test) 5 mHz mbw 100 mHz Specified noise psd Predicted noise psd

  47. The GOCE mission: gravity gradiometry Accelerometer equations: Common mode: Differential mode: V ... gravitational tensor

  48. The GOCE mission: gravity gradiometry Measurement tensor: Attitude: Gravitational tensor:

  49. The GOCE mission: attitude & drag control Ion thruster (for drag compensation) Micro thruster (for attitude control) Field emission electric propulsion system (FEEPS) Gas: Indium (Austrian system) Caesium (Italian system) Gas: Xenon thrust level: 1 - 20 mN thrust level: 0.0001 - 0.1 mN

  50. The GOCE mission: observation sensitivities SST (hi-lo): SGG: Gradiometer data Orbit perturbations Sat. alt. smoother Sat. alt. smoother SGG amplifier SST amplifier

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