Tidal Deformation of Planets and Satellites: Models and Methods for Laser- and Radar Altimetry vorgelegt von Diplom Physiker Gregor Steinbr¨ugge geb. in Berlin von der Fakult¨atVI { Planen Bauen Umwelt der Technischen Universit¨atBerlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften - Dr. rer. nat. - genehmigte Dissertation Vorsitzender: Prof. Dr. Dr. h.c. Harald Schuh Gutachter: Prof. Dr. J¨urgenOberst Gutachter: Prof. Dr. Nicolas Thomas Gutachter: Prof. Dr. Tilman Spohn Tag der wissenschaftlichen Aussprache: 27.03.2018 Berlin 2018 2 Contents Title Page 1 Contents 3 List of Figures 7 List of Tables 9 1 Introduction 15 1.1 Structure of the Dissertation . 16 1.1.1 Icy Satellites . 17 1.1.2 Mercury . 20 1.2 Theory of Tides . 21 1.2.1 Tidal Potentials . 21 1.2.2 Response of Planetary Bodies to Tidal Forces . 23 1.3 Measuring Tidal Deformations . 25 1.3.1 Measurement Concepts . 25 1.3.2 Laser Altimetry . 25 1.3.3 Radar Altimetry . 26 1.4 Missions and Instruments . 27 1.4.1 REASON and the Europa Clipper Mission . 27 1.4.2 GALA and the JUICE Mission . 28 1.4.3 BELA and the BepiColombo Mission . 29 2 Research Paper I 31 2.1 Introduction . 32 2.2 Instrument Performance Modeling . 32 2.2.1 Link Budget . 32 2.2.2 Signal-to-Noise Ratio . 33 2.3 Expected Science Performance . 37 2.3.1 Topographic Coverage . 37 2.3.2 Slope and Roughness . 37 2.4 Tidal Deformation . 40 2.4.1 Covariance Analysis . 40 2.4.2 Numerical Simulation . 41 2.5 Discussion . 42 2.6 Conclusion . 43 Bibliography 43 3 3 Research Paper II 47 3.1 Introduction . 48 3.2 Methods . 48 3.2.1 Structural Models . 49 3.2.2 Rheological Models . 51 3.3 Results . 53 3.3.1 Tidal Love Numbers . 53 3.3.2 Inner Core Radius . 53 3.3.3 Phase-lags . 54 3.4 Discussion and Conclusion . 56 Bibliography 57 4 Research Paper III 61 4.1 Introduction . 62 4.2 Method and Model Description . 62 4.2.1 Ganymede Tides . 62 4.2.2 Instrument and Mission Setup . 63 4.2.3 General Model Description . 63 4.2.4 Instrument Performance Model . 65 4.2.5 Spacecraft Pointing Error . 65 4.2.6 Other Error Sources . 66 4.2.7 Numerical Simulation . 66 4.3 Application and Results for the GALA Experiment . 66 4.3.1 Measurement Error . 66 4.3.2 Implication on the Ice Thickness . 67 4.4 Discussion . 68 4.4.1 Operation Scenario . 68 4.4.2 Dependence on the Slope Distribution . 69 4.4.3 Ambiguity in the Structural Model . 69 4.4.4 Linear Combination of h2 and k2 ....................... 69 4.4.5 The Elastic Case vs. the Visco-elastic Case . 70 4.5 Conclusion . 71 Bibliography 71 5 Research Paper IV 75 5.1 Introduction . 76 5.2 Instrument Description and Measurement Principle . 76 5.3 Radar Altimetric Performance . 78 5.3.1 Signal to Noise Ratio . 78 5.3.2 Geometric Performance Model . 79 5.3.3 Point Target Simulator . 80 5.3.4 Influence of the Ionosphere . 81 5.4 Tidal Inversion . 82 5.5 Implications for Europa's Interior . 83 5.6 Discussion . 83 5.7 Conclusion . 85 Bibliography 85 4 6 Discussion 87 7 Synthesis 93 A Tidal Potential of Mercury 95 A.1 Second Order Eccentricity . 95 A.2 Mathematica Notebook . 97 Bibliography 99 Bibliography 99 113Acknowledgments 113 5 6 List of Figures 2.1 BELA PFD as a function of altitude . 35 2.2 BELA range error as a function of altitude . 37 2.3 BELA topographic coverage after two years of operation . 38 2.4 BELA's return pulse width measurement accuracy . 39 2.5 Mercury's surface roughness as derived from DTM data . 41 3.1 Mercury structural model . 52 3.2 Mercurys inner core size as a function of tidal Love numbers . 55 3.3 Mercury's Love numbers as a function of tidal phase-lag . 56 4.1 Maximum and measurable tidal double amplitudes on Ganymede . 65 4.2 Contours of decadic logarithm of the SNR as a function of spacecraft altitude and surface roughness. 67 4.3 PFD vs. surface roughness . 67 4.4 Ganymede h2 vs. ice thickness . 68 4.5 Expected error of the Ganymede h2 measurement . 69 4.6 Love number h2 in dependence of Ganymede's outer ice shell thickness . 70 4.7 Linear combination of k2 and h2 in dependence of Ganymede's outer ice thickness. 70 5.1 Delay / Doppler principle . 77 5.2 REASON range error estimates . 81 5.3 17F12v2 ground tracks with cross-over locations . 82 5.4 Tidal Love numbers as a function of structural models of Europa . 84 6.1 Time varying orbital eccentricity of Europa . 89 6.2 Reconstruction of Europa's global shape using REASON altimetry . 90 7 8 List of Tables 1.1 List of publications included in this thesis . 16 2.1 BELA instrument parameters. 36 2.2 Cross-over observable error budget calculated for a rms roughness of 12.1 m at 200 m baseline, 6.4 m at 50 m baseline and an albedo of 0:19. 42 3.1 Parameters used for Mercury's core . 50 3.2 Rheologic parameters used in the computation of the tidal Love numbers. 54 4.1 Ganymede equilibrium and gravity parameters . 63 4.2 Comparison between the BELA and assumed GALA instrument parameters . 64 4.3 GALA error contributions . 67 4.4 GALA error budget . 68 4.5 Reference model of Ganymede's interior structure . 68 4.6 Slope dependence of the error budget . 69 4.7 Constraints for the structural Ganymede models . 70 5.1 DTM data sets used to derive Europa's surface roughness . 80 5.2 Estimated REASON range error and Europa h2 accuracy . 83 5.3 Interior structure parameters of Europa . 84 6.1 Comparison of the estimated measurement results of the three instruments stud- ied in this thesis. 87 A.1 G2mq coefficients according to Kaula (1964). 96 9 10 Abstract In this thesis, methods are developed and studied for radar and laser altimetry.