Lunar Gravimetry

1 Introduction.- 2 Fundamentals of lunar gravity field recovery.- 2.1 Scientific rationale.- 2.2 State-of-the-art of lunar gravity field modelling.- 2.3 Future solutions.- 3 Assessment of modem lunar gravity field models through orbit analysis.- 3.1 Introduction.- 3.2 The role of model calibration.- 3.3 Covariance analysis of GLGM-2 and LP75G.- 3.4 Long-term orbit behaviour.- 3.5 Discussion and outlook based on later Lunar Prospector products.- 4 Ill-conditioning of the lunar gravimetric inverse problem.- 4.1 Setting the stage.- 4.2 The multiple roles of regularisation in lunar gravimetry.- 4.3 Regularisation methods and the view on the estimation process.- 4.4 Information content and effect of the bias on the quality description.- 4.5 Searching for the optimal regularisation parameter.- 5 Lunar gravity field modelling experiments with European data sets.- 5.1 Introduction.- 5.2 The Lunar Prospector tracking campaign at Weilheim.- 5.3 Orbit determination using Weilheim data.- 5.4 Gravity field recovery using Weilheim data.- 6 Towards a global data set.- 6.1 Introduction.- 6.2 SST concepts.- 6.2.1 Low—low configurations — the MORO study.- 6.2.2 High—low configurations — the SELENE experiment.- 6.3 Covariance analysis of low—low selenopotential recovery.- 6.3.1 Time-wise approach in the time-domain — the Colombo method.- 6.3.2 The linear low—low SST observation equation.- 6.3.3 Formal errors based on low—low range rate measurements..- 6.3.4 A note on omission errors.- 6.4 Full-scale simulation of low—low selenopotential estimation.- 6.4.1 The simulation setup.- 6.4.2 Gravity field recovery results.- 7 Epilogue.- 7.1 Conclusions.- 7.2 Recommendations for further research.- A Fundamentals of selenography.- B The generalised singular value decomposition(GSVD).- C Some useful coordinate transformations.- D The Euler-Lagrange equation and the range rate SST signal.- D.1 The Euler-Lagrange formalism.- D.2 Satellite velocity and the conservative forcing function in inertial space.- D.3 The forcing function in body-fixed rotating coordinates.- D.4 The low-low range rate SST signal equation.