Note: Intro -- THE MEASUREMENTOF GRAVITOMAGNETISM:A CHALLENGING ENTERPRISE -- Contents -- List of Figures -- List of Tables -- Preface -- The Usual Decomposition -- The Decomposition Using Trace-Less Parts -- Decomposition Into Two Parts -- Decomposition Into Divergence-Free Parts -- Part IOVERVIEW -- Introduction -- 1.1. The Experimental Basis of General Relativity -- 1.2. Testing Gravitomagnetism -- 1.2.1. The Gravitomagnetic Field in Astrophysical Scenarios -- 1.2.2. The Gravitomagnetic Field of the Earth -- 1.2.3. The Gravitomagnetic Fields of the Sun and of Mars -- 1.3. LAGEOS and GP-B -- 1.3.1. The LAGEOS Tests -- 1.3.2. The GP-B Test -- 1.4. Is It Really Necessary to Perform Experiments to DirectlyMeasure Gravitomagnetism ? -- 1.5. Purpose of the Book -- 1.6. Acknowledgements -- Mach's Principle -- 2.1. Introduction -- 2.2. Absolute Versus Relative -- 2.3. Mach's Principle and General Relativity -- 2.4. Gravitomagnetism -- 2.5. Tact of the Natural Investigator -- 2.6. Quantum Theory and Inertia -- 2.7. Discussion -- Part IITHEORY -- Gravitoelectromagnetism:A Brief Review -- 3.1. Introduction -- 3.2. Linear Perturbation Approach to GEM -- 3.3. Gravitational Larmor Theorem -- 3.4. Spacetime Curvature Approach to GEM -- 3.5. Spin-Rotation-Gravity Coupling -- Analogies and Differences betweenGravito-Electromagnetism andElectromagnetism -- 4.1. Introduction -- 4.2. Direct Deduction of the Gravito-Electromagnetic Faraday-Henry Law -- 4.3. Is There a Gravito-Magnetic Meissner Effect? -- 4.4. Inconsistencies of the Gravito-Electromagnetic Analogy -- 4.5. Discussion and Conclusions -- Quasi-Inertial Coordinates -- 5.1. Introduction -- 5.2. Fermi-Walker Transport of a Tetrad -- 5.3. Gyroscope Held Fixed -- 5.4. Geodetic Precession of Freely-Falling Gyroscope -- 5.5. Construction of Quasi-Inertial Coordinates -- 5.5.1. The Basis Tetrad. , 5.5.2. Coordinate Transformations -- 5.5.3. Metric in Quasi-Inertial Frame -- 5.6. Spin Precession in the Quasi-Inertial Frame -- 5.7. Aberration -- 5.8. Two Sources-Sun and Earth -- 5.9. Local Inertial Frame of Earth -- 5.10. Summary -- The Lense-Thirring Effect on theOrbit of a Test Particle -- 6.1. The Orbit of a Test Particle in Space -- 6.2. The Derivation of the Lense-Thirring Effect on the Orbit ofa Test Particle: the Lagrangian Approach -- 6.3. The Derivation of the Lense-Thirring Effect on the Orbit ofa Test Particle: the Gaussian Approach -- 6.4. An Extension of the Gravitational Larmor Theorem -- 6.5. The Gravitomagnetic Stern-Gerlach Force -- Post-Newtonian OrbitalPerturbations -- 7.1. Introduction -- 7.2. The Equations of Motion -- 7.3. The Perturbing Potential -- 7.4. Orbital Perturbations -- 7.4.1. Precession of the Pericenter -- 7.4.2. Precession of the Orbital Plane -- 7.4.3. The Change in the Mean Motion -- 7.5. Time Difference Induced by Precession -- 7.5.1. Time Difference due to Pericenter Precession -- 7.5.2. Time Difference due to Orbital Precession -- 7.6. The Sidereal Period and the Gravitomagnetic Clock Effect -- 7.7. An Alternative Derivation of the Gravitomagnetic SiderealEffect for Circular and Equatorial Orbits -- Part IIIEXPERIMENT -- Recent Developments in TestingGravitomagnetism with SatelliteLaser Ranging -- 8.1. Introduction -- 8.1.1. The Gravitoelectric Effects -- 8.1.2. The Gravitomagnetic Effects -- 8.2. The Major Systematic Errors -- 8.2.1. The Non-Gravitational Errors -- 8.2.2. The Gravitational Errors -- 8.3. Some New Observables for Measuring the Lense-ThirringEffect -- 8.3.1. The Supplementary Orbital Planes Option -- 8.3.2. Other Approaches -- 8.4. The Impact of the 1st Generation of Earth Gravity Modelsfrom CHAMP and GRACE -- 8.4.1. The Full-Range Even Zonal Harmonics Observables. , 8.4.2. The Partial-Range Even Zonal Harmonics Observables -- 8.4.3. Combinations With the Other Existing Geodetic Satellites -- 8.5. The Use of Data from the Altimeter Satellite Jason-1 -- 8.5.1. A Possible Combination of Nodes and the Gravitational Errors -- 8.5.2. The Impact of the Observational Errors of Ajisai and Jason-1 -- 8.5.3. The Impact of the Non-Gravitational Perturbations of Ajisai -- 8.5.4. The Impact of the Non-Gravitational Perturbations on Jason-1 -- 8.6. The 2nd Generation of the GRACE-only Earth GravityModels and the First CHAMP/GRACE Combined Model -- 8.6.1. EIGEN-GRACE02S -- 8.6.2. GGM02S -- 8.6.3. EIGEN-CG01C -- 8.7. A Quantitative Assessment of the Impact of the SecularVariations of the Even Zonal Harmonics on the PerformedTest with the Nodes of the LAGEOS Satellites -- 8.7.1. Numerical Simulations -- 8.7.2. The J˙eff -- 8.7.3. Summary -- 8.8. Discussion and Conclusions -- 8.8.1. The Use of Ajisai and Jason-1 -- 8.8.2. The LAGEOS-LAGEOS II Node-Node-Perigee Combination -- 8.8.3. A New Dedicated Satellite? -- Acknowledgments -- The LAGEOS Satellites:Non-Gravitational Perturbationsand the Lense-Thirring Effect -- 9.1. Introduction -- 9.2. The Osculating Orbital Elements and the Gaussian PerturbativeEquations -- 9.3. The Non-Gravitational Perturbations:A Brief Review -- 9.3.1. Visible Radiation Effects: Direct Solar Radiation Pressure -- 9.3.2. Visible Radiation Effects: Earth Albedo -- 9.3.3. The LAGEOS Satellites Spin-Axis Modeling -- 9.3.4. Thermal Thrust Effects -- 9.3.5. The Asymmetric Reflectivity Effect -- 9.4. Numerical Simulation -- 9.5. The Lense-Thirring Effect Error Budget and the NGP -- 9.6. Conclusions -- On the Impossibility of Using theNode of Nearly Polar Satellites forMeasuring the Lense-Thirring Effect -- 10.1. The Use of GP-B Data -- 10.1.1. The Static and Time-Varying Part of the Earth Gravitational Field. , 10.2. On the (Im)possibility of Using a Polar Lares -- 10.3. Conclusions -- Error Budget for theGravitomagnetic Clock Effect -- 11.1. Introduction -- 11.2. The Impact of the Orbital Injection Errors -- 11.2.1. The Imperfect Cancellation of the Keplerian Periods -- 11.2.2. The Imperfect Cancellation of the Post-Newtonian Periods -- 11.2.3. The Impact of the Classical Gravitational Perturbations -- 11.2.4. The Impact of the Errors in the Inclinations -- 11.2.5. The N−Body Gravitational Perturbations -- 11.2.6. The Impact of the Non-Gravitational Perturbations -- 11.3. Conclusions -- Is it Possible to Measure theLense-Thirring Effect in theGravitational Fields of the Sun andof Mars? -- 12.1. The Solar Gravitomagnetic Field -- 12.1.1. Compatibility of the Estimated Extra-Precessions of Planetary Periheliawith the Lense-Thirring Effect -- 12.1.2. Analysis of Other Independent Data -- 12.2. Testing Gravitomagnetism with Mars Global Surveyor inthe Field of Mars -- 12.3. Discussion and Conclusions -- On the Detectability of the Earth'sGravitomagnetic Field in LaboratoryExperiments -- 13.1. Introduction -- 13.2. Proposed Earth Based Laboratory Experiments -- 13.2.1. A Foucault Pendulum at South Pole -- 13.2.2. A Magnetic-Gravitomagnetic Experiment -- 13.2.3. A Michelson-Moreley-Type Experiment -- 13.2.4. The Use of Ring Laser Gyroscopes -- 13.2.5. A Terrestrial Version of the Gravitomagnetic Clock Effect -- 13.3. Discussion and Conclusions -- Atom Interferometry andGravitomagnetism -- 14.1. Introduction -- 14.2. The Sagnac Effect -- 14.2.1. The Sagnac Effect for Light -- 14.2.2. The Operational Definition of Rotation -- 14.2.3. The Sagnac Effect for Matter Waves -- 14.3. Basics About Atomic Interferometry -- 14.3.1. The Non-Relativistic Hamiltonian for Atoms -- 14.3.2. The Hamiltonian for the Energy Levels -- 14.3.3. The Center-of-Mass Hamiltonian. , 14.3.4. The Dipole Interaction -- 14.3.5. Two-Level-System -- 14.3.6. The Beam Splitting -- 14.3.7. The Observed Interference Pattern -- 14.4. The Phase Shift for Gravito-Inertial Effects -- 14.4.1. Coupling to Acceleration -- 14.4.2. The Sagnac-Effect -- 14.4.3. The Space Project HYPER -- 14.4.4. Comparison with Other Methods -- Appendix AThe Inclination Functions -- Appendix BThe Classical Orbital Precessions -- B.1. The Node Coefficients -- B.2. The Pericenter Coefficients -- Appendix CWEB Resources -- References -- INDEX.