The Gravity Field of the Earth

From Classical and Modern Methods

1st Edition - January 1, 1967

Author: Michele Caputo

Editor: J. Van Mieghem

eBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 2 2 3 8 - 7

International Geophysics Series, Volume 10: The Gravity Field of the Earth: From Classical and Modern Methods explores the theory of the gravity field of the earth based on both… Read more

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International Geophysics Series, Volume 10: The Gravity Field of the Earth: From Classical and Modern Methods explores the theory of the gravity field of the earth based on both classical and modern methods. Classical method involves observations of gravity taken over the earth's surface, while the modern method uses observations of variation of orbital elements of artificial satellites caused by the gravity field of the earth. This book is organized into two parts encompassing 12 chapters. Part I describes the solution of physical problems that are treated as Dirichlet problems or solved by means of integral equations. This part also deals with the determination of the geoid form from ground gravity measurements using the Stokes formula. The method of obtaining the Stokes formula by means of an integral equation is also outlined. Part II contains modern mathematical techniques developed to utilize the observations of artificial satellites for geodetic purposes. This book could be used as a textbook for students in the fields of geodesy, geophysics, or astronomy.

PrefacePart I Chapter I. General Theory 1. Introductory Considerations; the Coordinates 2. Morera's Functions 3. Gravity Potential with a Triaxial Ellipsoid as Equipotential Surface 4. Values of Gravity at the Ends of the Semiaxes 5. Pizzetti's Theorem 6. Modulus of the Gravity Vector and the Conditions on the Parameters 7. Modulus of the Gravity Vector in Terms of the Coordinates Chapter II. the Gravity Field of the Biaxial Case 8. Gravity Potential Having a Biaxial Ellipsoid as Equipotential Surface 9. The Pizzetti and Clairaut Theorems for the Biaxial Model 10. The Somigliana Theorem 11. International Gravity Formula and Other Gravity Formulas 12. The International Gravity Formula Extended into Space 13. The Shape of the Earth as Obtained from Gravity Measurements 14. Spherical Harmonics Expansion of the Potential of the Normal Gravity Field 15. Dimensions of the Earth as Obtained from Gravity Data and Satellite Data 16. The Flattening of the Earth's Equator Chapter III. The Gravity Field of the Triaxial Case: the Moon 17. First-Order Theory of the Field Having a Triaxial Ellipsoid as an Equipotential Surface: The Moon 18. Comparison with the Expansion of the Potential in Terms of the Moments of Inertia 19. The Shape of the Moon 20. The Density Distribution within the Moon 21. Is the Surface of the Moon Equipotential? Chapter IV. Gravitational Potential for Satellites 22. Equations of Motion of a Satellite in the Biaxial Field 23. The Case of a Prolate Ellipsoid 24. The Motion of a Satellite in the Field Described in Section 23 25. Motion of a Satellite in a Nonbiaxial Field Chapter V. Determination of the Geoid from Terrestrial Data 26. The Determination of the Geoid 27. Brun's Equation and the Equation of Physical Geodesy 28. A Boundary-Value Problem 29. Stoke's Formula 30. The Surface Density Distribution which Gives the Perturbing Potential 31. Introduction to the Integral Equations Method for Stokes Formula 32. Stoke's Formula by the Integral Equation Method 33. Relations between the Spectral Components of the Geoid, of the Potential, and of the Modulus of Gravity Chapter VI. The Adjustment of the Parameters of the Field 34. Problems arising from Satellite Results 35. The Nonrotating Field 36. The Adjustment of the Parameters Chapter VII. A Simplified Biaxial Model 37. A Simple, Accurate Model for the Nonrotating Field: Introduction 38. The Potential of the Simplified Model 39. Properties of the Simplified Model 40. The Gravity Vector 41. The Clairaut and Pizzetti Theorems 42. Spherical Harmonic Expansion 43. The Actual Field Chapter VIII. Determination of the Geoid from Unreduced Terrestrial Data 44. The Method of Levallois 45. The Method of Molodenski Chapter IX. Some Geophysical Implications 46. The Hydrostatic Equilibrium of the Earth 47. Comparison with Stresses Associated with Regional and Continental Loads 48. Other Implications 49. Implications on the MoonPart II Chapter I. Satellite Motion in a Central Field 1. Introduction 2. Equations of Motion in the Plane of the Orbit 3. The Polar Equation of the Orbit 4. Elements of the Elliptic Orbit: The True, Eccentric, and Mean Anomalies 5. Kepler's Equation 6. Other Elliptic Elements 7. Relations between the Elliptic Elements Chapter II. Satellite Motion in Noncentral Fields 8. The Nahewirkungsgesetz and the Fernwirkungsgesetz 9. The Earth Gravitational Potential and the Coordinates of the Satellite 10. Some Identities to Be Used in the Expression of the Terrestrial Gravitational Potential by Means of Orbital Elements 11. The Expression of the Legendre Functions by Means of the Orbital Elements 12. Preliminary Expression of the Earth's Potential by Means of the Orbital Elements 13. Terrestrial Gravitational Potential Expressed in Orbital Elements 14. Lagrangian Brackets 15. Equations of Motion Expressed in Terms of the Orbital Elements and the Lagrangian Brackets 16. Integrated Changes of the Orbital Elements 17. Study of the Earth's Polar Flattening 18. Study of the Flattening of the Earth's Equator 19. Study of the Third-Order Zonal Harmonic 20. Nonlinear Perturbations of Zonal Harmonics 21. The Solution Including the Fourth-Order Terms 22. Variation of the Orbital Elements 23. Other Perturbations 24. Analysis of Satellite Observations 25. Lunar Satellites Chapter III. The Geoid 26. The GeoidReferencesAuthor IndexSubject Index