The Gravity Field of the Earth
From Classical and Modern Methods
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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.
Table of Contents
Preface
Part 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 Moon
Part 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 Geoid
References
Author Index
Subject Index
Product details
- No. of pages: 216
- Language: English
- Copyright: © Academic Press 1967
- Published: January 1, 1967
- Imprint: Academic Press
- eBook ISBN: 9781483222387
About the Author
Michele Caputo
About the Editor
J. Van Mieghem
Affiliations and Expertise
Royal Belgian Meteorological Institute, Uccle, Belgium
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