Book contents
- Frontmatter
- Contents
- Preface
- List of abbreviations
- 1 Introduction – Fundamental definitions – Motivation
- 2 Concepts and elementary theory
- 3 Reference systems and frames
- 4 Observational techniques – ephemerides
- 5 Rigid Earth precession and nutation
- 6 Deformable Earth – Love numbers
- 7 Nutations of a non-rigid Earth
- 8 Anelasticity
- 9 Ocean and atmospheric corrections
- 10 Refinements of non-rigid nutation
- 11 Comparison observation-theory
- 12 Conventions
- 13 Mars nutations
- Appendix A Rotation representation
- Appendix B Clairaut theory
- Appendix C Definitions of equinoxes
- Bibliography
- Index
2 - Concepts and elementary theory
Published online by Cambridge University Press: 05 May 2015
- Frontmatter
- Contents
- Preface
- List of abbreviations
- 1 Introduction – Fundamental definitions – Motivation
- 2 Concepts and elementary theory
- 3 Reference systems and frames
- 4 Observational techniques – ephemerides
- 5 Rigid Earth precession and nutation
- 6 Deformable Earth – Love numbers
- 7 Nutations of a non-rigid Earth
- 8 Anelasticity
- 9 Ocean and atmospheric corrections
- 10 Refinements of non-rigid nutation
- 11 Comparison observation-theory
- 12 Conventions
- 13 Mars nutations
- Appendix A Rotation representation
- Appendix B Clairaut theory
- Appendix C Definitions of equinoxes
- Bibliography
- Index
Summary
Gravitational potential
Within the Earth itself, the gravitational potential at some point P due to the Sun (or any of the other celestial bodies) varies with the location of P, inversely as its distance from the body. The gravitational attraction on the mass elements of the Earth varies as the inverse square of the same distance. (We are using the word “attraction” here with the specific meaning of “the force exerted per unit mass.”) Suppose that the potential, as a function of the location of P, is separated into two parts: one that depends linearly on the position vector from the Earth's center of mass to P (including, in general, a term that is independent of the position) and the remainder of the potential function that is non-linear in the vector. The first part produces a uniform attraction on mass elements throughout the Earth, and is responsible for the relative orbital motion of the celestial body and the Earth. It is the second part that is responsible for the variation of the gravitational attraction over the volume of the Earth. This part of the potential is designated as the tide generating potential (TGP) or, for brevity, as the tidal potential. The reason for this nomenclature is simple: it generates the ocean tides as well as deformations of the solid Earth, referred to as solid Earth tides. (The term “solid Earth” is generally applied to the whole of the Earth excepting the fluid layers at the surface, namely, the oceans and the atmosphere.) It is the same tidal potential that generates Earth rotation variations too. Thus, the contents of this book relate to the effects of the TGP.
Axes associated with Earth rotation
Variations in the Earth's rotation are most naturally conceived of as variations in the direction or the magnitude (or both) of the Earth's angular velocity vector_, also called the rotation vector. (Throughout this book we use the bold notation for denoting vectors.)
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- Precession, Nutation and Wobble of the Earth , pp. 12 - 76Publisher: Cambridge University PressPrint publication year: 2015