Theory of the Earth's Shape

PrefaceFirst Part Physical Geodesy 1. Origin, Structure and Form of the Earth 1.1 The Earth as a Planet of the Solar System 1.2 The Earth's Physical Structure 1.3 Brief Historical Survey of the Ideas Concerning the Earth's Form and Size 2 Elements of Potential Theory 2.1 Principles of Field Theory 2.2 Harmonic Functions 2.3 Newtonian Potential 2.4 Boundary-Value Problems of Potential Theory 3 Reference Surfaces. Coordinate Systems 3.1 Level Surfaces 3.2 The Level Spheroid 3.3 The Level Ellipsoid 3.4 Coordinate Systems 3.5 Altitude Systems 4 The Perturbing Potential 4.1 Bruns' Formula. The Third Boundary-Value Problem for the Geoid 4.2 The Third Boundary-Value Problem for the Earth's Physical Surface 4.3 Expansion of the Perturbing Potential in Spherical Harmonics. The Spherical Approximation of the Boundary Condition for the Geoid 4.4 The Gravity Anomaly in External Space 5 The Determination of the Geoid by Gravity Methods 5.1 Stokes' Formula 5.2 Generalization of Stokes' Formula 5.3 Determination of the Gravimetric Deflection of the Vertical 5.4 The Gravity Reduction 5.5 Types of Reductions Used in Physical Geodesy 5.6 Practical Determination of the Components of the Deflection of the Vertical and of the Geoid Undulations 6 Determination of the Geoid by Astro-Gravimetric Methods 6.1 The Astro-Geodetic Levelling 6.2 The Astro-Gravimetric Levelling 7 Determination of the Earth's Physical Surface 7.1 Molodenski's Problem 7.2 Determination of the Perturbing Potential by Using Green's Formulae 7.3 Solving the Main Integral Equation 7.4 Geometrical Interpretation of the Solution of Molodenski's Equation 7.5 The Deflection of the Vertical on the Earth's Physical SurfaceSecond Part Ellipsoidal Geodesy 8 The Rotation Ellipsoid as Reference Surface in Geodesy 8.1 The Parameters of the Reference Ellipsoid 8.2 The Parametric Equations of the Rotation Ellipsoid 9 Curves on the Surface of the Reference Ellipsoid 9.1 The Coordinate Lines 9.2 Normal Sections 9.3 The Geodetic Line 10 The Reduction of the Geodetic Observations on the Reference Ellipsoid's Surface 10.1 The Reduction of the Astronomical Observations 10.2 The Reduction of the Azimuthal Observations 10.3 The Reduction of the Zenithal Observations to the Normal to the Ellipsoid 10.4 The Reduction of the Distances on the Ellipsoid 11 Solving the Geodetic Triangles on the Reference Ellipsoid 11.1 The Spherical Excess 11.2 Solving Small Geodetic Triangles by Means of Legendre's Theorem 11.3 Solving Small Geodetic Triangles by the Additament Method 12 Calculation of the Geodetic Coordinates on the Reference Ellipsoid 12.1 Solving the Basic Geodetic Problems for Small Geodetic Distances 12.2 Gauss' Method (Method of the Mean Arguments) for Solving the Basic Geodetic Problems for Medium Geodetic Distances 12.3 Solving the Basic Geodetic Problems for Large Geodetic Distances 12.4 Differential FormulaeThird Part Astro-Geodetic Triangulation 13 The Notion of Performing Astro-Geodetic Triangulation 13.1 General Considerations 13.2 Error Propagation in the Astro-Geodetic Triangulation 14 Measurements in Astro-Geodetic Triangulation 14.1 Angle Measurements 14.2 Distance Measurements 14.3 Relative Measurements of Gravity 14.4 Levelling Measurements 14.5 Determinations of Geodetic Astronomy 15 Adjustment of the Astro-Geodetic Triangulation 15.1 General Considerations 15.2 Adjustment of the Triangulation Network by Means of the Method of Conditioned Observations 15.3 Adjustment of the Triangulation Network by Means of the Method of Indirect Observations 15.4 Weight Determination After Adjustment 15.5 Processing of the Observations in Free Geodetic Networks 16 The 1st-Order Astro-Geodetic Triangulation Network of the Socialist Republic of Romania 16.1 The Network Layout 16.2 Marking and Constructing the Station Points of the Network 16.3 Angle and Distance Measurements as well as Astro-Geodetic Determinations Carried out at the Station Points of the Network 16.4 The Network AdjustmentFourth Part Three-Dimensional Geodesy 17 Basic Equations of Three-Dimensional Geodesy 17.1 Coordinate Systems Used in Three-Dimensional Geodesy 17.2 Origin, Methodology and Purpose of Three-Dimensional Geodesy 17.3 Basic Equations of Three-Dimensional Geodesy 18. Elementary Calculations in Three-Dimensional Geodesy 18.1 The Calculation Principle in the Local System 18.2 Choice of the Local Geodetic Trihedron 18.3 Calculating the Coordinates of a Point 18.4 Determining the Local Astronomical Vertical 18.5 Orientation Calculation in the Local System 18.6 Calculation of a Geodetic Traverse 18.7 Triangulation Calculations 19 Basic Methods for Developing the Geodetic Networks by Means of the Earth's Artificial Satellites 19.1 General Considerantions 19.2 Elements of an Artificial Satellite's Orbit 19.3 Geodetic Artificial Satellites 19.4 Methods of Observing Artificial Satellites 19.5 Spatial Triangulation 19.6 Spatial Trilateration 19.7 Vector Network 20 Triangulation Calculations Using Artificial Satellites 20.1 Identification of the Recorded Stars 20.2 Calculation of the Coordinates on the Photographic Plate of the Recorded Stars 20.3 Comparison of the Measured and Calculated Values 20.4 Linearization of the Satellite's Position on the Photographic Plate 20.5 Returning to the Global System 20.6 General Adjustment of a Spatial Triangulation by Means of Artificial Satellites 21 Some Examples of Spatial Triangulation Operations 21.1 The France — Algeria Connexion 21.2 The European Continent — Azores Islands Connexion 21.3 The World Network of Triangulation by Means of Artificial Satellites 21.4 Western European Triangulation by Means of Satellites (West) 21.5 Brief Survey of Other Triangulation Operations by Means of Artificial Satellites 22 General Survey of Other Geometrical Methods of Spatial Geodesy by Means of Artificial Satellites 22.1 The 4-Laser Method 22.2 The Optical-Telemetric Method 22.3 The Orbital Method 22.4 The Method of the Simultaneity Circle 22.5 Experiment of Using Laser MeasurementsFifth Part Methods for Determining the Terrestrial Ellipsoid and the Geoid 23 The Determination of the Reference Ellipsoid by Using Astro-Geodetic Methods 23.1 Determining the Reference Ellipsoid from Measurements of Meridian and Parallel Arcs 23.2 Determining the Reference Ellipsoid by Using the Method of Surfaces 23.3 Determining the Reference Ellipsoid by Using Differential Relations 24 The Determination of the Earth's Form from Astro-Geodetic and Gravity Measurements 24.1 Global Determination of the Geoid 24.2 Determining the Earth's Physical Constants 24.3 Determining the Gravity Field and the Parameters of the General Terrestrial Ellipsoid 25 Dynamic Geodesy 25.1 Non-Perturbed Orbits 25.2 Relationships Between the Elements of the Satellite Orbit and the Geocentric, Topocentric and Rectangular Coordinate Systems 25.3 Perturbed Orbits 25.4 The Luni — Solar Perturbation 25.5 Perturbations of the Artificial Satellites' Orbits Caused by the Resistance of the Atmosphere and by Radiation Pressure 25.6 Determining the Parameters of the Earth's Gravitational Field by Using Artificial Satellites 25.7 The Geoid Determination 25.8 Satellite Altimetry 25.9 Interpretation of the Results of Satellite Geodesy 26 The Geodetic Reference SystemSixth Part Determination of the Recent Movements of the Earth's Crust 27 Geodetic Methods for Determining the Recent Movements of the Earth's Crust 27.1 Introductory Remarks 27.2 Repeated Geometrical Levelling 27.3 Triangulation-Trilateration Networks for Determining the Horizontal Movements of the Earth's Crust 27.4 Astro-Geodetic Methods for Determining the Movements of the Continents 27.5 Other Methods Used for Determining the Crustal Movements 28 Processing the Geodetic Observations Carried Out for Determining the Recent Crustal Movements 28.1 A Functional-Stochastic Model for the Three-Dimensional Determination of the Recent Movements of the Earth's Crust within Areas of Limited Size 28.2 Particular Functional-Stochastic Models for Determining the Recent Crustal Movements 28.3 Possibilities of Adjusting the Repeated Geodetic Observations 28.4 Accuracy Estimation and Statistical Analysis of the Determinations of Recent Crustal Movements 29 Examples of Daterminations of Recent Movements of the Earth's Crust 29.1 Map of the Recent Crustal Movements in Eastern Europe 29.2 Map of the Vertical Crustal Movements on the Territory of the Socialist Republic of Romania 29.3 Utilization of Some Improved Functional-Stochastic Models for Determining the Vertical Crustal Movements 29.4 Other Examples of Determining Recent Movements of the Earth's CrustFuture Prospects in the Light of Present Geodetic AchievementsReferencesAbbreviationsIndex