Geodetic Heights Intro Foreword Contents 1 Introduction References 2 General Coordinates in mathcalR3 2.1 Outline 2.2 Definitions and Reminds 2.3 Relevant Examples 2.3.1 Cartesian Coordinates 2.3.2 Spherical Coordinates 2.3.3 Ellipsoidal Coordinates References 3 The Earth Gravity Field: Basics 3.1 Outline 3.2 Basic Definitions of Gravity and Gravity Potential 3.3 Plumb Lines and Equipotential Surfaces 3.4 The Gravity Field Outside a Brillouin Sphere 3.5 The Normal Gravity Field 3.6 Definition of the Geoid References 4 The Anomalous Potential and Its Determination 4.1 Outline 4.2 The Anomalous Potential 4.3 The Runge Krarup Theorem: A Mathematical Intermezzo 4.4 Optimal Degree of Global Models or Smoothing by Truncation 4.5 Collocation Theory or Smoothing by Prior Information 4.6 On the Relation Between Potential and the Surface Gravimetric Observables 4.6.1 Gravimetry 4.6.2 Levelling Combined with Gravimetry 4.6.3 Radar Altimetry on the Oceans 4.7 The Geodetic Boundary Value Problem (GBVP) References 5 Geodetic Coordinate Systems 5.1 Outline 5.2 On the Continuation of Gravity into the Topographic Layer 5.3 The Hotine Marussi Triad (Λ Φ W) 5.4 The Helmert Triad (Λ Φ H) 5.5 The Molodensky Triad (λ h*) References 6 The Relation Between Levelling Geodetic and Other Unholonomic Heights 6.1 Outline 6.2 The Observation Equation of ΔL in Terms of Dynamic Heights 6.3 The Observation Equation of ΔL in Terms of Normal Heights 6.4 The Observation Equation of ΔL in Terms of Orthometric Heights 6.5 Levelling and Normal Orthometric Heights: An Unholonomic Coordinate 6.6 Conclusions References 7 The Height Datum Problem 7.1 Outline 7.2 Formulation of the Global Unification of the Height Datum.