Intrinsic Geodesy

The science of Geodesy has undergone far-reaching changes in the last half century. The impact of new technology, from electromag­ netic distance measurements to the use of artificial satellites, has been great, and is still largely to be felt. These changes have forced the practitioners of the ancient art of Earth measurement to alter their way of thinking about the space that surrounds us, something fundamentally more difficult than absorbing a new technology. A key influence in this modem change in geodetic thinking has been the work of Antonio Marussi, in his scientific publications from 1947 onwards, through his students and collaborators at the Uni­ versity of Trieste, and in the series of symposia on three-dimensional Geodesy which he organised with his great friend and collaborator, Martin Hotine. His influence on the latter, stemming from their first meeting at the General Assembly of the International Association of Geodesy in Oslo in 1948, was remarkable in itself, leading as it did to the ultimate publication of Hotine's Mathematical Geodesy in 1969. Front Matter....Pages I-XVII Front Matter....Pages 1-1 From Classical Geodesy to Geodesy in Three Dimensions....Pages 3-12 Foundations of Intrinsic Geodesy....Pages 13-58 Generalized Legendre Expansions for Any Curve Whatever, Traced Out Upon Any Surface Whatever....Pages 59-65 Generalized Legendre Expansions in Space....Pages 66-69 Generalized Legendre Expansions for Any Curve Whatever in Space....Pages 70-74 The Tidal Field of a Planet and the Related Intrinsic Reference Systems....Pages 75-83 Front Matter....Pages 85-85 On the Curvature and Torsion of the Gravity Field....Pages 87-91 Generalization of Dalby’s Theorem for Any Surface Whatever....Pages 92-97 Front Matter....Pages 99-99 Principles of Intrinsic Geodesy Applied to the Field of Somigliana....Pages 101-108 The First Fundamental Problem of Geodesy Developed for the Field of Somigliana....Pages 109-117 Differential Parameters in the Normal Gravity Field....Pages 118-122 Front Matter....Pages 123-123 On the Representation of the Geoid on the Ellipsoid....Pages 125-130 Some Remarks on the Use of Conformal Representations in Three-Dimensional Geodesy....Pages 131-134 On the Three-Dimensional Computation of Geodetic Networks and Anomalies....Pages 135-141 The Adjustment of Geodetic Networks in the Three-Dimensional Ellipsoidal Model Space of Somigliana....Pages 142-146 Front Matter....Pages 147-147 Some Integral Properties of the Conformal Representations of Surfaces on Surfaces....Pages 149-152 The a Priori Determination of the Modulus of Linear Deformation in the Gauss Conformal Representation....Pages 153-156 Representations Between Surfaces Defined by Means of the Quadratic Form Which Determines Their Modulus of Deformation....Pages 157-166 Front Matter....Pages 167-167 An Analogy Between the Laws of Propagation of Light in Continuous Isotropic Refracting Media and Conformal Representations....Pages 169-172 The Torsion of a Ray of Light in a Continuous Isotropic Refracting Medium....Pages 173-176 Front Matter....Pages 177-177 The Motion of a Free Particle and of a Spherical Pendulum in the Microgravitational Field of a Gravitationally Stabilized Satellite in Circular Orbit in a Central Field....Pages 179-189 Back Matter....Pages 190-219