1.1 Definition of geodesy
According to the classical definition ofFriedrich Robert Helmert (1880), “geodesy (γη = Earth, δαιω = I divide)is the science of the measurement and mapping of the Earth’s surface”. Helmert’s definition is fundamental to geodesy, even today. The surface of the Earth, to a large extent, is shaped by the Earth’s gravity, and most geodetic observations are referenced to the Earth’s gravity field. Consequently, the above definition of geodesy includes the determination of the Earth’sexternal gravity field. Since ancient times, the reference system for the survey of the Earth has been provided by extraterrestrial sources (stars). This demands that the Earth’s orientation in space be implied into the focus of geodesy. In recent times, the objective of geodesy has expanded to include applications in ocean and space research. Geodesy, in collaboration with other sciences, is also now involved in the determination of the surfaces and gravity fields ofother celestial bodies, such as the moon (lunar geodesy) and planets (planetary geodesy). Finally, the classical definition has to be extended to includetemporal variations of the Earth’s figure, its orientation, and its gravity field.
With this extended definition, geodesy is part of thegeosciences andengineering sciences, including navigation and geomatics (e.g.,Nat. Acad. Sciences, 1978;Plag and Pearlman, 2009;Herring, 2015). Geodesy may be divided into the areas of global geodesy, geodetic surveys (national and supranational), and plane surveying.Global geodesy includes the determination of the shape and size of the Earth, its orientation in space, and its external gravity field. Ageodetic survey deals with the determination of the Earth’s surface and gravity field over a region that typically spans a country or a group of countries. The Earth’s curvature and gravity field must be considered in geodetic surveys. Inplane surveying (topographic surveying, cadastral surveying, and engineering surveying), the details of the Earth’s surface are determined at a local level, and thus, curvature and gravity effects are most often ignored.
There is a close relation between global geodesy, geodetic surveying, and plane surveying. Geodetic surveys are linked to reference frames (networks) established by global geodesy, and they adopt the parameters for the figure of the Earth and its gravity field. On the other hand, the results of geodetic surveys contribute to global geodesy. Plane surveys, in turn, are generally referenced to control points established by geodetic surveys. They are used extensively in the development of national and state map-series, cadastral and geoinformation systems, and in civil engineering projects. The measurement and data evaluation methods applied in national geodetic surveys, nowadays, are mostly similar to those used in global geodetic work. In particular, space methods (satellite geodesy), which have long been a dominant technique in global geodesy, are now also commonly employed in regional and local surveys. This also requires a more detailed knowledge of the gravity field at regional and local scales.
With the corresponding classification in the English and French languages, the concept of “geodesy” (la géodésie, “höhere Geodäsie” afterHelmert) in this text refers only to global geodesy and geodetic surveying. The concept of “surveying” (la topométrie, Vermessungskunde or “niedere Geodäsie” after Helmert) shall encompass plane surveying.
In this volume, geodesy is treated only in the more restrictive sense as explained above (excluding plane surveying), and is limited to the planet Earth. Among the numerous textbooks and handbooks on surveying, we mention Brinker and Minnick (2012),Kahmen (2006),Nadolinets et al. (2017), andGhilani (2022). For lunar and planetary geodesy, seeNothnagel et al. (2010) andWiezorek (2015), and alsoPetit and Luzum (2010) andLuzum et al. (2011).
1.2 The objective of geodesy
Based on the concept of geodesy defined in [1.1], the objective of geodesy with respect to the planet Earth may be described as follows:
The objectiveof geodesy is to determine the figure and externalgravity field of the Earth, as well as its orientation in space, as a function of time, from measurements on and exterior to the Earth’s surface.
Thisgeodetic boundary-value problem incorporates a geometric (figure of the Earth) and a physical (gravity field) part; both are closely related.
By thefigure of the Earth, we mean the physical and the mathematical surface of the Earth as well as a geodetic reference model (e.g.,Moritz, 1990).
Thephysical surface of the Earth is the border between the solid or fluid masses and the atmosphere. Theocean floor may be included in this definition, being the bounding surface between the solid terrestrial body and the oceanic water masses. The irregular surface of the solid Earth (continental and ocean floor topography) cannot be represented by a simple mathematical (analytical) function. Continental topography is therefore described pointwise bycoordinates ofcontrol (reference)points. Given an adequately dense control network, the detailed structure of this surface can be determined by interpolation of data from sp
