1.2 Brief history of geodesy

Geodesy: a very old and fully modern science

According to Friedrich Robert Helmert (1843-1917), geodesy is the science “of measurements and mappings of the Earth's surface”. A principle tool and output of geodesy is a reference frame allowing to describe the position of points relative to each other.

For a long time, geodetic concepts were based on a static view of the Earth, and reference frames were based on fixed coordinates. Over the last three decades, the development in our understanding of the solid Earth and the total Earth system has made clear that the Earth's surface undergoes continuous deformations changing the relative position of all points on a wide range of time scales. The invention and rapid improvement of the space-geodetic technologies have provide a wealth of observations documenting the surface deformations, irregularities in the Earth's movement in space and the extent of mass movements in the Earth's system. At the same time, scientific and societal applications pose increasing requirements on the accuracy and reliability of positioning as well as navigation. Consequently, the realization and maintenance of reliable reference frames on local, regional and global scales as well as the provision of techniques for high-precision positioning has received growing attention within geodesy.

Historically, geodesy may be separated into four different phases related to the view of the Earth's shape and dynamics and the main target of research (Soffel, 1989):

• A: From 200 BC up to the middle of the 17^th century: the radius of a spherical Earth: In early attempts to determine the overall shape of the Earth, the concept of an (approximately) spherical Earth had to compete with the idea of a flat, disk-like Earth floating on an world's ocean. Based on the assumption of a spherical shape of the Earth, Eratosthenes (276-195 BC) was able to determine the Earth's radius experimentally, and thus, he is considered as the founder of scientific geodesy. The deviation in his determination from the true radius was of the order of 16% (see Torge, 1975). Posidonius (135 - 51 BC) was able to improve this result to an accuracy of about 11%. No further substantial progress was made in the determination of the shape of the Earth until the invention of the Keplerian telescope in 1611 and the method of triangulation in 1589 by Tycho Brahe. Applying these means for the first time, Snellius already in 1615 achieved an accuracy of 3.4%. In 1669/70, Abbe J. Picard even determined the radius with an accuracy of 0.1%.
• B: From the middle of the 17^th century to the middle of the 19^th century: the oblateness of an rotational ellipsoid: The oblateness of the Earth was discovered by J. Richter in 1672 in an analysis of pendulum oscillations. However, before that, in 1666 J. D. Cassini had observed for the first time the oblateness of Jupiter at its poles. By studying the equilibrium configuration of rotating fluids, Christian Huygens (1629-1695) and Isaac Newton (1643-1727) came to the conclusion that the overall shape of the Earth should be a rotational ellipsoid. The oblateness of such an Earth-ellipsoid became the characteristic target quantity in this phase.
• C: From the middle of the 19^th century to the middle of the 20^th century: the geoid: In the first half of the 19th century it was discovered (by P.-S. Laplace, C. F. Gauss, F. W. Bessel, and others) that in general, the physical direction of the plumb line does not coincide with the normal of the rotational ellipsoid representing the model Earth. Consequently, the rotational ellipsoid represents only a rough model for the global figure of the Earth. Therefore, the ellipsoid was replaced by the geoid defined as level surface of constant geo-potential (sum of gravity and centrifugal potential) at “mean sea level” and extended onto the continents. The determination of the geoid became the main goal of geodesy since 1880 and is likely to remain one of the major goals of geodetic research in the future.
• D: Since the middle of the 20^th century: dynamics of the Earth's surface and relativistic models of the Earth system: The improvement in measuring accuracy through the development of satellite geodesy, laser distance measurements to the moon and radio-interferometry with long baselines, a fundamental change in the concept of geodesy was induced. This change can be characterized by three transitions, namely (1) from a static to a dynamical view, (2) from considering the solid Earth alone to a Earth system approach, and (3) from a “Newtonian” treatment to “Einstein's theory of gravity.“

An illustrative example of the first two transitions mentioned for phase D is the variations in the Length of Day (LOD). Initially, Earth rotation was considered a paragon of uniform motion and therefore served for the definition of the second as the 86,400^th part of the sideral LOD. However, using an electric quartz clock, in 1934/35 A. Scheibe and U. Adelsberger detected seasonal changes in the LOD of the order of several 10^-3 s/day. Subsequently, a large number of dynamical processes have been identified that affect the Earth rotation on time scales ranging from sub-daily to 10⁹ years. The causes for LOD changes are (1) exterior due to tides and solar winds, (2) interior to the solid Earth due to core rotation and core-mantle interaction as well as convection and (3) surface processes due to atmosphere, ocean and solid Earth interactions and mass relocations on the solid Earth surface (see Lambeck, 1980, 1988 for an overview). The strong dynamic coupling of the solid Earth to atmosphere and ocean as well as exterior forces required not only the transition from a static view to a dynamical view but also the consideration of the complete Earth system instead of the isolated treatment of the solid Earth.

For most terrestrial measuring techniques, relativistic effects can safely be neglected (see Table 1.6. in Soffel, 1989). At present, only gravimetry is able to penetrate into the relativistic regime. The development of superconducting gravimeters allows to measure gravity with an accuracy better than 10^-10 g approx. 1 nm/s² = 0.1 mugal while relativistic effects are of the order of 10^-9 g. However, the situation is drastically different in the case of frequency and time, where relativity plays an important role (for a more detailed discussion, see Soffel, 1989, pages 28-31). Anticipated improvements in the accuracy of time measurements are likely to change geodesy substantially over the next few years.

Additional readings:

• History of Geodesy, see Wikipedia: History of Geodesy