Gravity Field Theory

Gravity keep all things on the earth surface on the ground. Gravity method is one of the oldest geophysical methods. It is used to solve many geological problems. This method can be integrated with the other geophysical methods to prepare more accepted geophysical model. Understanding the theory and the principles concepts considered as an important step to improve the method. Chapter one attempt to discuss Newton’s law, potential and attraction gravitational field, Geoid, Spheroid and geodetically figure of the earth, the gravity difference between equator and poles of the earth and some facts about gravity field.

GEODESIC ALGORITHMS: AN EXPERIMENTAL STUDY

<p><strong>Abstract.</strong> The figure of the Earth can be modelled either by a cartesian plane, a sphere or an (oblate) ellipsoid, in decreasing order with respect to the approximation quality. Based on those models, we experimentally study the accuracy-performance trade-offs of various methods for some basic geodesic problems. For our experiments we use the open source libraries Boost Geometry and GeographicLib. Our results can be used as a reference for practitioners that want to use the most efficient method with respect to some given accuracy. Geodesic computations are building blocks for many higher level algorithms such as k-nearest neighbour problems, line interpolation, area and buffer, to name a few.</p>

The International Association of Geodesy: from an ideal sphere to an irregular body subjected to global change

The history of geodesy can be traced back to Thales of Miletus (∼600 BC), who developed the concept of geometry, i.e. the measurement of the Earth. Eratosthenes (276–195 BC) recognized the Earth as a sphere and determined its radius. In the 18th century, Isaac Newton postulated an ellipsoidal figure due to the Earth's rotation, and the French Academy of Sciences organized two expeditions to Lapland and the Viceroyalty of Peru to determine the different curvatures of the Earth at the pole and the Equator. The Prussian General Johann Jacob Baeyer (1794–1885) initiated the international arc measurement to observe the irregular figure of the Earth given by an equipotential surface of the gravity field. This led to the foundation of the International Geodetic Association, which was transferred in 1919 to the Section of Geodesy of the International Union of Geodesy and Geophysics. This paper presents the activities from 1919 to 2019, characterized by a continuous broadening from geometric to gravimetric observations, from exclusive solid Earth parameters to atmospheric and hydrospheric effects, and from static to dynamic models. At present, we identify geodesy as the discipline of quantifying global change by geodetic measurements.

Deformations of celestial bodies

This chapter studies various gravitational effects arising from the non-sphericity of celestial bodies. It first considers the quadrupole expansion of the potential, as well as the causes of the non-sphericity of the bodies. Finally, it turns to the figure of the Earth. To calculate the proper potential of the Earth, it attempts to determine its deformation due to a perturbing potential. Doing this accurately requires knowledge of the internal structure of the Earth and use of the techniques of the mechanics of continuous media. In this approach, the internal stress–strain relationships of a body are described by various phenomenological parameters and it becomes possible to study the response of the body (deformation, oscillations, etc.) to the field of an external force.