As the Earth`s surface deviates from its spherical shape by less
than 0.4 percent of its radius and today's satellite missions
collect their gravitational and magnetic data on nearly spherical
orbits, sphere-oriented mathematical methods and tools play
important roles in studying the Earth's gravitational and magnetic
field. Geomathematically Oriented Potential Theory presents the
principles of space and surface potential theory involving
Euclidean and spherical concepts. The authors offer new insight on
how to mathematically handle gravitation and geomagnetism for the
relevant observables and how to solve the resulting potential
problems in a systematic, mathematically rigorous framework. The
book begins with notational material and the necessary mathematical
background. The authors then build the foundation of potential
theory in three-dimensional Euclidean space and its application to
gravitation and geomagnetism. They also discuss surface potential
theory on the unit sphere along with corresponding applications.
Focusing on the state of the art, this book breaks new
geomathematical grounds in gravitation and geomagnetism. It
explores modern sphere-oriented potential theoretic methods as well
as classical space potential theory.
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