Relativity, Gravitation, and GPS: Filling the Voids

This work presents the fundamentals of the science of general relativity and gravitation (GR) and the principles of application of this science in the technology of geographical positioning systems (GPS). Of the science of GR, the topics covered include: tensor analysis, including the development of the metric tensor, tensor calculus and the Riemann-Christoffel tensor; the geodetic equation; the equations of gravitational fields in the absence and in the presence of matter; the generally covariant reformulation of Maxwellian electromagnetism; relativising physical relationships; the Newtonian approximation; the Schwarzschild solution; the relativistic precession of Mercury’s orbit; and the Schwarzschild black hole. In the section on GPS, the topics covered include: the structure of the GPS; the synchronization of clocks in an Earth-Centered Earth-Fixed (ECEF) coordinate system; the setup and behaviour of clocks on satellites in the Space Segment; frequency shifts of signals from satellite-based clocks; the principles of the determination of local time and position by receivers; and relativistic sources of errors of timing and their compensation. The book seeks to provide a full development of basic GR principles and their application in the technology of GPS. The presentation is integral and self-sufficient. That is, for the reader with the prerequisite background, there should be no need to refer to other works in order to assimilate the material presented. Therefore, several concepts and methods, that elsewhere are not discussed or are axiomatically presented, are here developed in a logically satisfactory manner. These include: - the general form of the metric tensor - raising and lowering the indices of tensors - the Schwarzschild Solution - the dynamic significance of the semi-latus rectum and the eccentricity - the expressions of the eccentricity timing error and its compensation used in the Control Segment and in the receivers of users - the forms of the correction of parameters of the ephemeris of GPS satellites - a rationale for the selection of an angle of orbital inclination of about 55 degrees for all the satellites of the GPS. Rational completeness of the presentation is the objective expressed in the book's subtitle: 'Filling the Voids. In Part II, a poem - "The Illusions of Space, Time, and Spacetime" - is presented that conveys the author’s ‘philosophic’ views on the nature of time, space, and spacetime. This poem complements the discussion in the Introduction of the myth of the ‘spacetime fabric’ that has appeared in recent scientific and popular presentations of GR.