caa a22 4500 467905991 CHVBK 20180406152834.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s10701-006-9050-3 doi (NATIONALLICENCE)springer-10.1007/s10701-006-9050-3 Aspects of the Mach-Einstein Doctrine and Geophysical Application (A Historical Review) [Elektronische Daten] [W. Schröder, H. Treder] The present authors have given a mathematical model of Mach's principle and of the Mach-Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach-Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by C. Neumann, Mach, Friedländer and Einstein—result from the Riemannian dynamics with the Mach-Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t2. In this paper, secular consequences of the Mach-Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation $$\dot{\alpha}$$ of the parameter α is the order of magnitude $$\dot{\alpha}=-H_0 \alpha$$ , where H0 is the instantaneous value of the Hubble constant: $$H_0 =\left({\dot{R}/R} \right)_0 \approx \left( {0.5-1.0} \right) \times 10^{-10}a^{-1}$$ . The relation of the secular consequences of the Mach-Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed. Springer Science+Business Media, Inc., 2006 celestial mechanics nationallicence Dirac's hypothesis nationallicence Mach-Einstein doctrine nationallicence Mach's principle nationallicence palaeogeophysics nationallicence Schröder W. Geophysical Commission, Hechelstrasse 8, D-28777, Bremen, Germany aut Treder H. Geophysical Commission, Hechelstrasse 8, D-28777, Bremen, Germany aut Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/6(2006-06-01), 883-901 0015-9018 36:6<883 2006 36 10701 https://doi.org/10.1007/s10701-006-9050-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-006-9050-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Schröder W. Geophysical Commission, Hechelstrasse 8, D-28777, Bremen, Germany aut NATIONALLICENCE 700 1- Treder H. Geophysical Commission, Hechelstrasse 8, D-28777, Bremen, Germany aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/6(2006-06-01), 883-901 0015-9018 36:6<883 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer