Authors:
W. Schröder Geophysical Commission Hechelstrasse 8, D-28777 Bremen, Germany

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H.-J. Treder Geophysical Commission Hechelstrasse 8, D-28777 Bremen, Germany

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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 Galilei 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, too. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion laws R ~ t or R ~ t2. In this paper secular consequences of the Mach-Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research resulted in a secular decrease of the Earth's flattening and in the 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 a of the parameter a is of the order of magnitude a=-H0a, where H0 means the instantaneous value of the Hubble constant: H0=(R/R0)˜(0.5-1.0)·10-10a-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.

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Acta Geodaetica et Geophysica
Language English
Size B5
Year of
Foundation
2013
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó Springer
Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2213-5812 (Print)
ISSN 2213-5820 (Online)

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