Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-06-23
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
47 pages
Scientific paper
Attempts to merge the Einsteinian gravity with Newonian run into logical inconsistencies coming from the fact that in Newton's gravity time is absolute and speed of propagation of gravity is assumed to be infinite. Such an assumption was in a focus of attention of many scientists in 19th century interested in finding out if, indeed, the speed of propagation of gravity is infinite. For this purpose, by analogy with electrodynamics,some retarded potentials replacing Newtonian were suggested. Using one of such potentials Gerber correctly calculated the perihelion shift for Mercury in 1902. However, subsequent attempts at calculation of the bending of light using Gerber-style calculations were not successful. Recently Gine' (Chaos, Solitons and Fractals 42, 1893 (2009)) was able to reobtain both the perihelion shift and bending of light using retarded potential. His equations however are not those obtained by Einstein and the results coincide with those by Einstein only at the level of leading order terms of infinite series expansions. The obtained differential equations of motion are of delay-type. When applied to two-body dynamics such equations lead to orbital quantization. In this work,we use Einsteinian approach to reproduce this quantization. The developed formalism is tested by calculating the number of allowed stable orbits for planets and those for regular satellites of heavy planets resulting in good agreement with observational data. The paper also briefly discusses quantum mechanical nature of rings of heavy planets.
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