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Quantum Signatures of Solar System Dynamics  Arkady L. Kholodenko
;  Date: 
1 Aug 2007  Abstract:  Let w(i) be a period of rotation of the ith planet around the Sun (or w(j;i)
be a period of rotation of jth satellite around the ith planet). From
empirical observations it is known that the sum of n(i)w(i)=0 (or the sum of
n(j)w(j;i)=0) for some integers n(i)(or n(j)) (some of which allowed to be
zero), different for different satellite systems. These conditions, known as
ressonance conditions, make uses of theories such as KAM difficult to
implement. To a high degree of accuracy these periods can be described in terms
of the power law dependencies of the type w(i)=Ac^i (or w(j;i)= A(i)m^i) with
A,c (respectively, A(i),m) being some known empirical constants. Such power law
dependencies are known in literature as the TitiusBode law of
planetary/satellite motion. The resonances in Solar system are similar to those
encountered in old quantum mechanics. Although not widely known nowadays,
applications of methods of celestial mechanics to atomic physics were, in fact,
highly successful. With such a success, the birth of new quantum mechanics is
difficult to understand. In short, the rationale for its birth lies in
simplicity with which the same type of calculations are done using new methods
capable of taking care of resonances. The solution of quantization puzzle was
found by Heisenberg. In this work new uses of Heisenberg’s ideas are found.
When superimposed with the equivalence principle of general relativity, they
lead to quantum mechanical tratment of observed resonances in the Solar system.
To test correctness of our theoretical predictions the number of allowed stable
orbits for planets and for equatorial stable orbits of satellites of heavy
planets is calculated resulting in surprisingly good agreement with
observational data.  Source:  arXiv, 0707.3992  Services:  Forum  Review  PDF  Favorites 


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