## Quantum Signatures of Solar System Dynamics

**Authors:** Arkady L. Kholodenko

Let ω(i) be period of rotation of the i-th planet around the Sun
(or ω_{j}(i) be period of rotation of j-th satellite around the i-th planet). From
empirical observations it is known that within margins of experimental errors
Σ_{i} n_{i}ω(i) = 0 (or
Σ_{j} n_{j}ω_{j}(i) = 0) for some
integers n_{i} (or n_{j} ), different for
different satellite systems. These conditions, known as resonance conditions,
make uses of theories such as KAM difficult to implement. The resonances in
Solar System are similar to those encountered in old quantum mechanics where
applications of methods of celestial mechanics to atomic and molecular physics
were highly successful. With such a successes, 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 can be done using
methods of quantum mechanics capable of taking care of resonances. The solution
of quantization puzzle was found by Heisenberg. In this paper new uses of
Heisenberg?s ideas are found. When superimposed with the equivalence
principle of general relativity, they lead to quantum mechanical treatment of observed
resonances in the Solar System. To test correctness of theoretical predictions
the number of allowed stable orbits for planets and for equatorial stable orbits
of satellites of heavy planets is calculated resulting in good agreement with
observational data. In addition, the paper briefl?y discusses quantum mechanical
nature of rings of heavy planets and potential usefulness of the obtained results
for cosmology.

**Comments:** 61 pages.

**Download:** **PDF**

### Submission history

[v1] 21 Aug 2009

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