WHO SAYS STELLAR AND ATOMIC SYSTEMS CAN’T BE ANALOGOUS?
The Rydberg atoms (highly excited atoms with high values of their principal quantum numbers) are very interesting in that they approximate a semi-quantized Bohr model of the atoms which was based on a direct analogy to the Solar System. Ordinarily, atoms in their ground state and very low energy states have properties quite unlike the Solar System. But that is not always the case.
Consider what happens when the atomic counterpart in the comparison is also in a very high-energy state. The following excerpts are from a recent paper by Kalinski et al in Physical Review A 67, 032503, 2003.
“We predict the existence of a self-sustained one-electron wave packet moving on a circular orbit in the helium atom. The wave packet is localized in space, but does not spread in time. This is a realization within quantum theory of a classical object that has been called a “Rutherford atom,” a localized planetary electron on an unquantized circular orbit under the influence of a massive charged core.” “[W]e provide the first demonstration of the existence of what has been called  a “Rutherford atom,” i.e., the wave function for a single electron moving on an unquantized stable and nonspreading planetary orbit about a massive charged core.”
When a proper comparison is made between high-energy state atoms and high-energy state stellar systems, like the Solar System and most exoplanet systems, the stellar/atomic analogies and self-similarity are quite strong. This is not a naïve idea and one should not have to feel defensive about the concept. It is those who would deny strong stellar/atomic analogies for highly excited atoms who are in error.
I should add that for Rydberg atoms to be analogous to Bohr/Rutherford planetary atoms, BOTH their principal and orbital angular momentum quantum numbers (n and l) need to be very high. In the less common case of very high n, but relatively low l, you get a system that is more analogous to a very puffed up Red Giant star, i.e., an atom that is hugely expanded but still has a roughly spheroidal electron wavefunction.
Robert L. Oldershaw
Discrete Scale Relativity/Fractal Cosmology