How This Isomorphism Was Predicted
     In the first half of this century, the phycisist Niels Bohr was awarded the Nobel Prize for using the Bohr/Rutherford model to explain the hydrogen atom. This model was based on a direct analogy between atoms and the Solar System. Subsequently this model faltered for atoms more complex than hydrogen, and atomic/stellar analogies came to be regarded as "naive" or "quack" ideas.

     More recently, however, it has been recognized that Rydberg atoms (highly excited atoms with principal quantum numbers [n] ranging into the hundreds) are far more analogous to stellar systems than had been realized. Consequently the idea of stellar/atomic analogies has been rehabilitated among those who understand that atoms become more and more classical as n increases, and that Rydberg atoms are often called "planetary atoms" for good reason.

     Moreover, the similarities between what might appear to be radically different types of systems populating vastly different size scales were predicted by a discrete fractal model of the cosmos, called the Self-Similar Cosmological Paradigm. Reviews of this paradigm can be found at :

http://rloldershaw.people.amherst.edu/NOF.HTM

Select "A Fractal Universe?" for a rough "sketch" of the model

or "Self-Similar Cosmological Model: ..." for a more detailed review.

     Briefly, the SSCP describes the cosmos as a highly stratified, nested hierarchy which may be unbounded with respect to scale. We can observe systems on the Atomic, Stellar and Galactic Scales of the hierarchy, and it is proposed that for each major class systems on a given Scale, there is a class of self-similar analogues on all other Scales. According to this hypothesis and empirically-derived scale transformation equations, excited atoms in neutral or partially ionized states are analogous to main sequence stars. This analogy and the self-similar scaling equations have been supported by quantitative correlations between the sizes, rotation periods, oscillation frequencies, magnetic dipole moments, angular momenta, etc. of analogue systems.

     If the self-similarity between atoms and main sequence stars is valid, then the stars would have shapes that are similar to those of atoms. Alas, we can only observe the detailed shape of one star: the Sun. Though its shape fits with the analogy, many more stellar shapes would be needed for a scientific comparison. Unfortunately, nearly all stars are "point" sources and cannot be resolved by existing telescopes. Their detailed shapes remain unknown. But all is not lost. Stellar systems, like planetary nebulae, that eject their outer layers offer us an indication of what those shapes might be, if we are allowed the assumption that the ejected shells retain the basic morphology that they had before being ejected. Recent Hubble Telescope results support this assumption by showing that very young planetary nebulae have many of the same basic shapes as mature planetary nebulae, and implying that the shapes are traceable back at least to the birth of these systems (eg. Sky and Telescope, April 1997 , pg. 12).

     Obviously we would not expect the ejected shells to retain the exact shapes and full symmetry that they might have had prior to their explosive ejection events. Indeed, it is remarkable that so much specific structure and symmetry is retained in shells that have expanded by huge factors.

     The degree of similarity between the fundamental shapes found in these atomic and stellar scale systems seems to exceed what one would expect to occur by chance, or by subjective choosing of unrelated systems. Moreover, this example of cosmological self-similarity was predicted more than a decade ago.