I’ve abbreviated a genuine Quora question here because it enables me to make a point. The full question suggested that we might learn something about our place in the universe from this fact.
It’s not a stupid question. It could lead to an understanding of the fractal nature of the universe and a theory of scale, perhaps.
And it permits me to confess that when I was fifteen I thought along these lines too. My path to wisdom has been a long path and we all have to start somewhere.
The problem is that the ‘facts’ included in the question are completely incorrect, as I subsequently learned.
First - electrons do not move around a nucleus in a manner that is in any sense similar to the way planets move around a sun.
Electrons are bound to the positrons in the atom through electro/magnetic fields. These bind them to particular shell configurations. Electrons are minute quantum particles which means they maintain duality - being both waves and particles - see Twin (or Double or Two) Slit Experiment.
http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html
Electrons can only shift between shells by the absorption or emission of quantised amounts of energy.
NONE of these things is true of planets. Planets orbit their sun due to the gravitational force. Planets are macro state bodies and do not do the wave / particle duality thing - they have well defined locations at all times. You cannot perform a Double Slit Experiment with a planet. Planets occupy orbits, not shells. Planets have defined orbits and cannot change them by the absorption or emission of quantised radiation.
So - NO. There is no similarity between chemistry and astronomy.
No - there is no connection so it cannot have any significance.
It therefore tells us nothing about our place in the universe.
If only the universe were as simple as I thought it was when I was fifteen I’d have it all sorted by now.
And that is the wisdom we can learn from this question. Reality is not simplified for fifteen year old minds like a Star Trek universe. It’s complex. One has to work at it. Asking questions, even naive questions, is a way of making progress. Learning to ask better questions IS progress.
Hope this helps.