this post was submitted on 10 Dec 2023
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Bertrand's theorem states that stable orbits are only possible for one single inverse distance relation (in classical mechanics): inverse square
If the law is not inverse square (or harmonic oscillator), there will be no long lasting orbits, no galaxy clusters, no galaxies, no star systems, no planet and moon pairs.
If the electrostatic force wasn't inverse square, electromagnetic force would look much different. No gauss law would be possible.
Inverse square relationship is really neat
There's a lot of things which are required to be exactly as we observe them to be for our surroundings to work out as we observe them to be. If they weren't we wouldn't be here to observe, or, at the very least, we'd be quite different.
Also as to other universes: Who says that any random universe with other laws ties together objects based on their mass. For all we know their attractive force could be relative to photon emissions and elves keep the orbit stable by strategically shining torches at the sky (ok that's not that likely evolutionary speaking but we're talking physics).
That's why it's interesting that inverse square is in electrostatic and gravitational forces only. Weak and strong force don't follow inverse square. And we don't see the highly complex organization inside the nucleus that we see outside it (otherwise we'd have stable orbits inside the nucleus as well)