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 Originally Posted by OngBonga
I'm curious if mojo has any suggestions.
In your definition, you have defined "perfect" as an unphysical property, so no, I can't prove you wrong.
(unlike the dark matter, which you took me too much at face value when I said we haven't observed it to interact in any way but gravitation. I should have said, we have observed that it does not interact electromagnetically - which includes chemically. It is through electromagnetic interactions that stuff has a surface to be grabbed and manipulated, which is how you move things into your digestive system and then digest it. Still can't eat dark matter in any meaningful way.)
I could take odds with the utility of your definition of perfect circle, as pertains to physics, but not as pertains to mathematics.
I wont do this, as it's stupid. The rigorous mathematical definition is so useful.
Mathematically, a circle is a perfect circle, 'cause that's the only kind of circle. Anything less than perfect is decidedly not a circle, no matter how circular.
The closest thing in physics would be something like the surface of a neutron star or the equator of a black hole's event horizon. The problem here is that you are kinda really talking about smoothness, and if you think circular has a tricky definition, then you'll find "smooth" to be even more fundamentally fun.
Gravitational orbits tend to become more and more circular over time. In general an orbit is elliptical. The measure of how much more of an ellipse it is than a circle is called the eccentricity. The orbit will shed eccentricity over many periods and will tend to circularize over time. This is, as you may have guessed, asymptotic behavior.
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