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Comment by lhd1 | Hacker News Reader

One of the cool facts about gravity is that the gravitational field of a body 'feels' spherical at a distance, even if those bodies are not spherical themselves. There are higher multipoles but they are increasingly suppressed the further you are from the body. So at least for gravity the spherical approximation turns out to be good and justified.

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Beyond a "cool fact", this is the only reason that physics works, where I'm defining physics as the human study of physical laws, not the laws themselves. If we couldn't neglect higher moments systems from planetary motion to the large scale structure of the universe would be computationally intractable.

And it's not just gravity, it's also electromagnetism: charge arrangements (i.e. ions) look like point charges at a distance, meaning you can neglect the electron orbital structure. Light sources act like point sources at a distance too.

A lot of the equations you learn in introductory physics rely on the higher moments vanishing.

- The planetary motion equations (Kepler's laws) assume gravity as a point source (the three body problem can be approximated by replacing two of the bodies with 1)

- E = mgh -> assumes a homogeneous gravitational field, which is a special case of gravitational monopole near an equipotential surfaced. And of course parabolic motion and pendula only work because this holds.

And if they were intractable, motions would be so irregular that pheneomena such as billion-year stable orbits would not be possible... leading to a lack of evolution and life generally. So it is a very good and necessary thing that cows remain mathematically spherical.

This point of view is essentially codified in effective field theory, which tells us why so much of classical physics (EM, fluids, gravity) can be seen as low order approximations of some more complete theory that we found later on. One of the great insights from 20th century physics imo.

for simulating gravity in particular you can do one better, since a sphere is in turn gravitationally indistinguishable from a point mass due to the https://en.wikipedia.org/wiki/Shell_theorem#Force_on_a_point...

and you can do one better than that - Birkhoff's theorem, the relativistic analogue of the shell theorem.

https://en.wikipedia.org/wiki/Birkhoff%27s_theorem_(relativi...

This deserves a simulator

Ah yes, indeed, the well-known point-cow approximation!

The point-cow is simply the zero-dimensional generalization of the spherical cow.

Hence for all practical purposes, zero-dimensional cows are spherical.

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