The Circle and Sphere - Why so prevelant in the Universe?

Techno-Raver

The stars are spherical. So are the planets. Galaxies are seemingly circular on a flat plane. Atoms are spherical, and so are cells within our bodies. The orbits are circular, and if the universe expanded in all directions equally from a singularity, then the universe itself must be spherical.

Any thoughts about why this may be?

russ_watters

Orbits are eliptical, atoms are not spherical (they are modeled that way), cells are not spherical, and the universe does not have a 3 dimensional shape.

The planets and sun are roughly spherical because of gravity.

chroot

Well, that was easy, wasn't it?

- Warren

Integral

Stars and planets are only approximately spherical. Atoms are not spherical, any attempt to apply macro concepts to the quantum world is bond to be wrong. Orbits are not circular. Any guess about the shape of the universe is apt to be as wrong as your guesses about the shape of atoms.

The frequency of near spherical "heavenly" bodies is due to the [itex] \frac 1 {r^2} [/itex] nature of gravitational forces.

Edit: Russ beat me to it!

rbj

i think that although all of the cavaets above are true, there is something about the spherical shape in 3 space that should be noted:

of any solid (3-dimensional) shape with a fixed volume V, the surface area of the sphere is less than the surface area of any other 3-dim shape of the same volume.

in flat (2-dimensional) space, of any shape with fixed area A, the circle is the shape that has perimeter smaller than any other 2-dim shape of the same area.

Mk

Also, if we want to tear apart the rest of your question into little-bitty bite-sized pieces, galaxies are not all circular on a flat plane either, but they are kept together by gravity, so are generally roundish.

http://en.wikipedia.org/wiki/Image:H...ence_photo.png

Farsight

Techno-raver: perhaps it might be easier to think about this if you asked yourself an opposite question, such as "Why aren't planets square?" You probably end up with what rbj was saying.

DaveC426913

Farsight proposes an excellent exercise: if not circular or spherical, what shape would make more sense? And why?

kleinjahr

Any other shape and the corners get knocked off.
Do a timelapse study of an ice cube melting and you'll see the corners melting first.

DaveC426913

I have this one-framer cartoon in my head:

God is in his workroom, marble dust coating everything, holding a hammer and chisel, and standing in front of the Earth - a perfect cube.

Mrs. God is standing behind him in the doorway, hair in curlers, saying "What's with all the sharp corners? You'll put your eye out!"

DaveC426913

Consider that, on any body large enough to have gravity (which is ... anything), any point that sticks above any other has a downhill slope. With enough jostling, every hill will be reduced to rubble, and every pile of rubble will be reduced to sand. Ultimately, everything will end up flattened at the bottom and every hole wil be filled. There's only one shape in the universe whereupon nothing is higher than anything else and nothing is lower than anything else.


(Note use of the words "higher" and "lower", which only have meaning in the presence of .. .gravity!)

BoTemp

I agree with what was said above; elliptical (approximately circular) orbits are a consequence of 1/r^2 gravity law, the spherical symmetry of the gravitational law is also responsible for spherical bodies.

On a slightly related note, why is pi so prevalent in physics? A great many E&M equations have it (u_0 being defined as 4pi x 10^-9), although that may just be a consequence of the units used. Same deal with the Einstein equation of gravity (G_ab = 8*pi*G/c^4 T_ab). Consequence of our units, or some deeper meaning? Thoughts?

Chaos' lil bro Order

Everyone answered your question well, most objects that are thought of as circular/spherical, are only modeled as such. However, I think you are looking for a concept like that found in Hydrodynamics where a water droplet conserves volume because its at its lowest energy while doing so. Anytime you ask such a broad question, the answer, once boiled down, is likely to reduce to 'because in doing so, it reaches its lowest rest energy'.

arildno

For biological systems, the sphere is just about the worst shape to use, since it places a severe limit on how big/how efficient the organism can be.

To see this in simplified form:
1. Let V stand for a volume, S for the associated surface
2. Let N stand for "needed nutrients (stuff) per unit volume", and let P stand for "amount of stuff able to permeate the surface, per unit surface area"

Thus, if a cell/organism is to survive, we evidently need the inequality:
[tex]P*S\geq{N}*V[/tex]
or, rewritten:
[tex]\frac{V}{S}\leq\frac{N}{P}[/tex]
For a spherical object with radius r, this indicates a maximal size given by:
[tex]r\leq\frac{3N}{P}[/tex]

Rather than being spherical, then, many structures in the cell have extremely wrinkled surfaces (like the mitochondria, Golgi apparatus, and so on), making them more efficient in the uptake process.

Note that for a BIOLOGICAL system, ensuring adequate access to nutrients is along with minimizing energy expenditure and gene propagation the most important issues. None of these issues are really relevant for a non-biological system. This explains that common "strategies" for non-biological systems might not be optimal for the biological systems.

rbj

the [itex]4 \pi[/itex] that you'll find in Coulomb's Law or with any other inverse-square law ([itex]G[/itex] would have to be modified) is because of this concept of flux and flux density that is, in my opinion, a first principle which results in the [itex] 1/r^2 [/itex]. it's really [itex] 1/(4 \pi r^2) [/itex] and [itex] 4 \pi r^2 [/itex] is the surface area of a sphere of radius [itex] r [/itex]. this concept of flux and flux density is used in Gauss's Law which is applicable to any inverse-square field.

DaveC426913

As Arildno points out, unlike many natural processes which, for a given volume, tend to minimize surface area, biological systems often need interfaces where, for a given volume, surface area is maximized.

arildno

I agree whole-heartedly with your caveat "sometimes"..