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

1. Jun 27, 2006

### 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?

2. Jun 27, 2006

### Staff: Mentor

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.

3. Jun 27, 2006

### chroot

Staff Emeritus
Well, that was easy, wasn't it? :rofl:

- Warren

4. Jun 27, 2006

### Integral

Staff Emeritus
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 $\frac 1 {r^2}$ nature of gravitational forces.

Edit: Russ beat me to it!

5. Jun 27, 2006

### 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.

6. Jun 27, 2006

### Mk

7. Jun 27, 2006

### 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.

8. Jun 27, 2006

### DaveC426913

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

9. Jul 6, 2006

### 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.

10. Jul 6, 2006

### 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!"

11. Jul 6, 2006

### 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!)

12. Jul 7, 2006

### BoTemp

Pi?

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?

13. Jul 8, 2006

### 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'.

14. Jul 8, 2006

### 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:
$$P*S\geq{N}*V$$
or, rewritten:
$$\frac{V}{S}\leq\frac{N}{P}$$
For a spherical object with radius r, this indicates a maximal size given by:
$$r\leq\frac{3N}{P}$$

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.

Last edited: Jul 8, 2006
15. Jul 8, 2006

### rbj

the $4 \pi$ that you'll find in Coulomb's Law or with any other inverse-square law ($G$ 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 $1/r^2$. it's really $1/(4 \pi r^2)$ and $4 \pi r^2$ is the surface area of a sphere of radius $r$. this concept of flux and flux density is used in Gauss's Law which is applicable to any inverse-square field.

16. Jul 8, 2006

### 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.

17. Jul 8, 2006

### arildno

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

18. Apr 4, 2009

### j4d4

So, if I took a few atom's and jettisoned them in to the vacuum of space what shape would they take? Would they become spherical? If they do then wouldn't you think the shape of an atom on Earth might be distorted due to magnetic or gravitational influence's? Or do they just stay the same?

19. Apr 4, 2009

### DaveC426913

Two and half years dormant, but ...

Jettisoning a few atoms into space would not cause them to take on any shape. You'd have a bunch of atoms dispersing from your point of origin. You need to rethink the experiment.

20. Apr 5, 2009

### GoldenEagles

I get the impression that there is a consensus forming in regards to this thesis that the sun is supposedly spherical because of the law of gravity. But why is the law of gravity configured to make a sun or a planet spherical? What is the purpose being served by these spherical shapes? Do spheres have special properties that allow these astronomical components to operate more efficiently for their intended purpose? For example, if a planet was not spherical, you could not have sunrises, and sunsets, especially in terms of this nice transition between daylight and nighttime that every planet in the solar system enjoys. So, a planet is probably spherical, not simply because gravity makes it that way, but because the design of gravity has in mind producing evenly dispersed periods of day and night on planetary bodies, and that would be for the benefit of the occupants thereof. Sun's are spherical, not simply because gravity makes them that way, but because the design of the law of gravity has in view the need for the light emanated therefrom (i.e from a sun) to be visible at all points, to illuminate all bodies in a particular solar system. Also, the sun needs to be spherical to allow for uniform orbital paths for the planets. I don't think a planet could actually orbit anything but a sphere. So, the law of gravity must have these things in view as a design criteria when it comes to the formation of solar systems.

Though I am not sure that this gravity answer has universal application. Does it apply to dew drops? I don't think so. I seem to remember something about the principle of surface tension producing round dew drops. Now of course, certain natural laws are behind this phenomena of surface tension, but why were these natural laws crafted in such a manner, as to cause them to produce round dew drops? Isn't it because it is about the most pleasing shape to the eye, that can be imagined?

And moreover, does the gravity thesis apply to human eyeballs? I don't think so. I don't think you can reasonably argue that human eyeballs are spherical because of gravity. I think they are made spherical to achieve a certain optical functionality that would not be possible with any other shape.

Does the gravity thesis apply to ball bearings? I don't think so. Neither does it apply to basket balls, baseballs, marbles, and high pressure under sea exploration vehicles. Why were canon balls made to be spherical? I don't think it was because of gravity. Why are crystal balls made into spherical shapes? It wasn't because of gravity. They are made that way for a purpose. When you are jewing gum, and you blow a bubble, why does the bubble form a sphere? I don't think it is because of gravity. And that goes to all cases where liquid bubbles are formed. I don't think gravity can explain those spherical shapes.

Last edited: Apr 5, 2009