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? :rofl:

- 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 $\frac 1 {r^2}$ 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:Hubble_sequence_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]

Any other shape and the corners get knocked off.

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]

Any other shape and the corners get knocked off.

Consider that, on anybody 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]

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?

 

[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:
$$P*S\geq{N}*V$$
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.

 

[rbj]

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?

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.

 

[DaveC426913]

For biological systems, [ sometimes ][ ed. ] the sphere is just about the worst shape to use...

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"..

 

[j4d4]

So, if I took a few atom's and jettisoned them into 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?

 

[DaveC426913]

Two and half years dormant, but ...

So, if I took a few atom's and jettisoned them into 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?

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.

 

[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.

 

[Loren Booda]

I believe 1/r² functions represent a majority of 3-dimensional mathematical constraints on objects at the quantum through cosmological levels, so probabilistically objects would tend to be spherical structures. If an object, composed primarily of sine or cosine waves, were created or destroyed by agglomeration or impact, it would eventually evolve toward the ideal of sphericity.

Decompose our universe into singularities of most fundamental mass, charge and spin. In first order, the first and second actions would yield spherical and the third circular symmetric force fields. Fourier series also seem to indicate that the cosmos can be reduced to circular harmonics more readily than to noncircular.

 

[Vanadium 50]

Do spheres have special properties that allow these astronomical components to operate more efficiently for their intended purpose?

Science says nothing about the "intended purpose" of stars and other bodies. Whose intent? There's no scientific answer to that question.

Further, you are making the assumption that all objects with the same shape have that shape for the same reason. That's not true - wheels are round for a different reason that manhole covers are round.

 

[loup]

sphere,
the surface tension is maximum.
And the surface area is the smallest.
That's why bubbles are all circle, am I right?

And why an orange is a shpere,

I think, to a cell, why it has intention to grow towards a particular side? Sphere, because every side are evenly grow, so it is sphere.

 

[GoldenEagles]

The principles of surface tension, raindrops and spheres are discussed in these two interesting videos.

Julius Sumner Miller - Physics - Soap Bubbles pt. 1

https://www.youtube.com/watch?v=kvrsAhuvs3M

Julius Sumner Miller - Physics - Soap Bubbles pt. 2

https://www.youtube.com/watch?v=ckr3VkLiJp0

In the second video he discusses the principle of spheres mentioned above, in terms of least surface area, and greatest internal volume, and the idea that spheres represent natures lowest energy state. Correct me if I am misstating that. That all amalgamations of atoms tend towards a spherical shape, because it takes the least energy to maintain that structure? I wonder why that would be.

 

[russ_watters]

Correct me if I am misstating that. That all amalgamations of atoms tend towards a spherical shape, because it takes the least energy to maintain that structure? I wonder why that would be.

I'm not sure what an "amalgamation of atoms" is, but molecules are not necessarily spherical. Large masses are spherical because of gravity and geometry, as discussed earlier in the thread. There is no mystery here, no reason to think this was some key "design" feature.

 

[cragar]

but molecules are not necessarily spherical

Then what shape are molecules?

Very interesting videos

 

[russ_watters]

Then what shape are molecules?

Very interesting videos

Lots of different shapes. DNA is a helix. Water molecules are V-shaped.

 

[cragar]

got ya

 

[Mapes]

Though I am not sure that this gravity answer has universal application. Does it apply to dew drops? I don't think so. ... And moreover, does the gravity thesis apply to human eyeballs? ...ball bearings?

These are great questions that enable a comparison and contrast of dominant physical laws. The one I find most interesting is the question about eyeballs. I wonder if the primary (but not sole) influence on the evolution of our eyeballs is the advantage of rotation around two orthogonal axes. But the surface tension issue must arise also from the need to enclose the vitreous humor.

I'm less intrigued by the sphericity of bubbles and planets, as these questions can all be reduced to energy minimization (or more fundamentally, the Second Law). We can ask why the universe was constructed in such a way to enable energy conservation and thermodynamics as we know it, but now we've moved from physics to some flavor of philosophy.

 

[DaveC426913]

But the surface tension issue must arise also from the need to enclose the vitreous humor.

I Learned something recently from my Optician. The vitreous humour serves no anatomical purpose once the eye is formed. It could be drained completely and replaced with saline with no untoward effects.

 

[Chaos' lil bro Order]

I Learned something recently from my Optician. The vitreous humour serves no anatomical purpose once the eye is formed. It could be drained completely and replaced with saline with no untoward effects.

Yes, but its vital in creating part of the turgor pressure needed to inflate the eyeball, so saying that replacing it with saline solution means that the saline would then provide the turgor pressure. That is certainly an anatomical purpose, unless you want your lens resting on your retina and you enjoy blindness.


@Mapes

Certainly the ball and socket physicality is important and efficient when one's shifts one's gaze upwards or sideways. But the primary reason the eye is spherical has to do with how light is refracted in the lens. We know the lens is not spherical but rather a flattened sphere not dissimilar to the geometry of a magnifying glass. Clearly there must must be space between the lens and retina for the refracted light to converge onto a point on the retina, so a spherical eyeball makes sense.