Why everything is shaped like a circle?

[blossom]

hi,

As I said in the title our universe has a lot of circular or spherical ( no angles) objects such as
planets, water drops, planets orbit, tornados, water movment in a sink, bubbles..etc.
So, other than reducing friction and space...why everything is curved??

thanks

 

[xxChrisxx]

Planets are round because of gravity.

Water drops and bubbles are because spheres have the least suface tension for a given surface area/volume (I think, need clarification on this)

Orbits are generally elliptical not circular.

Nor too sure about the sink and tornados though, but I suspect its the same thing that governs as they are both vortices.

 

[turbo]

hi,

As I said in the title our universe has a lot of circular or spherical ( no angles) objects such as
planets, water drops, planets orbit, tornados, water movment in a sink, bubbles..etc.
So, other than reducing friction and space...why everything is curved??

thanks

There are objects in space that are irregular and non-circular, generally because they are small enough not to assume a spherical shape due to self-gravity. Think asteroids.

 

[Bob S]

Ask Copernicus (1473-1543) why he developed the heliocentric model for planetary motion. Review Kepler's equations for planetary motion, and why the most general planetary orbit is an ellipse (circle is special case).
Suppose you had a drop of water (about 1/10 cubic cm) and the surface tension minimized the surface area. What shape has minumum surface area for a given volume?

 

[Andy Resnick]

Another very general argument is based on the energy of a sharp bend (or corner, crease, etc)- the energy density is very high in the neighborhood of a 'sharp angle'.

Atomically sharp objects (AFM tips, for example) are slightly rounded. To change a trajectory along a discontinuous (or piecewise continuous) curve requires infinite energy (applied over an infinitesimal time).

 

[fleem]

As for orbits, most orbits are in the same orientation of spin as their parent object simply because when they were forming from dust, the collisions of those primal dust particles caused them to match the global flow/angular rotation. Also there were forces causing parent bodies to spin faster than their orbiting satellites. So for a planet orbiting in the same direction as its parent's spin, where the parent's spin is faster than the orbit, tidal effects will cause the orbit to become more circular. Specifically, the tidal bulge of the parent accelerates the planet more when it is at periapsis (closest point in its orbit) than at apoapsis (farthest point).

 

[SW VandeCarr]

hi,

As I said in the title our universe has a lot of circular or spherical ( no angles) objects such as
planets, water drops, planets orbit, tornados, water movment in a sink, bubbles..etc.
So, other than reducing friction and space...why everything is curved??

thanks

In a very general sense, it has to due with the scaling of electromagnetic and gravitational forces. At human scales in the Earth's gravitational field , naturally round (spheroidal) objects are rare; the exceptions being bubbles and water drops at millimeter scales where surface tension dominates. At planetary and stellar scales, round objects are dominant once you get up to the largest asteroids. At galactic scales you get mostly discs and spirals. At larger scales you get strings and sheets of galaxies with large voids.

Circular motions in fluids and curvature in biological forms have other explanations. Corollas forces in the former, and surface area minimizing natural selection in the latter. In general matter made of polymers doesn't have sharp edges.

 

[maverick_starstrider]

Well both the electromagnetic force and gravity are spherically symmetric. Thus, since all things try to minimize energy, one will often find something in an equilibrium state that is spherical.

 

[rcgldr]

Crystals are not circular. They are polygons with relatively sharp edges.

 

[maverick_starstrider]

Crystals are not circular. They are polygons with relatively sharp edges.

Well they are still minimizing the energy of a spherically symmetric potential. They try to maximize their distance. In the limit of sides a polygon becomes a circle. There are of course structures like diamond that don't really follow this but I'm just pointing out that this bonding is somewhat dictated by spherical symmetries.

 

[rcgldr]

Crystals are not circular. They are polygons with relatively sharp edges.

Well they are still minimizing the energy of a spherically symmetric potential. They try to maximize their distance. In the limit of sides a polygon becomes a circle. There are of course structures like diamond that don't really follow this but I'm just pointing out that this bonding is somewhat dictated by spherical symmetries.

I don't get this. Salt crystals are cubic, some other crystals are hexagonal. From what I read, there are different causes for the crystals to form the way they do.

http://en.wikipedia.org/wiki/Crystal#Properties
http://en.wikipedia.org/wiki/Crystal_structure#The_seven_crystal_systems

 

[maverick_starstrider]

I don't get this. Salt crystals are cubic, some other crystals are hexagonal. From what I read, there are different causes for the crystals to form the way they do.

http://en.wikipedia.org/wiki/Crystal#Properties
http://en.wikipedia.org/wiki/Crystal_structure#The_seven_crystal_systems

a simple substance with a fully filled valence shell (i.e. fully bonded) will form the lattice which minimizes it bond length potential and cross-interaction potentials. All point groups/symmetry groups that I can think of have identical bond angles between their bonds. This is ultimately a result of the spherical symmetry of the coulombic force. You get things like orthorhombic and such when your bonds are not identical (you have two different types of atoms with two different bonds). But ultimately the result is still an energy minimization with respect to spherically symmetric potentials.

 

[kldickson]

My understanding is that on a large scale, when you've got a lot of molecules that aren't in a solid state, that the simplest and most uniform method of dispersion or cohesion between the molecules in a substance is a sphere.

In a solid state, other molecules are affected by their molecular bonds.

Orbits are usually elliptical, not circular; refer to Kepler's equations.

I think you're making some false equivalencies.

 

[SW VandeCarr]

My understanding is that on a large scale, when you've got a lot of molecules that aren't in a solid state, that the simplest and most uniform method of dispersion or cohesion between the molecules in a substance is a sphere.

In a solid state, other molecules are affected by their molecular bonds.

That doesn't explain the spheroid shape of largest asteroids (Ceres) or large moons and smaller planets that are thought to be mostly solid (Mercury, Mars, the Moon, and most other large moons).

 

[kldickson]

SW VandeCarr, Ceres, if I remember correctly, is solid rock and not an accretion of material.

The planets and our moon, on the other hand, are accretions of material; the moon, for example, was formed when an asteroid hit the Earth early in its life and some of the material coalesced in orbit to form the moon.

In terms of their not-quite-spherical shape, the large-scale squished sphere seems to be a result of its rotation, which slightly distorts it (compare what happens when you grip two ends of a rope and whirl it around; as you whirl it faster, the catena shape narrows because of the 'centrifugal force' 'pushing' it outward from where it is suspended (yes, I know centrifugal force isn't an actual force, but rather a pseudoforce from the standpoint of non-inertial observing). On a smaller scale, there are such things as plate tectonics and meteor impacting to deal with.

 

[kldickson]

Mea culpa; Ceres is also an accretion of material, but it is not irregular; in fact, it is also roughly spherical. However, wonkily shaped asteroids are just rock.

 

[SW VandeCarr]

SW VandeCarr,

The planets and our moon, on the other hand, are accretions of material; the moon, for example, was formed when an asteroid hit the Earth early in its life and some of the material coalesced in orbit to form the moon.

That's true. My point is that at these scales, gravity is the shaping force, and it can occur by accretion and redistribution of solid crystalline material, not necessarily requiring fluid states. In fact it's interesting to ask why there aren't any solid crystalline rocks with "wonky" shapes as large or larger than Ceres.

 

[lstellyl]

As a general thing to think about, I think this is an important question to have answered.

Although this is my opinion, I think most of the answers thus far have been somewhat... specific.

The fact that things are "circular" or "spherical" is because circles and spheres are special... mathematically and physically.

As has already been noted... when you have attractive forces like gravity, large volumes of mass generally assume a spherical shape because that is the lowest potential

Similarly, spheres have the least surface area per volume, and again in molecules and (as was said) water droplets... this minimizes the potential and as such this is the general shape that molecules and droplets assume (though most of the time there are other offsets that the potential depends on)

Crystals, also mentioned, are like that because of the attraction/repulsion of the anions and cations (who have spherical potentials) and minimize themselves this way (and give rise to polygonal type structures due to the varying sizes of the ions)

Just think about it... circles and spheres are "unbiased"... they are the same in every direction, and as a result many natural things take on relatively spherical or circular shapes when there is nothing else to "bias" the direction to "be"

I don't know if that really makes sense... but yeah, that is my response.

 

[vin300]

a simple substance with a fully filled valence shell (i.e. fully bonded) will form the lattice which minimizes it bond length potential and cross-interaction potentials. All point groups/symmetry groups that I can think of have identical bond angles between their bonds. This is ultimately a result of the spherical symmetry of the coulombic force. You get things like orthorhombic and such when your bonds are not identical (you have two different types of atoms with two different bonds). But ultimately the result is still an energy minimization with respect to spherically symmetric potentials.

Satisfactory answer

 

[SW VandeCarr]

Satisfactory answer

Except that it ignores issues of scale. Why is Ceres spheroidal (about 1450 km diameter) while most smaller asteroids are not?

 

[cragar]

deep down everything is quantized into wave packets and these probably have
smooth contours.

 

[vin300]

Anything that is completely homogenous without any external force would be spherically formed, all solids, liquids gases
There's a youtube vid showing a huge water drop in zero gravity which distorts if touched and slowly regains originality

 

[SW VandeCarr]

Anything that is completely homogenous without any external force would be spherically formed, all solids, liquids gases
There's a youtube vid showing a huge water drop in zero gravity which distorts if touched and slowly regains originality

Still not understanding my question. The asteroids are generally considered to be the remnants of a planet which was destroyed (or never quite got together), possibly due at least in part, to the tidal effects of Jupiter's gravity. Up to a certain size, asteroid shapes are highly irregular. The largest ones however, are recognizable spheroids. Smaller rocky asteroids hold their irregular shape because of electromagnetic forces predominating over gravitational forces. However, at some point, gravity becomes strong enough to mold the shape into a spheroid. What is this point and can it be calculated, assuming we can estimate the mass densities of the asteroids? Could a large irregularly shaped rocky asteroid (larger than any known asteroid) made of a single piece of hard granite-like material exist?

 

[blossom]

Wow, that is really a lot of information!
Thank you all. Do you think that second year student in physics department should know
all of this?

There is so much to learn here.

Thanks again

 

[SW VandeCarr]

Wow, that is really a lot of information!
Thank you all. Do you think that second year student in physics department should know
all of this?
Thanks again

Speaking for myself, the questions I raised are directed to the Physics Forum members. The initial question is not an easy one to answer.

 

[astronomer22]

I respect and appreciate the answers provided by everyone here to "blossom"s question.
Putting just a though across...
Can the shape of objects be related to the container in which that object is contained?
Is everything more or less spherical because the universe as a whole is supposed to be spherical.
Conversely, if everything...particularly the largest objects are almost spherical, can that provide a clue to the actual shape of our universe?

 

[GRB 080319B]

Is energy minimization with respect to spherically symmetric potentials related to the inverse- square law?

http://en.wikipedia.org/wiki/Inverse_square_law" : "The inverse-square law generally applies when some force, energy, or other conserved quantity is radiated outward radially from a source. Because the surface area of a sphere (which is 4πr^2) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it must spread out over an area that is proportional to the square of the distance from the source. Hence, the radiation passing through any unit area is inversely proportional to the distance from the source."

 

[vin300]

The simple reason stated by many for the spheroidal shape of bigger astronomical bodies is gravity that pulls all mass equally around the centre of mass to form a sphere and then obviously the centrifugal force causes bulging towards the equatorial plane, since the centre of gravity of the mass is fixed, it exerts equal forces in all directions(so huge bodies appear spheroidal from a distance, although there are variations at the surface level, just as you would see a smaller uneven asteroid to be a spot(implies spherical) from a distance.
It's jupiter's terrific gravity that keeps the asteroids from formng a planet

 

[SW VandeCarr]

The simple reason stated by many for the spheroidal shape of bigger astronomical bodies is gravity that pulls all mass equally around the centre of mass to form a sphere and then obviously the centrifugal force causes bulging towards the equatorial plane, since the centre of gravity of the mass is fixed, it exerts equal forces in all directions(so huge bodies appear spheroidal from a distance, although there are variations at the surface level, just as you would see a smaller uneven asteroid to be a spot(implies spherical) from a distance.
It's jupiter's terrific gravity that keeps the asteroids from formng a planet

I can see how a body with a semi-fluid core and plate tectonics would be molded by gravity into a spheroid. Such cores are also,I believe, more likely in larger bodies, at least early in their history. Also the larger the body, the smaller surface irregularities are in proportion. The Moon and Mars are two spherodal bodies which once had fluid cores, but apparently no longer do.

My question is hypothetical. Can a solid irregular body as large as Ceres exist if, for whatever reason, it never had a molten core? Such a body would have a larger surface to mass ratio than a spheroid and of equal volume and density and could cool throughout more quickly. (I know radioactivity also plays a role, but let's ignore that.) Also the variation of gravitational potentials over its surface would be large. Can such a beast exist? How would gravity under such conditions mold a solid slab of cold rock with a volume equal to Ceres into a spheroid? Could such a large irregular cold solid body arise from the violent breakup of a planet like Mars? I think it possibly could.