The Mountain Altitude Constant And Molecular Bonds

Every once in a while, there is a posting here that I just cannot wait to get written. This posting is one of them. Today, I would like to show readers a vivid example of how many relatively simple things that there are all around us that no one has yet pointed out.

Many mountain formations are formed by tectonic collisions, between continental land masses or between one of those continental land masses and the Pacific Tectonic Plate. Other mountains are formed as volcanoes by magma emergence from below. The rules of collisions are neatly explained in physics texts, and there are also laws in physics governing emergence such as Graham's Law of Effusion.

So, why is it that geologists do not usually apply the same kind of numbers and formulae to the formation of mountains?

After writing the posting "The Scale Of Gem Formation", on this blog, I got to wondering if any similar principles might apply elsewhere. This posting was my rule about why gems that refract light are of the size scale that they are. Such gems are of the scale to be worn as jewelry, but never as big as cars or hills or mountains.

The reason is that transparency to light means that the component atoms are lined up in rows so that the light can pass between the atoms. Since these gems are formed by extreme tectonic pressure, the practical maximum size of light-refracting gems would be halfway between the scale of the earth and the scale of the component atoms in the gem. No light-refracting gems larger than this can be cut because the geologic pressures could not line up the atoms in perfect rows if it was closer in scale to that of the earth than that of the atoms.

I thought about mountains which are, like gems, the product of tectonic movement. Why are mountains as high as they are? Why aren't they higher, or lower, or why do they exist at all? I could not find any answers online. If the size of the earth which hosts the tectonic movement was the key to the scale of gems, then it might also be the key to the scale of mountains. There must be physical laws somewhere as to why a mountain is as high as it is.

The earth has gravity, but since it is rotating it also must have outward centrifugal force which is the opposite of gravity. This rotation is what drives the gradual tectonic movement of continental land masses across the surface of the earth. It also drives the movement of glaciers during the ice ages. What happens is that the spin of the earth pulls toward the equator and also in the direction of it's eastward rotation. When an object on the surface is large enough, such as the continental land mass or the glacial ice sheet, this "Equatorial Force" as I called it in the posting by that name on this blog, affects parts of the mass more than others so that it is pulled both toward the equator and also eastward.

This tectonic and glacial movement is a similar principle to that of tides, except that it is caused by the centrifugal force of the earth's spin rather than by gravity. Tides are not caused by gravity, but by a difference in gravity. The moon, and to a lesser extent the sun, create tides in the earth's oceans because the depth of the ocean means that the moon's gravitational pull is stronger at the surface of the water than it is at the bottom. The tides created by the sun are less than half that of the moon because, even though the sun's gravity is far greater than that of the moon, it is so much further away that the difference in it's gravity between the surface of the ocean and the bottom is much less. The center of our galaxy exerts tremendous gravitational force on us but it is so far away that the difference in gravity is negligible and there are no tides as a result. There are negligible tides in North America's Great Lakes because the lakes are not deep enough for there to be any noticeable difference in the moon's gravitational force at the surface, compared to the bottom.

This outward centrifugal force of the earth's rotation must be much weaker than the earth's gravity. If it were stronger, the earth would not even hold together. If the two forces were equal, objects on the earth's surface would be weightless. Anyone who has ever been on a carnival or amusement park ride is familiar with centrifugal force.

The article on www.wikipedia.org , "Centrifugal Force (Rotating Reference Frame)", under the heading "Earth", provides the seemingly obscure fact that the outward centrifugal force created by the earth's rotation is 1/289 that of the earth's gravity at the equator, where the centrifugal force is greatest.

However, I decided that this ratio of the centrifugal force to gravity must be manifested in some way by the world around us. Gravity pulls toward the center of the earth, but the rotational force which moves continental land masses so that they move across the surface and collide to create mountains operates at right angles to gravity. We know that the magma emergence along lines which forms mountains also operates by the spin of the earth, whether the resulting mountains form in lines on the land or sea floor or at a point as a volcano.

So, the continental land masses are held down by gravity but are also moved laterally by the centrifugal force of spin and this lateral force is 1/289 that of the gravity pulling toward the center of the earth. My reasoning is that, if gravity is pulling toward the center of the earth with a force that is 289 times greater than the centrifugal force driving continental land masses laterally, which collide to form mountains, then this must be a factor in how high those mountains will end up being, relative to the radius of the earth.

Next, we have to consider the nature of tectonic collisions.

If there were two continental land masses being driven in diametrically opposite directions across the earth's surface so that they collided to force up the land at the collision front to form mountains, then we could reason that the maximum altitude of such mountains would be 1/289 of the earth's radius. In the same way that gems which refract light, because the atoms were lined up in essentially perfect rows by tectonic pressure, cannot be closer to the earth in scale than to the component atoms, mountains formed as a result of centrifugal force of earth's rotation cannot exceed the ratio of that force to the gravity which holds the mass down to the radius of the earth.

However, that is not what happens. The centrifugal force driving tectonic movement tends to pull continental land masses in the same direction so that, when there are collisions, they will be between a moving continental land mass and a stationary one, or with the stationary Pacific Tectonic Plate.

Since collisions take place between a moving continental mass and a stationary one, we must actually divide the 1/289 in half to get our Mountain Altitude Constant so that it is 1/578. This is because the moving continental land mass and the stationary one which it collides with are both composed of similar types of rock. This means that the mountain building which takes place as a result of the collision will be divided between the two land masses so that we can expect the altitude of the mountains to be only about half of what they would be if there was kinetic energy in both masses.

The radius of the earth, the distance to the center to which gravity pulls, is about 6250 km or 4000 miles. If we divide this distance by 578, we get about 10.8 km or 6.9 miles. Sure enough, the very highest mountains in the world, both collision and volcanic mountains, come close to this figure but none exceed it. This is true of collision mountains in the Himalayas like Everest and K2, and also volcanic mountains like Mauna Kea and Mauna Loa if we measure their altitude from the ocean floor on which they originate. Mountains thus have a lot in common with gems which refract light.

The reason that all mountains are not this high is due to the nature of the continental land masses. The mass is not something like perfectly malleable clay, but has a certain brittleness as well as elasticity on a large scale. So, when a collision takes place, instead of a single row of maximum height mountains at the collision front, multiple rows of much lower mountains tend to form.

Newton's Inverse Square Law also comes into play. If two mountains are of the same conic shape, but one is twice as high as the other, it will have four times the volume. Also, much of the kinetic energy of collision goes not into raising mountains but into lifting the rock strata of the continental mass. The resulting spaces are where oil and natural gas tend to collect over millions of years.

This same principle applies to glacial movement which forms hills, but that is obviously limited in scale first, but the availability of soil and loose rock to form such hills and second, by the altitude of the weather which forms the glacial sheets of ice.

But anyway, physicists have a fraction with which they are all familiar that is 1/137. This is known as the Fine Structure Constant and described the strength of electromagnetic interactions. Now, geologists have their fraction too and that is 1/578 which is the Mountain Altitude Constant. This is the maximum altitude of mountains on earth, whether collision or volcanic, in relation to the radius of the earth.

MOLECULAR BONDS AND MOUNTAIN ALTITUDES

Today, let's have a look at another explanation for the altitudes of mountains relative to the size of the earth.

The thought occurred to me that the altitudes of mountains, indeed any irregularities in the earth's surface, are proportional to the size of the earth in the same ratio that the strength of chemical bonds in molecules is in proportion to the nuclear bonds in atoms. I have never heard of this being pointed out before.

First, let's recall my doctrine that is often referred to on the cosmology blog, that any large-scale structure must reflect the nature of it's building blocks. The most obvious example is that of orbits. Electrons are in orbitals around atoms, and this is reflected in the orbits of the large-scale astronomical bodies that are made out of these atoms. This is the way it must be because there is only a limited amount of information with which to construct the large-scale bodies.

Most of the matter in the universe is made of atoms, which often combine to form molecules. The chemical bonds which atoms form when they combine into molecules can be divided into ionic and covalent bonds. Ionic bonds are found where one atom loses an electron to another, so that one then has a net negative charge and the other a positive charge thus drawing the two atoms together by opposite charge attraction. Covalent bonds, which tend to be found in the carbon-based structures of living things, are where two atoms are bound together by the sharing of an electron. Chemical bonds involve only the outermost electrons in the orbitals around an atom.

The structure of a planet like the earth involves both chemical and nuclear bonds. It is the chemical bonds which bind atoms together into molecules, but it is the nuclear bonds which hold the atoms themselves together. The nucleus of an atom is composed of protons, which all have a positive electric charge. Since the basic rules of electric charges tell us that like charges repel, that means the protons in the nucleus should fly apart so that the atom would not be able to exist. The reason this does not happen is that there is binding energy in the nucleus which overcomes this like-charge repulsion, and holds the nucleus together. This nuclear bond is far far stronger than the chemical bonds which bind atoms together into molecules.

My reasoning is that the spherical surfaces of atoms are symmetrical, but the spheres bound together as molecules are not. This can easily be seen in the nature of water molecules, consisting of one oxygen and two hydrogen atoms. The oxygen atom is so much larger, and the two hydrogen atoms are on one side, that this makes the molecule polar. This means that the water molecule is more negatively-charged on one side, and more positively-charged on the other side. The result is that water molecules line up end-to-end, negative-to-positive. This is known as hydrogen bonding and is why liquid water and ice can exist, since water molecules are actually lighter than air by weight.

If the fact that water molecules are not symmetrical has such an effect, shouldn't the fact that no molecules are really symmetrical also have some effect? I have found that this question ultimately leads to why mountains and other irregularities of the earth's surface are of the scale that they are relative to the size of the entire earth. Imagine the earth as a model of an atom, with the size of the earth itself representing the strength of the nuclear bonds holding it's atoms together, and the surface irregularities representing the strengths of the molecular bonds between atoms.

We saw in "The Mountain Altitude Constant" that it is the centrifugal force of the earth's rotation, in relation to gravity, which determines what the maximum practical altitudes of mountains will be. But centrifugal force actually requires the asymmetrical forms of molecules to produce surface irregularities like mountains, hills and, continental shelves.

Centrifugal force alone will not produce surface irregularities, except for an equatorial bulge on the spinning planet. The irregular surface features that we see on earth are rooted in the irregular, asymmetrical structures of molecules. If the earth was composed of different atoms, but with no molecular bonding, it would simply produce a layered planet with a smooth surface.

On earth, and the other terrestrial planets, the primary surface manifestation of molecular bonds is in rock and water. An all-iron planet, composed of atoms of iron but without molecular bonds, would form a smooth surface except possibly an equatorial bulge. Waves are a reflection of the molecular bonds in water, and the hydrogen bonds between water molecules.

A molten surface even if composed of molecules, without any force to produce waves, would be smooth because structural bonds would not form between molecules and there would be no reason for it to be anything other than smooth. The molten surface would be unable to accommodate any force which might produce surface irregularities. The sun's surface is smooth, even though it rotates, with the exceptions of an equatorial bulge, and occasional sunspots and solar flares. The reason being that the sun is too hot for molecular bonds to exist.

To get surface altitude variations like we have on earth, it is necessary to have a surface composed of molecules. Just as a large-scale structure must reflect the nature of it's building blocks, the earth must reflect the natures of the atoms and molecules of which it is composed. This will be manifested as the great difference in the strengths of nuclear bonds, relative to the chemical bonds which hold atoms together into molecules, showing up as surface altitude irregularities relative in scale to the size of the planet.

It does not matter if the variations in surface altitude are ultimately formed by tectonic movement driven by the planet's rotation, volcanic activity, glaciation or, impacts from space. These surface irregularities include mountains, hills and, continental shelves, and are ultimately formed by irregularly-shaped molecules being thrust against one another by some such force. It is the asymmetry of those molecules which shows up as surface altitude irregularities.

Theoretically, it should not matter if the planet is larger because a larger planet would have greater centrifugal force of rotation, and higher irregularities would form so that their proportion relative to the size of the planet would remain constant. Neither should it make a difference how dense was the material of which the planet was composed. If the planet were more dense it would be smaller, and the surface irregularities lower, but the relative proportion would remain the same, and would be that of the strength of the molecular bonds relative to the strengths of the nuclear bonds.

This is very closely related to what we saw in "The Chemical-Nuclear-Astronomical Relationship", on the physics and astronomy blog, where the approximate size that in space becomes spherical in relation to the size it has to be to initiate fusion and begin to shine as a star, is closely proportional to the proportion in magnitude between the strength of chemical bonds and the strength of nuclear bonds.

There is another way that we can see the effects of the asymmetry of molecules, that of eddys and whirlpools in air and water. We saw this in the posting, "Polarity, Turbulence And, Liquification", on the physics and astronomy blog www.markmeekphysics.blogspot.com . These are ultimately based on spinning molecules, which are asymmetrical. One direction of spin of many molecules predominates over the opposite direction, and the eddy or whirlpool forms. The lines of water molecules which form by hydrogen bonding are polar, and the two gases which compose almost all of the air, nitrogen and oxygen, are both diatomic, which means that molecules usually pair together. If we were dealing with single and symmetrical atoms, this would not be the case. This asymmetry of molecules must show up all around us because a large-scale structure must reflect the nature of it's building blocks.