Fractal Cosmology
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8. Demonstrations from the Aspect of Space

From now, I'm going to calculate each ratio one by one.
All data used in these demonstrations are from the findings of modern science.
The purpose of these demonstrations is, as explained previously, to confirm if all ratios would be constant.

First, I will start with [atomic nucleus : galactic nucleus].
The ratio of [elementary particle : star] will be calculated in the end, for it needs some complicated explanation.

For some calculations, I'll use the mean radius of elements, the shapes of which are mostly spherical and compact.
But for some others, I'll use the mean diameter or a rough magnitude of elements, the shapes of which are mostly irregular.

(1) Atomic nucleus : galactic nucleus

The atom has a nucleus at its center.
The nuclear radius is about 1/100,000 of the atomic radius, i.e. 10^-13 cm.

The galaxy generally has a nucleus at its center, too, and its diameter does not exceed 1 light-year.
In case of the Milky Way Galaxy, the nuclear diameter is observed to be about 0.65 light-years.

Recently, quasars have been revealed as being the nuclei of active galaxies, and, their diameter is estimated to be no larger than 1 light-year.

Therefore, we may regard the nucleus of the Milky Way Galaxy as a standard.
Then the mean radius of galactic nuclei can be decided as 0.33 light-years.

Radius of atomic nucleus : radius of galactic nucleus
= 10^-13 cm : 0.33 light-years
= 10^-18 km : 3.12×10^12 km
= 1 : 3.12×10^30

(2) Atom : galaxy

The atomic radius is usually said to be 1 angstrom, i.e. 10^-8 cm.
Galactic diameters are ranging from 10,000 to 100,000 light-years so that we may take 30,000 light-years for the mean galactic radius.

Atomic radius : galactic radius
= 1 angstrom : 30,000 light-years
= 10^-13 km : 2.84×10^17 km
= 1 : 2.84×10^30

(3) Molecule : Group of galaxies

There are so many kinds of molecules and their sizes so various that it is very hard to determine the mean molecular size.
To regard their shapes as spherical, small molecules are said as ranging from 1 to 10 angstroms in diameter.

In an organism, proteins are the typical macromolecules, and they consist of amino acids.
Therefore, the amino acids may be regarded as the typical molecules in the organisms.
The size of amino acids in the alpha-helix structure, the typical protein folding, is about 5 angstroms.

Considering these factors collectively, we may take 5 angstroms for the mean molecular diameter of the organisms.

Several or dozens of galaxies gather to form a Group.
The typical extent of Groups is observed to be about 1.5 million light-years in diameter.

Molecular diameter: Group's diameter
= 5 angstroms : 1.5 million light-years
= 5×10^-13 km : 1.42×10^19 km
= 1 : 28.4×10^30

(4) Macromolecule : Cluster of galaxies

The primary organic elements in the organisms are the macromolecules such as proteins, nucleic acids or polysaccharides.
There are many kinds of macromolecules so that determining the mean size must be very hard, too.
Therefore, it's better to find a typical one.

The protein occupies the largest portion in an organism.
And a typical protein consists of about 200 amino acids.
So, we may say that the typical macromolecule in an organism is the protein which is assembled with about 200 pieces of amino acids.
The size of such a typical protein is about 300 angstroms.

Atoms are united to make up a molecule, and, in turn, molecules are combined to organize a macromolecule.

Such a process is exactly repeated in the macro world, too.
Nearby galaxies are combined to make up a Group, and Groups gather to form a Cluster.
The Cluster is generally formed by more than 50 galaxies, and its extent is about 10 million light-years.

Size of the macromolecule : magnitude of the Cluster
= 300 angstroms : 10 million light-years
= 3×10^-11 km : 9.46×10^19 km
= 1 : 3.15×10^30

(5) Organelle : Supercluster

The actual physiological processes of the cell are performed by organelles such as mitochondria, microtubules, Golgi bodies, etc., which are organized with macromolecules.
There are many kinds of organelles, and their sizes are all different.

However, you may notice that they are measurable mostly in some microns.
The mean size of them, therefore, could be said to be 5 microns.
As a tenfold variation is permitted for these calculations, most organelles may be covered by it.

The last stage in the Cosmos is the Supercluster, as same as the last stage in the cell is the organelle.
Since 1980, astronomers have discovered Superclusters, the greatest structures in the Cosmos, such as Bubbles, Stakes and Great Walls.

The extent of these Superclusters generally reaches some hundreds of millions of light-years.
So, we may take 500 million light-years for the mean magnitude of Superclusters.
Then, it may cover most of them, considering the tenfold variation.

size of the organelle : magnitude of the Supercluster
= 5 microns : 500 million light-years
= 5×10^-9 km : 4.73×10^21 km
= 1 : 0.95×10^30

(6) Cell : Cosmos

The human body consists of around sixty trillion cells.
The shapes of cells are generally spherical, and their sizes are mostly ranging from 10 to 100 microns in diameter.
So, we may take 50 microns for the mean cellular diameter.
Then the mean cellular radius makes 25 microns.

The Cosmic radius is often mentioned differently by scientists.
Their opinions on the Cosmic radius may vary but converge in ranges from 10 to 30 billion light-years. At present, 15 billion light-years is widely accepted as the Cosmic radius.
So, we may take 15 billion light-years for the Cosmic radius.

Cellular radius : Cosmic radius
= 25 microns : 15 billion light-years
= 2.5×10^-8 km : 1.42×10^23 km
= 1 : 5.68×10^30

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