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Epilogue - Units, Constants, Data, and Links


Multiplication Factors
Common Names in SI Units
SI and British (fps) Unit Conversions
Unit Conversions
Natural Units
Physical Constants
Fabulous Formulas
Scales of the Universe
Planck Scale
Cosmological Constants (WMAP)
Astronomical Objects
Milky Way
Solar System Data
Ecliptic and Symbols
Periodic Table
Radioactive Isotopes
Electromagnetic Spectrum
Feynman Diagrams and Rules
Elementary Particle Data
Hadrons - Baryons and Mesons (in Strong Interaction)
Electrical Properties of some Materials, and Safety
Properties of Solids
Geological and Biological Evolutions
Genetic Code, Peptide, Chromosome, and DNA
Anatomy and Cell
Greek Alphabets, and Derivatives
The End

Finally, here's a recap of the previous webpages in the forms of tables and drawings. It could be a quick reference for finding out some properties of this world in terms of numbers.


Multiplication Factors

Million = 106, Billion = 109, Trillion = 1012, Quadrillion = 1015


Common Names in SI Units

SI names SI names


SI and British (fps) Unit Conversions


Unit Conversions

[click image to load]
online unit converters.
  • 1 ly. (light year) = 0.95x1018 cm
  • 1 pc. (parsec) = 3.26 ly
  • 1 AU = 1.496x1013 cm
  • 1 m (meter) = 100 cm
  • 1 micron = 10 - 4 cm
  • 1 ml = 1 cm3
  • 1 liter = 1000 ml
  • Temperature T (in oC) = T (in oK) - 273.15
  • Temperature T (in oF) = 1.8 x T (in oC) + 32
  • 1 ev (electron volt) = 1.602x10-12 erg
  • 1 joule = 107 ergs = 0.24 cal
  • 1 watt = 1 J/sec = 107 erg/sec
  • 1 mi/gal = 0.354 km/liter (auto fuel economy)
  • 1 knot = 1.15 mi/hr = 1.85 km/hr (maritime/air nav.)
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    Natural Units

    Natural units are often adopted in particle physics with c = = 1. Its use is supposed to simplify the notation of the formulas. The table below shows the various physical quantities in natural units in columns 4 (in [cm]) and 6 (in [erg]). The formula to convert them back to cgs units (i.e., explictly inserting back the c's and 's in the formula) are shown in columns 3, and 5 from the nature unit of [cm] or [erg] respectively. However, it doesn't seem to be that natural for converting some physical constants to natural units (see Hubble scale).

    Physical Quantity CGS Unit Conversion back to cgs Natural Unit [cm] Conversion back to cgs Natural Unit [erg]
    Velocity of Light (c) 2.998x1010 cm/sec   1   1
    Planck's Constant () 1.055x10-27 erg-sec   1   1
    Time sec c cm c/c erg-1
    Length cm 1 cm 1/(c) erg-1
    Energy erg 1/(c) cm-1 1 erg
    Mass gm (c2/c) cm-1 c2 erg
    Momentum gm-(cm/sec) c/c cm-1 c erg
    Angular Momentum gm-(cm/sec)-cm 1/ 1 1/ 1
    Velocity cm/sec 1/c 1 1/c 1
    Charge (erg-cm)1/2 1/(c)1/2 1 1/(c)1/2 1
    Gravitational Constant cm3/gm-sec2 (c/c4) cm2 1/[c4(c)] erg-2
    Mass Density gm/cm3 (c2/c) cm-4 [c2(c33)] erg4

    Conversion to Natural Units

    Note : c ~ 3x10-17 erg-cm is involved in many of the backward conversions to cgs units, since the unit of [erg]/c [cm-1]. This is closely related to the uncertainty principle : (E)(ct) = c.

    See examples of the conversion.


       Physical Constants

  • Velocity of light c = 2.998x1010 cm/sec
  • Gravitational Constant G = 6.6742x10-8 cm3/sec2-gm
  • Hubble constant Ho = 71 km/sec-Mpc = 1/13.7x109 years
  • Hubble parameter (dimensionless) h = Ho/100
  • Luminosity of the Sun = 3.86x1033 erg/sec
  • Mass of the Sun = 2x1033 gm
  • Distance from Sun to Earth = 1 AU = 1.5x1013 cm
  • Flight time of light from Sun to Earth = 499 sec = 8.3 Min.
  • Solar constant = 1.388x106 erg/cm2-sec
  • Diameter of the Earth = 1.3x109 cm
  • Mass of the Earth = 6x1027 gm
  • Mean radius of the Earth = 6371 km
  • Standard acceleration of gravity = 980.6 cm/sec2
  • 1o of latitude = 110.5 km (at equator) = 111.7 km (at poles)
  • 1o of longitude at equator = 111.3 km
  • Planck's constant h = 6.625x10-27 erg-sec = 4.136x10-15 ev-sec
  • Boltzmann constant k = 1.38x10-16 erg/Ko
  • kT = 0.0258 ev at T = 300oK
  • Avogadro's number = 6.023x1023 (# of particles)/mole
  • Gas constant = 8.314x107 erg/Ko-mole = R = pV/nT
  • Normal volume of perfect gas = 2.241x104 cm3/mole
  • Speed of sound = 34000 cm/sec
  • Hydrogen atom ground state energy = 13.6 ev = 2.18x10-11 erg
  • Bohr radius = 5.29x10-9 cm (classical e- orbital radius in H atom)
  • Electron rest mass = 9.109x10-28 gm
  • Electronic charge = 1.602x10-19 coul
  • Fine-structure constant = e2/c = 1/137
  • Mass of unit atomic weight = 1.6603x10-24 gm
  • Nucleon rest mass = 1.67x10-24 gm = 1 Gev / c2
  • Nuclear Radius = (1.25x10-13)A1/3 cm (A = mass number)

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      Fabulous Formulas
    [click image to load] online scientific calculator.

    Fabular Formulas Feedback Loop Least Action Principle Wave Equation, Quantization Taylor Series Taylor Series Taylor Series

    Year Author Discipline Subject Equation(s)
    1687 Isaac Newton Classical Mechanics Motion of Partilce
    1865 J. C. Maxwell Electrodynamics Electricity and Magnetism
    1872 L. Boltzmann Thermodynamics Tendency toward Disorder
    1905 Albert Einstein Special Relativity Constant Velocity of Light
    1915 Albert Einstein General Relativity Gravity - Warpped Spacetime
    1927 W. Heisenerg Quantum Theory Microscopic Particle
    1928 P. A. M. Dirac Quantum Field Theory Free Field Equation for Fermion
    1973 GSW Quantum Field Theory A Model of Elementary Particles

    The Eight Most Important Equations in Physics


    Scales of the Universe

    History of The University [view large image] Unicellular Organisms Multicellular Organisms

    Era Time
    @ end of era
    Size (observable)
    @ end of era
    @ end of era
    Relics & Observables Events (as re-constructed from theories)
    Planck era < 5.4x10-44 sec < 1.6x10-33 cm > 1.2x1019 Gev (3+1)D space-time;
    cosmic expansion
    Expansion started from a point to Planck scale; all forces united into one
    GUT era <10-35 sec < 3x10-25 cm > 1014 Gev High energy cosmic rays; fundamental interactions Separation of spacetime and matter; separation of gravitational, strong, and electroweak forces
    Inflation (Rate of Expansion >>> c) < 10-32 sec < 3x10-22 cm = observable size
    < 100 cm (unobs.)
    > 1014 Gev Un-observable universe;
    large scale structures
    Reheating; Unstable vacuum;
    quantum fluctuations
    Electro-weak era < 10-11 sec < 0.3 cm
    (see size scale)
    > 300 Gev Radiation; excess of matter over antimatter; separation of force (bosons), and matter (fermions) fields Radiation released in reheating; baryon-antibaryon asymmetry; separation of weak and electromagnetic forces; origin of mass
    Hadron era < 1 sec < 3x1010 cm > 1.7 Mev Formation of hadrons Axion as dark matter
    Weak decoupling < 4 min < 7x1012 cm > 100 kev neutron/proton ratio fixed Neutrinos decouple
    Nucleosynthesis < 1/2 hour < 5x1013 cm > 40 Kev Fraction of Light elements Nuclear reactions freeze out, stable nuclei form
    Radiation era Matter era < 0.24 My < 2x1023 cm > 0.6 ev Mass density fluctuations Matter density finally exceeds radiation density
    < 0.3 My < 3x1023 cm
    > 3000oK CMBR e- and p+ recombine into H atoms,
    universe became transparent to light
    Dark ages
    < 1 Gy < 1027 cm > 100oK 21 cm radio emission,
    First stars, heavy elements
    mass fluctuations grow, first small objects coalesce, reionization
    Galaxy formation < 2 Gy < 2x1027 cm > 70oK Stars, quasars, galaxies Collapse to galactic systems
    Bright age of Galactic Clusters < 12 Gy < 1028 cm > 3oK Solar system; decline of stellar formation from peak dark energy became dominant;
    formation of clusters of galaxies
    Present era ~ 13.7 Gy ~ 1.3x1028 cm ~ 2.73oK Supercluster Large scale gravitational instability

    A History of the University (click small image to enlarge)

    Topic Size Mass/Energy First Appearance Force and Phenomena
    Observable Universe a 1.3x1028 cm.
    (cosmic horizon)
    4x1022 Msun
    (including dark energy, ordinary and dark matters)
    0 sec. Gravity + Unknown repulsive force; an expanding space in the last 13.7x109 yrs, containing all the mass/energy of this world
    Superclusters a 1026 cm. 1016 Msun 11x109 yr. Gravity; largest scale of lumpiness
    Clusters of Galaxies a 1024 cm. 1015 Msun 6x109 yr. Gravity; galaxies in orbit around each other + dark matter
    Galaxies a 1022 cm. 1011 - 1014 Msun 7x108 yr. Gravity; aggregation of stars, gas, dust and dark matter
    Star Clusters a 1020 cm. 102 - 106 Msun 5x108 yr. Gravity; group of stars originated in an interstellar cloud
    Planetary Systems a 1016 cm. 0.1-100 Msun 1.8x108 yr. Gravity; system of non-luminous bodies as by-product in stellar formation
    Stars a 1011 cm. 0.1-100 Msun 1.8x108 yr. Gravity; contracting lump of gas with luminosity maintained by nuclear burning
    Earth g 109 cm. 6x1027 gm. 9.5x109 yr. Gravity; a planet in the habitable zone of the Solar system
    Multicellular Organisms b 104 - 10-1 cm. 107 - 10-3 gm. 13.5x109 yr. Residual Electromagnetic force; organisms composed of multiple cells
    Unicellular Organisms b 10-1 - 10-4 cm. 10-3 - 10-12 gm. 10.5x109 yr. Residual Electromagnetic force; one cell living unit
    Molecules c 10-5 - 10-8 cm. 10 - 10-3 ev. 3.8x105 yr. Residual Electromagnetic force; structure formed by combination of atoms
    Atoms c 10-8 cm. 10 ev. 3.8x105 yr. Electromagnetic force; system of electrons and nuclei
    Nuclei p 10-13 cm. 109 ev. 1 sec. Residual strong force; system of neutrons and protons
    Elementary Particles p 10-16 cm. > 10-3 - 1012 ev. < 10-32 sec. Weak, strong and electromagnetic forces; basic constituents of matter and force

    The Universe Now

    Note 1 - Field of Study: a = astronomy, b = biology, c = chemistry, g = geology, p = physics.
    Note 2 - The Mass M and Energy E are related by the formula E = mc2.
    Note 3 - 1 Msun = 2x1033 gm., 1 ev = 1.77x10-33 gm.
    Note 4 - The energy in "Atom" and "Molecule" refers to the binding energy, which holds the system together.
    Note 5 - points to a webpage of that subject.
    Note 6 - See animation on "Scale of the Universe".
    Note 7 - See a video on "History of the Universe" in one minute.

    See "Conversion of Natural Scale".


    Planck Scale

    Quantum Gravity
  • Planck Mass - MPL = (c/G)1/2 = 2.17x10-5 gm.
  • Planck Energy - EPL = MPLc2 = (c5/G)1/2 = 1.22x1019 Gev = 1.95x1016 erg.
  • Planck Temperature - TPL = EPL/kB = (c5/GkB2)1/2 = 1.42x1032 oK
  • Planck Length - LPL = GMPL/c2 = (G/c3)1/2 = 1.62x10-33 cm.
  • Planck Time - tPL = LPL/c = (G/c5)1/2 = 5.39x10-44 sec.
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    Cosmological Parameters (WMAP)

    WMAP Cosmological Parameters
    [click to enlarge]

    WMAP Cosmological Parameters [view large image]

    Critical Density = 3H02/8G = 0.9x10-29 gm/cm3 (from 2012 data).

    The WMAP team has released the final evaluation of the cosmological parameters on December 2012. These new values has been copied to the table (with 7-year's data) above. The new 9-year observations have confirmed the add-on of inflation to the Bing Bang model with tiny fluctuations growing to form the galaxies. The data also confirm that the universe is flat. See all the details in NASA/WMAP News.


    Astronomical Objects

    Astronomical Objects Galsxy Types Messier Objects

    Astronomical Objects

    Galaxy Types and Composition [view large image]

    Messier Objects [view large image]


    Milky Way


    Solar System Data

    Me = Mass of the Earth = 6x1027 gm.
    De = Diameter of the Earth = 1.3x109 cm.
    Distance from Sun to Earth = 1 AU = 1.5x1013 cm.
    Msun = 2x1033 gm.

    Object Mass (Me) Size (De) Distance (AU) Rotation (Day) Revolution (Year) Satellite (#) Surface Temp. (oC) Density (H2O) Atmospheric Composition
    Sun 3x105 100 0 25.38     +5500 1.4 H2 91%, He 9%
    Mercury 0.06 0.38 0.39 58 0.24 0 +350(day),
    5.4 Varies ~ O2 42%,
    N2 29%, H2 22%
    Venus 0.95 0.95 0.72 243 0.62 0 +475 5.3 CO2 96%, N24%
    Earth 1.00 1.00 1.00 1.00 1.00 1 +22 5.5 N2 78%, O2 21%
    Moon 0.012 0.27 1.00 27.32 1.00   +127 (day)
    -173 (night)
    3.3 He, Ne, H2, Ar
    Mars 0.11 0.53 1.52 1.00 1.88 2 -23 3.9 CO2 95%,N2 3%
    Asteroid < 10-4 < .07 ~ 2.7 < 17 1 - 50     2.7  
    Jupiter 318 11.2 5.20 0.4 11.86 16 -123 1.3 H2 90%, He 10%
    Saturn 95 9.4 9.54 0.4 29.46 >18 -180 0.7 H2 97%, He 3%
    Titan 0.022 0.4 9.54 15.95 29.46   -178 1.88 N2 95%, CH4 5%
    Uranus 15 3.9 19.2 0.7 84.0 >16 -218 1.3 H2 83%, He 15%
    Neptune 17 3.8 30.1 0.7 164.8 8 -228 1.6 H2 79%, He 18%
    Pluto 0.002 0.2 39.5 6.4 248 1 -230 2.1 N2 99.97%, CH4
    UB313§ 0.0025 ~ 0.23 ~ 97       ~ -248    
    Comet ~ 10-12 ~ 10-4 30 - 5x104   3 - 4x104     0.25  


    Ecliptic and Symbols

    Ecliptic Zodiac Astronomical Symbols Four Seasons

    A 300o view of the Ecliptic on January 24 - 26, 2017 above Palawan, Philippines by TWAN. [click to enlarge]


    Periodic Table

    Periodic Table 1 Periodic Table 2 Origin of Elements

    Periodic Table, Regular

    Periodic Table, Unconventional

    Periodic Table, Origin [view large image]


    Radioactive Isotopes

    Decay Modes Radioactive Levels

    Types of Decay Mode [view large image]

    Dosage Scale [view large image]

    Radioactive Isotopes

    List of Radioactive Isotopes (from ScienceStruck) [view large image]


    Electromagnetic Spectrum


    Feynman Diagrams and Rules (2nd Order S-Matrix for Nucleon-Pion Interaction) :

    Graphical Elements
    Feynman Rules Feynman Rules, Momentum Space

    Space-time Representations [view large image]

    Momentum Representations [view large image]

    Feynman Rules

    Feynman Diagrams


    Elementary Particle Data

    [view large image]

    Mass/Energy Scale - Mass for Elementary Particles, Binding Energy for Composite Particles, Beam Energy for Colliders.                      Optimization of Nuclear Forces


    Hadrons - Baryons and Mesons (in Strong Interaction)

    List of Baryons

    List of Baryons [view large image] (from Wikipedia)

    Symbols : I (isospin), J (total angular momentum), P (parity), u (up quark), d (down quark), s (strange quark), c (charm quark), b (bottom quark), Q (charge), S (strangeness), C (charm), B' (bottomness).

    List of Mesons

    List of Mesons [view large image] (from Wikipedia)


    Electrical Properties of some Materials, and Safety


    Properties of Solids


    Geological and Biological Evolutions


    HADEAN 4800 - 4000 Formation of Earth, solidification of crust,
    evidence of water, heavy bombardment.
    Prebiotic (see "A 2018 Update on the Theory of Prebiotic World").
    ARCHEAN 4000 - 2500 Beginning of rock record, evidence of plate
    , magnetic field generation.
    Protozoa (unicellular organism).
    PROTEROZOIC 2500 - 541 Free oxygen in the atmosphere, glaciation,
    solidification of inner core.
    Metazoa (multicellular organism).
        PALAEOZOIC ERA (Era of Ancient Life)
    CAMBRIAN 541 - 485.4 Deposition of Burgess Shale. Invertebrates (trilobites), corals,
    sea life of many types proliferating.
    ORDOVICIAN 485.4 - 443.4 Sea covered most of the planet. Vertebrates, first fish, mass extinction§.
    SILURIAN 443.4 - 419.2 High sea level. Land plants, jawed fishes, ammonoids.
    DEVONIAN 419.2 - 358.9 Gondwana, Laurasia beginning to form Pangaea. Amphibians, forests, sharks.
    CARBONIFEROUS 358.9 - 298.9 Swamps and coal bearing rocks. Insects, ferns.
    PERMIAN 298.9 - 252.2 Formation of Pangaea (the super-continent),
    desertification occurred.
    Reptiles, conifers.
        MESOZOIC ERA (Era of Middle Life, Age of Reptiles)
    TRIASSIC 252.2 - 201.3 Five million years "Dead Zone" in the tropics after end-Permian mass extinction. First dinosaurs.
    JURASSIC 201.3 - 145.0 Oldest surviving ocean floor. Height of dinosaurs, early mammals and birds.
    CRETACEOUS 145.0 - 66.0 Oil and gas deposits, broke up of Pangaea,
    global mountain building.
    End of the dinosaurs, first flowering plants.
        CENOZOIC ERA (Era of Modern Life, Age of Mammals)
    TERTIARY 66.0 - 2.588 Himalayas and Alps folded. Evolutionary separation of apes and
    monkeys, most mammals established.
    QUATERNARY 2.588 - present Last ice age. Modern man.

    Geological Periods

    Continental Drift Plate Tectonics Key

    Continental Drift
    [view large image]

    [view animation] (Esc) stop, (Refresh) resume

    Biological Evolution [view large image]


    Genetic Code and Peptide, Chromosome and DNA

    mRNA Structure   

    Genetic Code
    Peptide Ghain
    DNA Chromosome

    Genetic Code [view large image] and Peptide

    DNA and the C, G, A, T Bases [view large image]

    Chromatin see (1), see (2)


       Anatomy and Cell

    Cell [view large image]

    Nerve [view large image]

    Interstitial Fluid and Connective Tissues [view large image]

    Cytosketeton Network of protein filaments Structural support; cell movement No
    Flagella(cilia, microvilli) Cellular extensions Motility or moving fluids over surfaces Yes
    Centrioles Hollow microtubules Moving chromosomes during cell division No
    Plasma membrane Lipid bilayer in which proteins are embedded Regulates what passes into and out of cell; cell-to-cell communication Yes
    Endoplasmic reticulum Network of internal membranes; forms compartments and vesicles Rough type processes proteins for secretion and synthesizes phospholipids; smooth type synthesize fats and steroids No
    Nucleus Structure bounded by double membrane; contains chromosomes Control center of cell; directs protein synthesis and cell reproduction No
    Golgi complex Stacks of flattened vesicles Modifies and packages proteins for export from cell; forms secretory vesicles No
    Lysosomes Vesicles derived from Golgi complex that contain hydrolytic digestive enzymes Digest worn-out mitochondria and cell debris; play role in cell death No
    Autophagy Vesicles to collect debris within the cell Malfunction causes accumulation of cell damage leading to diseases and aging (see Malfunction of Autophagy) No
    Mitochondria Bacteria-like elements with inner membrane Battery of the cell by ATP synthesis; site of oxidative metabolism No
    Chromosomes (during cell division) / Chromatins Long threads of DNA that form a complex with protein Contain hereditary information Yes
    Nucleolus Site of rRNA synthesis Assembles ribosomes No
    Ribosomes Small, complex assemblies of protein, often bound to ER Site of protein synthesis Yes

    Cell organelles

    PKC - Absence or presence in prokaryotic cells.

    Brain [view large image]

    Senses [view large image]

    Organs Front

    Organs Inside

    Organ System Functions Components
    Circulatory Transports nutrients, gases (O2, CO2), hormones and wastes through the body Heart, blood vessels and blood
    Digestive Breakdowns and absorbs nutrients for growth and maintenance Mouth, esophagus, stomach, liver, pancreas, gallbladder, small and large intestines
    Relays chemical messages through the body for controlling physiological processes Hypothalamus, pineal, pituitary, thyroid, thymus, pancreas and adrenal glands
    Excretory Filters out cellular wastes, toxins and excess water or nutrients from the circulatory system Kidneys, ureters, bladder, urethra, lungs, sweat pores, and intestine
    Immune Destroys or removes invading microbes, viruses; the lymphatic system also removes fat, and excess fluids from the blood. Skin is the outermost defense against pathogens Spleen, thymus, bone marrow, lymph, lymph nodes and vessels, white blood cells, T- and B- cells, skin
    Musculo-skeletal Supports and moves organism; also protects delicate internal organs and provides attachment sites for the organs. Skeletal and smooth muscles; bones, cartilage, tendons, and ligaments
    Nervous &
    Relays electrical signals, directs movement, controls physiological processes, and responses to environment Brain, nervous system, and the five senses
    Reproductive manufactures cells for reproduction Female: ovaries, oviducts, uterus, vagina, and mammary glands;
    male: testes, as deferens, seminal vesicles, penis, and prostate gland
    Respiratory Provides gas exchange between the blood and the environment Nose, trachea, and lungs

    Human Organs


    Greek Alphabets, and Derivatives

                 [view large image]

    The End THE END