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Epilogue - Units, Constants, Data, and Links


Contents

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)
Messier Objects
Solar System Data
Ecliptic and Symbols
Periodic Table and Electromagnetic Spectrum
Elementary Particle Data
Geological and Biological Evolutions
Greek Alphabets, and Linguistics

Multiplication Factors

Multiplication Factors, SI Prefixes, and Symbols:


million = 106, billion = 109, trillion = 1012

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Common Names in SI Units

SI names SI names

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SI and British (fps) Unit Conversions



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Unit Conversions

  • 1 ly. (light year) = 1018 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
  • 1 knot = 1.15 mi/hr = 1.85 km/hr
  • 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
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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.
      There are five examples below to show how to run a reversed conversion from natural unit to cgs units (see Table) :

    1. Electromagnetic Wave Equation -
      In natural unit of [cm] (the natural unit is enclosed within the bracket [ ]) this equation is in the form :
      2E - E = 0
      Conversion back to cgs units in this case is very simple by substituting the natural unit [cm] with the cgs conversion factor c for the time variable. There is no conversion involved with the spatial variables. Then the equation in cgs units is recovered as:
      2E - (1/c2)E = 0

    2. Total Energy -
      E = (m2 + p2)1/2
      In natural unit of [erg], m is converted back to cgs by c2, while the conversion for p is c. Therefore the formula in cgs is :
      E = (m2c4 + p2c2)1/2

    3. Schrodinger Equation -
      In natural unit it has the form : -(1/2m) = i
      In converting from the natural unit of [erg], the left-handed side produces a factor of (1/c2)(c)2=2. On the right-handed side the converting factor is . Combining everything together, we recovered the equation in cgs :
      -(2/2m) = i
      Incidentally, for all cases, the same form in cgs units will be recovered whether the natural unit is in [cm] or [erg].

    4. Traveling (quantum) Wave -
      In natural unit with the energy E in [erg] : = exp[i(kx-Et)]. Backward conversion to cgs becomes = exp[i(kx-Et/)].

    5. Scales of the Universe - The formulas for the various scales (see table) are expressed in natural units. The following demonstrates the procedure of converting them back to the cgs units and in the process reproduces the numerical values quoted in the table.

      • Planck Scale - EPl = (8G)-1/2 which has a dimension of [erg] in natural unit. Substituting the numerical values and converting the result from erg to ev yields EPl = 0.8x103 [erg] = 5x1014 [ev] which is incorrect. The proper way is to perform a reversed conversion by multiplying (c5)1/2 (see Table) to arrive at the correct answer of EPl = 2x1027 ev. This is the "Reduced Planck Energy" with a factor of (8)-1/2 difference from the conventional definition (see "Planck Scale"). The natural unit can also be expressed in term of [cm-1] so that EPl = 0.8x103 [cm-1]. It becomes EPl = 0.8x103x(c4/c)1/2 cm-1 = 1.5x1032 cm-1 by reversed conversion, the reciprocal of which is the length scale LPl = 0.7x10-32 cm (see "Scale of the Universe").

      • Fermi Scale - EF = 1/(GF)1/2 = [Gev]/(1.17x10-5)1/2 = 3x1011 ev. The length scale is obtained by converting ev to erg, and then divided by c (changing the unit to cm-1), the reciprocal of which is LQCD = 0.6x10-16 cm. The conversion for this one and the next is straight forward because the natural unit is in unit of energy already.

      • QCD Scale - The natural unit for this one is just the coupling constant EQCD = QCD = 2x108 ev. The length scale is obtained by converting ev to erg, and then divided by c to change the dimension to cm-1, the reciprocal of which is LQCD = 10-13 cm.

      • Vacuum Scale - Evac = (vac)1/4 [erg]. Conversion back to cgs units involves multiplying (c53) to vac = 0.7x10-29, taking the 1/4 root, and translating to ev. The result is Evac = 1.5x10-3 ev. The length scale is obtained by multiplying vac (in the alternate natural dimension of [cm-1]) with (c/), then takes the 1/4 root, the reciprocal of which yields Lvac = 0.7x10-2 cm.

      • Hubble Scale - EH = (8G)1/2 in natural unit of [erg]. Conversion to cgs units involves taking the 1/2 root of 8G (with = 10-29), multiplying , then translating to ev. The result is EH = 2.5x10-33 ev. The multiplication factor is 1/c (when it is in natural unit of [cm-1]) in deriving the inverse length scale, and then takes the reciprocal LH = 0.8x1028 cm.
        BTW, the Hubble equation is originally derived from General Relativity, i.e., H =(dR/dt)/R = (8G/3)1/2 for k = 0 in cgs unit of sec-1. It has nothing to do with , which comes from quantum theory. However, in an effort to express this equation in unit of energy, it is artificially multiplied by and declared that (8G)1/2 is in natural unit of [erg] (also taking away a factor of 1/3). It is rather doubtful whether the uncertainty principle is applicable to such macroscopic object. Anyway, in a similar vein, it is multiplied by 1/c to pretend that it is in natural unit of [cm-1].

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    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
  • 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 = 6.625x10-27 erg-sec = 4.136x10-15 ev-sec
  • Avogadro's number = 6.023x1023 molecules/mole
  • Normal volume of perfect gas = 2.241x104 cm3/mole
  • kT = 0.0258 ev at T = 300oK
  • Gas constant = 8.314x107 erg/Ko-mole = R = pV/nT
  • Boltzmann constant = 1.38x10-16 erg/Ko
  • Speed of sound = 34000 cm/sec
  • Electronic charge = 1.602x10-19 coul
  • Fine-structure constant = e2/c = 1/137
  • Hydrogen atom ground state energy = 13.6 ev = 2.18x10-11 erg
  • Bohr radius = 5.29 nm
  • Mass of unit atomic weight = 1.6603x10-24 gm
  • Nucleon rest mass = 1.67x10-24 gm
  • Electron rest mass = 9.109x10-28 gm
  • Nuclear Radius = (1.3x10-13)A1/3 cm (A = mass number)
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       Fabulous Formulas



    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

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    Scales of the Universe

    Cosmo
    The Cosmos [view large image] Unicellular Organisms Multicellular Organisms

    Topic Size Mass/Energy First Appearance Force and Phenomena
    Macro-world
    Observable Universe a 4.6x1028 cm.
    (comoving radius)
    7.3x1022 Msun
    (including dark energy, ordinary and dark matters)
    0 sec. Gravity + Unknown repulsive force; an expanding space in the last 13.8x109 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
    Living-world
    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
    Micro-world
    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 Cosmic Table


    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".

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    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.
  • 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 (on 7-year results) above. In addition, the 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.

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    Messier Objects

    Messier Catalog Messier Objects

    Messier Catalog [view large image]

    Messier Objects [view large image]

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    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),
    -170(night)
    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  

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    Ecliptic and Symbols

    Ecliptic Zodiac Astronomical Symbols

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

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    Periodic Table and Electromagnetic Spectrum

    Periodic Table 1 Periodic Table 2

    Periodic Table, Regular [view large image]

    Periodic Table, Unconventional [view large image]




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    Elementary Particle Data


    [view large image]

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    Geological and Biological Evolutions

                                

    Era Period (MYA) GEOLOGICAL EVENTS BIOLOGICAL EVENTS
        PRE-CAMBRIAN ERA  
    HADEAN 4800 - 4000 Formation of Earth, solidification of crust,
    evidence of water, heavy bombardment.
    Prebiotic.
    ARCHEAN 4000 - 2500 Beginning of rock record, evidence of plate
    tectonics
    , 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]

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    Greek Alphabets, and Linguistics