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Units and Constants


Contents

Multiplication Factors
Common Names in SI Units
SI and British (fps) Unit Conversions
Unit Conversions
Physical Constants
Scales of the Universe
Planck Scale
Cosmological Constants (WMAP)
Messier Objects
Solar System Data
Ecliptic and Symbols
Periodic Table
Elementary Particle Data
Natural Units
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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    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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    Scales of the Universe

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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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    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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    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

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    Periodic Table

    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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    Natural Units

    Natural units are often adopted in particle physics with c = = 1 by changing the unit of time to (1/c) cm or erg-1 (the two different conversions are equivalent). Table 01 below shows the various physical quantities in natural units. The formula to convert them to dimension of cm or erg are also displayed for running the reversed conversion back to the CGS units.

    Physical Quantity CGS Unit Conversion to cm Natural Unit (cm) Conversion to erg 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 cm/c cm erg-1 erg-1
    Length cm cm cm (c) erg-1 erg-1
    Energy erg (c) cm-1 cm-1 erg erg
    Mass gm (/c) cm-1 cm-1 erg/c2 erg
    Momentum gm-(cm/sec) cm-1 cm-1 erg/c erg
    Angular Momentum gm-(cm/sec)-cm 1 1
    Velocity cm/sec c 1 c 1
    Charge (erg-cm)1/2 (c)1/2 1 (c)1/2 1
    Gravitational Constant cm3/gm-sec2 (c4/c) cm2 cm2 c4(c) erg-2 erg-2
    Mass Density gm/cm3 (/c) cm-4 cm-4 1/(c53) erg4 erg4

    Table 01 Conversion to Natural Units

      There are three examples below to show how to run a reversed conversion from natural unit to CGS units :

    1. Electromagnetic Wave Equation -
      In natural unit of [cm] (the unit is enclosed within the bracket [ ]) this equation is in the form :
      2E - E = 0
      Conversion back to SI units in this case is very simple by substituting the natural unit [cm]2 with the SI units c2[sec]2 in the denominator of the second term. Then the equation in SI units is recovered as:
      2E - (1/c2)E = 0

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

    3. Schrodinger Equation -
      In natural unit it has the form : -(1/2m) = i
      Converting from the natural unit of [erg], the left-handed side produces a factor of (1/c2[gm])(c/[cm])2=2/[gm-cm2]. On the right-handed side the converting factor is /[sec]. Combining everything together, we recovered the equation in SI :
      -(2/2m) = i
      Incidentally, for all cases the same form in SI units will be recovered whether the natural unit is in [cm] or [erg].

    4. Scales of the Universe - The formulas for the various scales are 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 convert 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 01) to arrive at the correct answer 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 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 (see Table 01), 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 to change the dimension 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 they are not derived from other CGS units.

      • 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. Conversion back to CGS units involves multiplying (c53) to vac ~ 10-29, 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 with (c/). The same procedure yields the reciprocal LPl = 0.7x10-2 cm.

      • Hubble Scale - EH = (8G)1/2 in natural unit of sec-1. Conversion back to CGS units involves taking the square root of 8G (with ~ 10-29), multiplying (converting from sec-1 to erg), then translating to ev. The result is EH = 2.5x10-33 ev. The multiplication factor is 1/c (converting from sec-1 to cm-1) in deriving the length scale LH = 0.8x1028 cm.


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