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Units and Constants


Contents

Multiplication Factors
Common Names in SI Units
SI and British (fps) Unit Conversions
Unit Conversions
Natural Units
Physical Constants
Scales of the Universe
Cosmological Constants (WMAP)
Astronomical Symbols
Greek Alphpbets, and Linguistics

Multiplication Factors

Multiplication Factors, SI Prefixes, and Symbols:



mega = 106, million = 106, billion = 109, trillion = 1012

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Common Names in SI Units

SI names

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SI and British (fps) Unit Conversions



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Unit Conversions

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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 SI units.

Physical Quantity SI Unit Transition to cm Natural Unit (cm) Transition 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

Table 01 Conversion to Natural Units

    There are three examples below to show how to run a reversed conversion from natural unit to SI 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].

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Physical Constants

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Scales of the Universe

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Cosmological Parameters (WMAP)

WMAP Cosmological Parameters

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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Astronomical Symbols

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Greek Alphpbets, and Linguistics