Constants & Units

Physical Constants

$\quad\rlap{a_0}$ $\qquad\rlap{\rm Bohr~radius}$ $\hskip150pt 5.29177 \times 10^{-9} {\rm ~cm}$
$\quad\rlap{c}$ $\qquad\rlap{\rm speed~of~light~in~vacuum}$ $\hskip150pt 2.99792 \times 10^{10}{\rm ~cm~s}^{-1}$
$\quad\rlap{e}$ $\qquad\rlap{\rm electron~charge}$ $\hskip140pt -4.80325 \times 10^{-10} {\rm ~statcoulomb~(=esu)}$
$\quad\rlap{\rm eV}$ $\qquad\rlap{\rm electron~volt}$ $\hskip150pt 1.60218 \times 10^{-12} {\rm ~erg}$
$\quad\rlap{G}$ $\qquad\rlap{\rm gravitational~constant}$ $\hskip150pt 6.67428 \times 10^{-8} {\rm ~dyne~cm}^2 {\rm ~g}^{-2}$
$\quad\rlap{h}$ $\qquad\rlap{\rm Planck's~constant}$ $\hskip150pt 6.62607 \times 10^{-27} {\rm ~erg~s}$
$\quad\rlap{k}$ $\qquad\rlap{\rm Boltzmann's~constant}$ $\hskip150pt 1.38065 \times 10^{-16} {\rm ~erg~K}^{-1}$
$\quad\rlap{m_{\rm e}}$ $\qquad\rlap{\rm electron~mass}$ $\hskip150pt 9.10938 \times 10^{-28} {\rm ~g}$
$\quad\rlap{m_{\rm p}}$ $\qquad\rlap{\rm proton~mass}$ $\hskip150pt 1.67262 \times 10^{-24} {\rm ~g}$
$\quad\rlap{R_\infty}$ $\qquad\rlap{\rm Rydberg~constant}$ $\hskip150pt 1.09737 \times 10^5 {\rm ~cm}^{-1}$
$\quad\rlap{R_\infty c}$ $\qquad\rlap{\rm Rydberg~frequency}$ $\hskip150pt 3.28984 \times 10^{15} {\rm ~s}^{-1}$
$\quad\rlap{\sigma}$ $\qquad\rlap{\rm Stefan-Boltzmann~constant}$ $\hskip150pt 5.67040 \times 10^{-5} {\rm ~erg~cm}^{-2}{\rm ~s}^{-1} {\rm ~K}^{-4}$
$\quad\rlap{\sigma_{\rm T}}$ $\qquad\rlap{\rm Thomson~cross~section}$ $\hskip150pt 6.65245 \times 10^{-25} {\rm ~cm}^2$
$\quad\rlap{u}$ $\qquad\rlap{\rm atomic~mass~unit}$ $\hskip150pt 1.66054 \times 10^{-24} {\rm ~g}$

Astronomical Constants

$\quad\rlap{\rm au}$ $\qquad\rlap{\rm astronomical~unit}$ $\hskip150pt 1.49598 \times 10^{13} {\rm ~cm}$
$\quad\rlap{H_0}$ $\qquad\rlap{\rm Hubble~constant}$ $\hskip150pt
72 {\rm ~km~s}^{-1}{\rm ~Mpc}^{-1}$
$\quad\rlap{\rm kpc}$ $\qquad\rlap{\rm kiloparsec}$ $\hskip150pt 10^3 {\rm ~pc}$
$\quad\rlap{L_\odot}$ $\qquad\rlap{\rm solar~bolometric~luminosity}$ $\hskip150pt 3.826
\hphantom{01~} \times 10^{33} {\rm ~erg~s}^{-1}$

$\quad\rlap{\rm ly}$ $\qquad\rlap{\rm light~year}$ $\hskip150pt 9.4605 \hphantom{0~}\times 10^{17} {\rm ~cm}$
$\quad\rlap{M_\odot}$ $\qquad\rlap{\rm solar~mass}$ $\hskip150pt 1.989 \hphantom{01~} \times 10^{33} {\rm ~g}$
$\quad\rlap{\rm Mpc}$ $\qquad\rlap{\rm megaparsec}$ $\hskip150pt 10^6 {\rm ~pc}$
$\quad\rlap{\rm pc}$ $\qquad\rlap{\rm parsec}$ $\hskip150pt 3.0856 \hphantom{0~} \times 10^{18} {\rm ~cm}$
$\quad\rlap{R_\odot}$ $\qquad\rlap{\rm solar~radius}$ $\hskip150pt 6.9598 \hphantom{0~} \times 10^{10} {\rm ~cm}$
$\quad\rlap{\rm yr}$ $\qquad\rlap{\rm year}$ $\hskip150pt 3.156 \times 10^7 \approx 10^{7.5} {\rm ~s}$

MKS and Gaussian CGS Units


$\quad\rlap {\rm Type}$ $\hskip60pt \rlap{\rm mks~unit}$ $\hskip50pt \rlap{\rm cgs~unit}$ $\hskip60pt {\rm conversion}$

$\quad\rlap {\rm mass}$ $\hskip60pt \rlap{\rm kg}$ $\hskip50pt \rlap{\rm g}$ $\hskip60pt 10^3 {\rm ~g} = 1 {\rm ~kg}$
$\quad\rlap {\rm length}$ $\hskip60pt \rlap{\rm m}$ $\hskip50pt \rlap{\rm cm}$ $\hskip60pt 10^2 {\rm ~cm} = 1 {\rm ~m}$
$\quad\rlap {\rm time}$ $\hskip60pt \rlap{\rm s}$ $\hskip50pt \rlap{\rm s}$
$\quad\rlap {\rm frequency}$ $\hskip60pt \rlap{\rm Hz}$ $\hskip50pt \rlap{\rm Hz}$ $\hskip60pt 1 {\rm ~Hz} = 1 {\rm ~s}^{-1}$
$\quad\rlap {\rm charge}$ $\hskip60pt \rlap{\rm coulomb}$ $\hskip50pt \rlap{\rm statcoulomb}$ $\hskip60pt 3 \times 10^9 {\rm ~statcouloumb} = 1 {\rm ~coulomb}$
$\quad\rlap {\hphantom{\rm charge}}$ $\hskip60pt \rlap{\hphantom{\rm coulomb}}$ $\hskip50pt \rlap{\hphantom{\rm statcoulomb}}$ $\hskip60pt \hskip15pt (1 {\rm ~statcoulomb} = 1 {\rm ~esu})$
$\quad\rlap {\rm current}$ $\hskip60pt \rlap{\rm ampere}$ $\hskip50pt \rlap{\rm statampere}$ $\hskip60pt 3 \times 10^9 {\rm ~statamp} = 1 {\rm ~amp}$
$\hskip60pt \hskip15pt \hskip120pt$ $(1 {\rm ~amp} = 1 {\rm ~coulomb~s}^{-1})$

$\quad\rlap {\rm electric~field}$ $\hskip60pt \rlap{{\rm v~m}^{-1}}$ $\hskip50pt \rlap{{\rm statvolt~cm}^{-1}}$ $\hskip60pt (1/3) \times 10^{-4}{\rm ~statvolt~cm}^{-1} = 1 {\rm ~v~m}^{-1}$
$\quad\rlap {\rm energy}$ $\hskip60pt \rlap{\rm joule}$ $\hskip50pt \rlap{\rm erg}$ $\hskip60pt 10^7 {\rm ~erg} = 1 {\rm ~joule}$
$\quad\rlap {\rm force}$ $\hskip60pt \rlap{\rm newton}$ $\hskip50pt \rlap{\rm dyne}$ $\hskip60pt 10^5 {\rm ~dyne} = 1 {\rm ~newton}$

$\quad\rlap {\rm magnetic~field}$ $\hskip60pt \rlap{\rm tesla}$ $\hskip50pt \rlap{\rm gauss}$ $\hskip60pt 10^4 {\rm ~gauss} = 1 {\rm ~tesla}$
$\quad\rlap{\rm resistance}$ $\hskip60pt \rlap{\rm Ohm}$ $\hskip50pt \rlap{{\rm sec~cm}^{-1}}$ $\hskip60pt (1/9) \times 10^{-11} {\rm ~s~cm}^{-1} = 1 {\rm ~Ohm}$
$\quad\rlap{\rm temperature}$ $\hskip60pt \rlap{\rm Kelvin}$ $\hskip50pt {\rm Kelvin}$

Other Constants and Units

$\quad\rlap {\rm arcmin}$ $\hskip60pt 1/60 {\rm ~deg}$
$\quad\rlap {\rm arcsec}$ $\hskip60pt 1/60 {\rm ~arcmin}$
$\quad\rlap {\rm Angstrom}$ $\hskip60pt 10^{-10} {\rm ~m}$
$\quad\rlap {\rm dB}$ $\hskip60pt 0.1\log_{10}(P_1/P_2)$

$\quad\rlap {\rm e}$ $\hskip60pt 2.71828\dots$
$\quad\rlap {\rm GHz}$ $\hskip60pt 10^9 {\rm ~Hz}$
$\quad\rlap {\rm Jy}$ $\hskip60pt 10^{-26} {\rm ~W~m}^{-2} {\rm ~Hz}^{-1} \quad {\rm (1~mJy} = 10^{-3} {\rm ~Jy,~1~}\mu{\rm Jy} = 10^{-6} {\rm ~Jy)}$
$\quad\rlap {\rm MHz}$ $\hskip60pt 10^6 {\rm ~Hz}$
$\quad\rlap {\mu{\rm m}}$ $\hskip60pt 10^{-6} {\rm ~m}$
$\quad\rlap \pi$ $\hskip60pt 3.14159\dots$
$\quad\rlap {\rm radian}$ $\hskip60pt (180/\pi) {\rm ~deg} \approx 206264.8 {\rm ~arcsec}$



Engineers and physicists prefer mks (meter, kilogram, second) units, so most radio astronomers use mks units to describe their equipment and the results of their observations.  Most astrophysicists prefer Gaussian cgs (centimeter, gram, second) units to describe astronomical sources.  Thus you have to deal with both systems of units and be able to convert between them in order to do astronomy.  J. D. Jackson's Classical Electrodynamics has an appendix explaining the different systems in detail.