# Appendix C Useful Information

This appendix is broken into several tables.

Table 3. Important Constants1

Symbol Meaning Best Value Approximate Value
$c$ Speed of light in vacuum $2.99792458 \times 10^8 \text{m/s}$ $3.00 \times 10^8 \text{m/s}$
$G$ Gravitational constant $6.67408(31) \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2$ $6.67 \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2$
$N_A$ Avogadro’s number $6.02214129(27) \times 10^{23}$ $6.02 \times 10^{23}$
$k$ Boltzmann’s constant $1.3806488(13) \times 10^{-23} \;\text{J} / \text{K}$ $1.38 \times 10^{-23} \;\text{J} / \text{K}$
$R$ Gas constant $8.3144621(75) \;\text{J} / \text{mol} \cdot \text{K}$ $8.31 \;\text{J} / \text{mol} \cdot \text{K} = 1.99 \text{cal} / \text{mol} \cdot \text{K} = 0.0821 \text{atm} \cdot \text{L} / \text{mol} \cdot \text{K}$
$\sigma$ Stefan-Boltzmann constant $5.670373(21) \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}$ $5.67 \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}$
$k$ Coulomb force constant $8.987551788 \dots \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2$ $8.99 \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2$
$q_e$ Charge on electron $-1.602176565(35) \times 10^{-19} \;\text{C}$ $-1.60 \times 10^{-19} \;\text{C}$
$\varepsilon _0$ Permittivity of free space $8.854187817 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \cdot \text{m}^2$ $8.85 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \text{m}^2$
$\mu _0$ Permeability of free space $4 \pi \times 10^{-7} \;\text{T} \cdot \;\text{m}/ \text{A}$ $1.26 \times 10^{-6} \;\text{T} \cdot \text{m} / \text{A}$
$h$ Planck’s constant $6.62606957(29) \times 10^{-34} \;\text{J} \cdot \text{s}$ $6.63 \times 10^{-34} \;\text{J} \cdot \text{s}$
Symbol Meaning Best Value Approximate Value
$m_e$ Electron mass $9.10938291(40) \times 10^{-31} \text{kg}$ $9.11 \times 10^{-31} \text{kg}$
$m_p$ Proton mass $1.672621777(74) \times 10^{-27} \text{kg}$ $1.6726 \times 10^{-27} \text{kg}$
$m_n$ Neutron mass $1.674927351(74) \times 10^{-27} \text{kg}$ $1.6749 \times 10^{-27} \text{kg}$
$\text{u}$ Atomic mass unit $1.660538921(73) \times 10^{-27} \text{kg}$ $1.6605 \times 10^{-27} \text{kg}$
Table 4. Submicroscopic Masses2

 Sun mass $1.99 \times 10^{30} \text{kg}$ average radius $6.96 \times 10^8 \text{m}$ Earth-sun distance (average) $1.496 \times 10^{11} \text{m}$ Earth mass $5.9736 \times 10^{24} \text{kg}$ average radius $6.376 \times 10^6 \text{m}$ orbital period $3.16 \times 10^7 \text{s}$ Moon mass $7.35 \times 10^{22} \text{kg}$ average radius $1.74 \times 10^6 \text{m}$ orbital period (average) $2.36 \times 10^6 \text{s}$ Earth-moon distance (average) $3.84 \times 10^8 \text{m}$ Table 5. Solar System Data
Prefix Symbol Value Prefix Symbol Value
tera T $10^{12}$ deci d $10^{-1}$
giga G $10^{9}$ centi c $10^{-2}$
mega M $10^{6}$ milli m $10^{-3}$
kilo k $10^{3}$ micro $\mu$ $10^{-6}$
hecto h $10^{2}$ nano n $10^{-9}$
deka da $10^{1}$ pico p $10^{-12}$
$10^{0} (= 1)$ femto f $10^{-15}$
Table 6. Metric Prefixes for Powers of Ten and Their Symbols
 Alpha A $\alpha$ Eta Η $\eta$ Nu Ν $\nu$ Tau Τ $\tau$ Beta Β $\beta$ Theta Θ $\theta$ Xi Ξ $\xi$ Upsilon Υ $\upsilon$ Gamma Γ $\gamma$ Iota Ι $\iota$ Omicron Ο $\o$ Phi Φ $\phi$ Delta Δ $\delta$ Kappa Κ $\kappa$ Pi Π $\pi$ Chi Χ $\chi$ Epsilon Ε $\epsilon$ Lambda Λ $\lambda$ Rho Ρ $\rho$ Psi Ψ $\psi$ Zeta Ζ $\zeta$ Mu Μ $\mu$ Sigma Σ $\sigma$ Omega Ω $\omega$ Table 7. The Greek Alphabet

Entity Abbreviation Name
Fundamental units Length $\text{m}$ meter
Mass $\text{kg}$ kilogram
Time $\text{s}$ second
Current $\text{A}$ ampere
Supplementary unit Angle $\text{rad}$ radian
Derived units Force $\text{N} = \text{kg} \cdot \text{m} / \text{s}^2$ newton
Energy $\text{J} = \text{kg} \cdot \text{m}^2 / \text{s}^2$ joule
Power $\text{W} = \text{J} / \text{s}$ watt
Pressure $\text{Pa} = \text{N} / \text{m}^2$ pascal
Frequency $\text{Hz} = 1/ \text{s}$ hertz
Electronic potential $\text{V} = \text{J} / \text{C}$ volt
Capacitance $\text{F} = \text{C} / \text{V}$ farad
Charge $\text{C} = \text{s} \cdot \text{A}$ coulomb
Resistance $\Omega = \text{V} / \text{A}$ ohm
Magnetic field $\text{T} = \text{N} / (\text{A} \cdot \text{m})$ tesla
Nuclear decay rate $\text{Bq} = 1 / \text{s}$ becquerel
Table 8. SI Units

 Length $1 \;\text{inch} \; (\text{in.}) = 2.54 \;\text{cm} \; (\text{exactly})$ $1 \;\text{foot} \; (\text{ft}) = 0.3048 \;\text{m}$ $1 \;\text{mile} \; (\text{mi}) = 1.609 \;\text{km}$ Force $1 \;\text{pound} \; (\text{lb}) = 4.448 \;\text{N}$ Energy $1 \;\text{British thermal unit} \; (\text{Btu}) = 1.055 \times 10^3 \text{J}$ Power $1 \;\text{horsepower} \; (\text{hp}) = 746 \;\text{W}$ Pressure $1 \;\text{lb} / \text{in}^2 = 6.895 \times 10^3 \;\text{Pa}$ Table 9. Selected British Units

 Length $1 \;\text{light year} \; (\text{ly}) = 9.46 \times 10^{15} \; \text{m}$ $1 \; \text{astronomical unit} \;(\text{au}) = 1.50 \times 10^{11} \; \text{m}$ $1 \;\text{nautical mile} = 1.852 \;\text{km}$ $1 \;\text{angstrom} ( \AA ) = 10^{-10} \text{m}$ Area $1 \;\text{acre} \;(\text{ac}) = 4.05 \times 10^3 \text{m}^2$ $1 \;\text{square foot} \; (\text{ft}^2) = 9.29 \times 10^{-2} \;\text{m}^2$ $1 \;\text{barn} \;(b) = 10^{-28} \;\text{m}^2$ Volume $1 \;\text{liter} \;(L) = 10^{-3} \; \text{m}^3$ $1 \;\text{U.S. gallon} \;(\text{gal}) = 3.785 \times 10^{-3} \;\text{m}^3$ Mass $1 \;\text{solar mass} = 1.99 \times 10^{30} \; \text{kg}$ $1 \;\text{metric ton} = 10^3 \;\text{kg}$ $1 \;\text{atomic mass unit} \;(u)= 1.6605 \times 10^{-27} \;\text{kg}$ Time $1 \;\text{year} \;(\text{y}) = 3.16 \times 10^7 \;\text{s}$ $1 \;\text{day} \;(\text{d}) = 86,400 \;\text{s}$ Speed $1 \;\text{mile per hour} \;(\text{mph}) = 1.609 \;\text{km} / \text{h}$ $1 \;\text{nautical mile per hour} \;(\text{naut}) = 1.852 \;\text{km} / \text{h}$ Angle $1 \;\text{degree} \;(^{\circ}) = 1.745 \times 10^{-2} \;\text{rad}$ $1 \;\text{minute of arc} \; ($‘ $) = 1/60 \;\text{degree}$ $1 \;\text{second of arc} \; (") = 1/60 \;\text{minute of arc}$ $1 \;\text{grad} = 1.571 \times 10^{-2} \;\text{rad}$ Energy $1 \;\text{kiloton TNT} \;(\text{kT}) = 4.2 \times 10^{12} \;\text{J}$ $1 \; \text{kilowatt hour} \;(\text{kW} \cdot h) = 3.60 \times 10^6 \;\text{J}$ $1 \;\text{food calorie} \;(\text{kcal}) = 4186 \;\text{J}$ $1 \;\text{calorie} \;(\text{cal}) = 4.186 \;\text{J}$ $1 \;\text{electron volt} \;(\text{eV}) = 1.60 \times 10^{-19} \;\text{J}$ Pressure $1 \;\text{atmosphere} \;(\text{atm}) = 1.013 \times 10^5 \;\text{Pa}$ $1 \;\text{millimeter of mercury} \;(\text{mm Hg}) = 133.3 \;\text{Pa}$ $1 \;\text{torricelli} \;(\text{torr}) = 1 \;\text{mm Hg} = 133.3 \;\text{Pa}$ Nuclear decay rate $1 \;\text{curie} \;(\text{Ci}) = 3.70 \times 10^{10} \; \text{Bq}$ Table 9. Other Units
 $\text{Circumference of a circle with radius} \; \text{r} \; \text{or diameter} \;\text{d}$ $C = 2 \pi r = \pi d$ $\text{Area of a circle with radius} \; r \;\text{or diameter} d$ $A = \pi r^2 = \pi d^{2}/4$ $\text{Area of a sphere with radius} \; r$ $A = 4 \pi r^2$ $\text{Volume of a sphere with radius} \; r$ $V = (4/3)( \pi r^3)$ Table 10. Useful Formulae

## Footnotes

1. 1 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
2. 2 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.