# Appendix C Useful Information

This appendix is broken into several tables.

Table 3. Important Constants1

Symbol Meaning Best Value Approximate Value
$latex c$ Speed of light in vacuum $latex 2.99792458 \times 10^8 \text{m/s}$ $latex 3.00 \times 10^8 \text{m/s}$
$latex G$ Gravitational constant $latex 6.67408(31) \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2$ $latex 6.67 \times 10^{-11} \;\text{N} \cdot \text{m}^2 / \text{kg}^2$
$latex N_A$ Avogadro’s number $latex 6.02214129(27) \times 10^{23}$ $latex 6.02 \times 10^{23}$
$latex k$ Boltzmann’s constant $latex 1.3806488(13) \times 10^{-23} \;\text{J} / \text{K}$ $latex 1.38 \times 10^{-23} \;\text{J} / \text{K}$
$latex R$ Gas constant $latex 8.3144621(75) \;\text{J} / \text{mol} \cdot \text{K}$ $latex 8.31 \;\text{J} / \text{mol} \cdot \text{K} = 1.99 \text{cal} / \text{mol} \cdot \text{K} = 0.0821 \text{atm} \cdot \text{L} / \text{mol} \cdot \text{K}$
$latex \sigma$ Stefan-Boltzmann constant $latex 5.670373(21) \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}$ $latex 5.67 \times 10^{-8} \;\text{W} / \text{m}^2 \cdot \text{K}$
$latex k$ Coulomb force constant $latex 8.987551788 \dots \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2$ $latex 8.99 \times 10^9 \;\text{N} \cdot \text{m}^2 / \text{C}^2$
$latex q_e$ Charge on electron $latex -1.602176565(35) \times 10^{-19} \;\text{C}$ $latex -1.60 \times 10^{-19} \;\text{C}$
$latex \varepsilon _0$ Permittivity of free space $latex 8.854187817 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \cdot \text{m}^2$ $latex 8.85 \dots \times 10^{-12} \;\text{C}^2 / \text{N} \text{m}^2$
$latex \mu _0$ Permeability of free space $latex 4 \pi \times 10^{-7} \;\text{T} \cdot \;\text{m}/ \text{A}$ $latex 1.26 \times 10^{-6} \;\text{T} \cdot \text{m} / \text{A}$
$latex h$ Planck’s constant $latex 6.62606957(29) \times 10^{-34} \;\text{J} \cdot \text{s}$ $latex 6.63 \times 10^{-34} \;\text{J} \cdot \text{s}$
Symbol Meaning Best Value Approximate Value
$latex m_e$ Electron mass $latex 9.10938291(40) \times 10^{-31} \text{kg}$ $latex 9.11 \times 10^{-31} \text{kg}$
$latex m_p$ Proton mass $latex 1.672621777(74) \times 10^{-27} \text{kg}$ $latex 1.6726 \times 10^{-27} \text{kg}$
$latex m_n$ Neutron mass $latex 1.674927351(74) \times 10^{-27} \text{kg}$ $latex 1.6749 \times 10^{-27} \text{kg}$
$latex \text{u}$ Atomic mass unit $latex 1.660538921(73) \times 10^{-27} \text{kg}$ $latex 1.6605 \times 10^{-27} \text{kg}$
Table 4. Submicroscopic Masses2
 Sun mass $latex 1.99 \times 10^{30} \text{kg}$ average radius $latex 6.96 \times 10^8 \text{m}$ Earth-sun distance (average) $latex 1.496 \times 10^{11} \text{m}$ Earth mass $latex 5.9736 \times 10^{24} \text{kg}$ average radius $latex 6.376 \times 10^6 \text{m}$ orbital period $latex 3.16 \times 10^7 \text{s}$ Moon mass $latex 7.35 \times 10^{22} \text{kg}$ average radius $latex 1.74 \times 10^6 \text{m}$ orbital period (average) $latex 2.36 \times 10^6 \text{s}$ Earth-moon distance (average) $latex 3.84 \times 10^8 \text{m}$ Table 5. Solar System Data
Prefix Symbol Value Prefix Symbol Value
tera T $latex 10^{12}$ deci d $latex 10^{-1}$
giga G $latex 10^{9}$ centi c $latex 10^{-2}$
mega M $latex 10^{6}$ milli m $latex 10^{-3}$
kilo k $latex 10^{3}$ micro $latex \mu$ $latex 10^{-6}$
hecto h $latex 10^{2}$ nano n $latex 10^{-9}$
deka da $latex 10^{1}$ pico p $latex 10^{-12}$
$latex 10^{0} (= 1)$ femto f $latex 10^{-15}$
Table 6. Metric Prefixes for Powers of Ten and Their Symbols
 Alpha A $latex \alpha$ Eta Η $latex \eta$ Nu Ν $latex \nu$ Tau Τ $latex \tau$ Beta Β $latex \beta$ Theta Θ $latex \theta$ Xi Ξ $latex \xi$ Upsilon Υ $latex \upsilon$ Gamma Γ $latex \gamma$ Iota Ι $latex \iota$ Omicron Ο $latex \o$ Phi Φ $latex \phi$ Delta Δ $latex \delta$ Kappa Κ $latex \kappa$ Pi Π $latex \pi$ Chi Χ $latex \chi$ Epsilon Ε $latex \epsilon$ Lambda Λ $latex \lambda$ Rho Ρ $latex \rho$ Psi Ψ $latex \psi$ Zeta Ζ $latex \zeta$ Mu Μ $latex \mu$ Sigma Σ $latex \sigma$ Omega Ω $latex \omega$ Table 7. The Greek Alphabet
Entity Abbreviation Name
Fundamental units Length $latex \text{m}$ meter
Mass $latex \text{kg}$ kilogram
Time $latex \text{s}$ second
Current $latex \text{A}$ ampere
Supplementary unit Angle $latex \text{rad}$ radian
Derived units Force $latex \text{N} = \text{kg} \cdot \text{m} / \text{s}^2$ newton
Energy $latex \text{J} = \text{kg} \cdot \text{m}^2 / \text{s}^2$ joule
Power $latex \text{W} = \text{J} / \text{s}$ watt
Pressure $latex \text{Pa} = \text{N} / \text{m}^2$ pascal
Frequency $latex \text{Hz} = 1/ \text{s}$ hertz
Electronic potential $latex \text{V} = \text{J} / \text{C}$ volt
Capacitance $latex \text{F} = \text{C} / \text{V}$ farad
Charge $latex \text{C} = \text{s} \cdot \text{A}$ coulomb
Resistance $latex \Omega = \text{V} / \text{A}$ ohm
Magnetic field $latex \text{T} = \text{N} / (\text{A} \cdot \text{m})$ tesla
Nuclear decay rate $latex \text{Bq} = 1 / \text{s}$ becquerel
Table 8. SI Units
 Length $latex 1 \;\text{inch} \; (\text{in.}) = 2.54 \;\text{cm} \; (\text{exactly})$ $latex 1 \;\text{foot} \; (\text{ft}) = 0.3048 \;\text{m}$ $latex 1 \;\text{mile} \; (\text{mi}) = 1.609 \;\text{km}$ Force $latex 1 \;\text{pound} \; (\text{lb}) = 4.448 \;\text{N}$ Energy $latex 1 \;\text{British thermal unit} \; (\text{Btu}) = 1.055 \times 10^3 \text{J}$ Power $latex 1 \;\text{horsepower} \; (\text{hp}) = 746 \;\text{W}$ Pressure $latex 1 \;\text{lb} / \text{in}^2 = 6.895 \times 10^3 \;\text{Pa}$ Table 9. Selected British Units
 Length $latex 1 \;\text{light year} \; (\text{ly}) = 9.46 \times 10^{15} \; \text{m}$ $latex 1 \; \text{astronomical unit} \;(\text{au}) = 1.50 \times 10^{11} \; \text{m}$ $latex 1 \;\text{nautical mile} = 1.852 \;\text{km}$ $latex 1 \;\text{angstrom} ( \AA ) = 10^{-10} \text{m}$ Area $latex 1 \;\text{acre} \;(\text{ac}) = 4.05 \times 10^3 \text{m}^2$ $latex 1 \;\text{square foot} \; (\text{ft}^2) = 9.29 \times 10^{-2} \;\text{m}^2$ $latex 1 \;\text{barn} \;(b) = 10^{-28} \;\text{m}^2$ Volume $latex 1 \;\text{liter} \;(L) = 10^{-3} \; \text{m}^3$ $latex 1 \;\text{U.S. gallon} \;(\text{gal}) = 3.785 \times 10^{-3} \;\text{m}^3$ Mass $latex 1 \;\text{solar mass} = 1.99 \times 10^{30} \; \text{kg}$ $latex 1 \;\text{metric ton} = 10^3 \;\text{kg}$ $latex 1 \;\text{atomic mass unit} \;(u)= 1.6605 \times 10^{-27} \;\text{kg}$ Time $latex 1 \;\text{year} \;(\text{y}) = 3.16 \times 10^7 \;\text{s}$ $latex 1 \;\text{day} \;(\text{d}) = 86,400 \;\text{s}$ Speed $latex 1 \;\text{mile per hour} \;(\text{mph}) = 1.609 \;\text{km} / \text{h}$ $latex 1 \;\text{nautical mile per hour} \;(\text{naut}) = 1.852 \;\text{km} / \text{h}$ Angle $latex 1 \;\text{degree} \;(^{\circ}) = 1.745 \times 10^{-2} \;\text{rad}$ $latex 1 \;\text{minute of arc} \; ($’ $latex ) = 1/60 \;\text{degree}$ $latex 1 \;\text{second of arc} \; (“) = 1/60 \;\text{minute of arc}$ $latex 1 \;\text{grad} = 1.571 \times 10^{-2} \;\text{rad}$ Energy $latex 1 \;\text{kiloton TNT} \;(\text{kT}) = 4.2 \times 10^{12} \;\text{J}$ $latex 1 \; \text{kilowatt hour} \;(\text{kW} \cdot h) = 3.60 \times 10^6 \;\text{J}$ $latex 1 \;\text{food calorie} \;(\text{kcal}) = 4186 \;\text{J}$ $latex 1 \;\text{calorie} \;(\text{cal}) = 4.186 \;\text{J}$ $latex 1 \;\text{electron volt} \;(\text{eV}) = 1.60 \times 10^{-19} \;\text{J}$ Pressure $latex 1 \;\text{atmosphere} \;(\text{atm}) = 1.013 \times 10^5 \;\text{Pa}$ $latex 1 \;\text{millimeter of mercury} \;(\text{mm Hg}) = 133.3 \;\text{Pa}$ $latex 1 \;\text{torricelli} \;(\text{torr}) = 1 \;\text{mm Hg} = 133.3 \;\text{Pa}$ Nuclear decay rate $latex 1 \;\text{curie} \;(\text{Ci}) = 3.70 \times 10^{10} \; \text{Bq}$ Table 9. Other Units
 $latex \text{Circumference of a circle with radius} \; \text{r} \; \text{or diameter} \;\text{d}$ $latex C = 2 \pi r = \pi d$ $latex \text{Area of a circle with radius} \; r \;\text{or diameter} d$ $latex A = \pi r^2 = \pi d^{2}/4$ $latex \text{Area of a sphere with radius} \; r$ $latex A = 4 \pi r^2$ $latex \text{Volume of a sphere with radius} \; r$ $latex V = (4/3)( \pi r^3)$ 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.