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
- 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.
- 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.