| @cindex physical constants |
| @cindex constants, physical |
| @cindex conversion of units |
| @cindex units, conversion of |
| This chapter describes macros for the values of physical constants, such |
| as the speed of light, @math{c}, and gravitational constant, @math{G}. |
| The values are available in different unit systems, including the |
| standard MKSA system (meters, kilograms, seconds, amperes) and the CGSM |
| system (centimeters, grams, seconds, gauss), which is commonly used in |
| Astronomy. |
| |
| The definitions of constants in the MKSA system are available in the file |
| @file{gsl_const_mksa.h}. The constants in the CGSM system are defined in |
| @file{gsl_const_cgsm.h}. Dimensionless constants, such as the fine |
| structure constant, which are pure numbers are defined in |
| @file{gsl_const_num.h}. |
| |
| @menu |
| * Fundamental Constants:: |
| * Astronomy and Astrophysics:: |
| * Atomic and Nuclear Physics:: |
| * Measurement of Time:: |
| * Imperial Units :: |
| * Speed and Nautical Units:: |
| * Printers Units:: |
| * Volume Area and Length:: |
| * Mass and Weight :: |
| * Thermal Energy and Power:: |
| * Pressure:: |
| * Viscosity:: |
| * Light and Illumination:: |
| * Radioactivity:: |
| * Force and Energy:: |
| * Prefixes:: |
| * Physical Constant Examples:: |
| * Physical Constant References and Further Reading:: |
| @end menu |
| |
| The full list of constants is described briefly below. Consult the |
| header files themselves for the values of the constants used in the |
| library. |
| |
| @node Fundamental Constants |
| @section Fundamental Constants |
| @cindex fundamental constants |
| @cindex constants, fundamental |
| @table @code |
| @item GSL_CONST_MKSA_SPEED_OF_LIGHT |
| The speed of light in vacuum, @math{c}. |
| |
| @item GSL_CONST_MKSA_VACUUM_PERMEABILITY |
| The permeability of free space, @math{\mu_0}. This constant is defined |
| in the MKSA system only. |
| |
| @item GSL_CONST_MKSA_VACUUM_PERMITTIVITY |
| The permittivity of free space, @math{\epsilon_0}. This constant is |
| defined in the MKSA system only. |
| |
| @item GSL_CONST_MKSA_PLANCKS_CONSTANT_H |
| Planck's constant, @math{h}. |
| |
| @item GSL_CONST_MKSA_PLANCKS_CONSTANT_HBAR |
| Planck's constant divided by @math{2\pi}, @math{\hbar}. |
| |
| @item GSL_CONST_NUM_AVOGADRO |
| Avogadro's number, @math{N_a}. |
| |
| @item GSL_CONST_MKSA_FARADAY |
| The molar charge of 1 Faraday. |
| |
| @item GSL_CONST_MKSA_BOLTZMANN |
| The Boltzmann constant, @math{k}. |
| |
| @item GSL_CONST_MKSA_MOLAR_GAS |
| The molar gas constant, @math{R_0}. |
| |
| @item GSL_CONST_MKSA_STANDARD_GAS_VOLUME |
| The standard gas volume, @math{V_0}. |
| |
| @item GSL_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT |
| The Stefan-Boltzmann radiation constant, @math{\sigma}. |
| |
| @item GSL_CONST_MKSA_GAUSS |
| The magnetic field of 1 Gauss. |
| @end table |
| |
| @node Astronomy and Astrophysics |
| @section Astronomy and Astrophysics |
| @cindex astronomical constants |
| @table @code |
| @item GSL_CONST_MKSA_ASTRONOMICAL_UNIT |
| The length of 1 astronomical unit (mean earth-sun distance), @math{au}. |
| |
| @item GSL_CONST_MKSA_GRAVITATIONAL_CONSTANT |
| The gravitational constant, @math{G}. |
| |
| @item GSL_CONST_MKSA_LIGHT_YEAR |
| The distance of 1 light-year, @math{ly}. |
| |
| @item GSL_CONST_MKSA_PARSEC |
| The distance of 1 parsec, @math{pc}. |
| |
| @item GSL_CONST_MKSA_GRAV_ACCEL |
| The standard gravitational acceleration on Earth, @math{g}. |
| |
| @item GSL_CONST_MKSA_SOLAR_MASS |
| The mass of the Sun. |
| @end table |
| |
| @node Atomic and Nuclear Physics |
| @section Atomic and Nuclear Physics |
| @cindex atomic physics, constants |
| @cindex nuclear physics, constants |
| @table @code |
| @item GSL_CONST_MKSA_ELECTRON_CHARGE |
| The charge of the electron, @math{e}. |
| |
| @item GSL_CONST_MKSA_ELECTRON_VOLT |
| The energy of 1 electron volt, @math{eV}. |
| |
| @item GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS |
| The unified atomic mass, @math{amu}. |
| |
| @item GSL_CONST_MKSA_MASS_ELECTRON |
| The mass of the electron, @math{m_e}. |
| |
| @item GSL_CONST_MKSA_MASS_MUON |
| The mass of the muon, @math{m_\mu}. |
| |
| @item GSL_CONST_MKSA_MASS_PROTON |
| The mass of the proton, @math{m_p}. |
| |
| @item GSL_CONST_MKSA_MASS_NEUTRON |
| The mass of the neutron, @math{m_n}. |
| |
| @item GSL_CONST_NUM_FINE_STRUCTURE |
| The electromagnetic fine structure constant @math{\alpha}. |
| |
| @item GSL_CONST_MKSA_RYDBERG |
| The Rydberg constant, @math{Ry}, in units of energy. This is related to |
| the Rydberg inverse wavelength @math{R} by @math{Ry = h c R}. |
| |
| @item GSL_CONST_MKSA_BOHR_RADIUS |
| The Bohr radius, @math{a_0}. |
| |
| @item GSL_CONST_MKSA_ANGSTROM |
| The length of 1 angstrom. |
| |
| @item GSL_CONST_MKSA_BARN |
| The area of 1 barn. |
| |
| @item GSL_CONST_MKSA_BOHR_MAGNETON |
| The Bohr Magneton, @math{\mu_B}. |
| |
| @item GSL_CONST_MKSA_NUCLEAR_MAGNETON |
| The Nuclear Magneton, @math{\mu_N}. |
| |
| @item GSL_CONST_MKSA_ELECTRON_MAGNETIC_MOMENT |
| The absolute value of the magnetic moment of the electron, @math{\mu_e}. |
| The physical magnetic moment of the electron is negative. |
| |
| @item GSL_CONST_MKSA_PROTON_MAGNETIC_MOMENT |
| The magnetic moment of the proton, @math{\mu_p}. |
| |
| @item GSL_CONST_MKSA_THOMSON_CROSS_SECTION |
| The Thomson cross section, @math{\sigma_T}. |
| |
| @item GSL_CONST_MKSA_DEBYE |
| The electric dipole moment of 1 Debye, @math{D}. |
| @end table |
| |
| |
| @node Measurement of Time |
| @section Measurement of Time |
| @cindex time units |
| @table @code |
| @item GSL_CONST_MKSA_MINUTE |
| The number of seconds in 1 minute. |
| |
| @item GSL_CONST_MKSA_HOUR |
| The number of seconds in 1 hour. |
| |
| @item GSL_CONST_MKSA_DAY |
| The number of seconds in 1 day. |
| |
| @item GSL_CONST_MKSA_WEEK |
| The number of seconds in 1 week. |
| @end table |
| |
| |
| @node Imperial Units |
| @section Imperial Units |
| @cindex imperial units |
| @cindex units, imperial |
| @table @code |
| @item GSL_CONST_MKSA_INCH |
| The length of 1 inch. |
| |
| @item GSL_CONST_MKSA_FOOT |
| The length of 1 foot. |
| |
| @item GSL_CONST_MKSA_YARD |
| The length of 1 yard. |
| |
| @item GSL_CONST_MKSA_MILE |
| The length of 1 mile. |
| |
| @item GSL_CONST_MKSA_MIL |
| The length of 1 mil (1/1000th of an inch). |
| @end table |
| |
| |
| @node Speed and Nautical Units |
| @section Speed and Nautical Units |
| @cindex nautical units |
| |
| @table @code |
| @item GSL_CONST_MKSA_KILOMETERS_PER_HOUR |
| The speed of 1 kilometer per hour. |
| |
| @item GSL_CONST_MKSA_MILES_PER_HOUR |
| The speed of 1 mile per hour. |
| |
| @item GSL_CONST_MKSA_NAUTICAL_MILE |
| The length of 1 nautical mile. |
| |
| @item GSL_CONST_MKSA_FATHOM |
| The length of 1 fathom. |
| |
| @item GSL_CONST_MKSA_KNOT |
| The speed of 1 knot. |
| @end table |
| |
| |
| @node Printers Units |
| @section Printers Units |
| @cindex printers units |
| |
| @table @code |
| @item GSL_CONST_MKSA_POINT |
| The length of 1 printer's point (1/72 inch). |
| |
| @item GSL_CONST_MKSA_TEXPOINT |
| The length of 1 TeX point (1/72.27 inch). |
| @end table |
| |
| |
| @node Volume Area and Length |
| @section Volume, Area and Length |
| @cindex volume units |
| |
| @table @code |
| @item GSL_CONST_MKSA_MICRON |
| The length of 1 micron. |
| |
| @item GSL_CONST_MKSA_HECTARE |
| The area of 1 hectare. |
| |
| @item GSL_CONST_MKSA_ACRE |
| The area of 1 acre. |
| |
| @item GSL_CONST_MKSA_LITER |
| The volume of 1 liter. |
| |
| @item GSL_CONST_MKSA_US_GALLON |
| The volume of 1 US gallon. |
| |
| @item GSL_CONST_MKSA_CANADIAN_GALLON |
| The volume of 1 Canadian gallon. |
| |
| @item GSL_CONST_MKSA_UK_GALLON |
| The volume of 1 UK gallon. |
| |
| @item GSL_CONST_MKSA_QUART |
| The volume of 1 quart. |
| |
| @item GSL_CONST_MKSA_PINT |
| The volume of 1 pint. |
| @end table |
| |
| |
| @comment @node Cookery |
| @comment @section Cookery |
| @comment @commentindex cookery units |
| |
| @comment @table @commentode |
| @comment @item GSL_CONST_MKSA_CUP |
| @comment The volume of 1 cup. |
| |
| @comment @item GSL_CONST_MKSA_FLUID_OUNCE |
| @comment The volume of 1 fluid ounce. |
| |
| @comment @item GSL_CONST_MKSA_TABLESPOON |
| @comment The volume of 1 tablespoon. |
| |
| @comment @item GSL_CONST_MKSA_TEASPOON |
| @comment The volume of 1 teaspoon. |
| @comment @end table |
| |
| |
| @node Mass and Weight |
| @section Mass and Weight |
| @cindex mass, units of |
| @cindex weight, units of |
| @table @code |
| @item GSL_CONST_MKSA_POUND_MASS |
| The mass of 1 pound. |
| |
| @item GSL_CONST_MKSA_OUNCE_MASS |
| The mass of 1 ounce. |
| |
| @item GSL_CONST_MKSA_TON |
| The mass of 1 ton. |
| |
| @item GSL_CONST_MKSA_METRIC_TON |
| The mass of 1 metric ton (1000 kg). |
| |
| @item GSL_CONST_MKSA_UK_TON |
| The mass of 1 UK ton. |
| |
| @item GSL_CONST_MKSA_TROY_OUNCE |
| The mass of 1 troy ounce. |
| |
| @item GSL_CONST_MKSA_CARAT |
| The mass of 1 carat. |
| |
| @item GSL_CONST_MKSA_GRAM_FORCE |
| The force of 1 gram weight. |
| |
| @item GSL_CONST_MKSA_POUND_FORCE |
| The force of 1 pound weight. |
| |
| @item GSL_CONST_MKSA_KILOPOUND_FORCE |
| The force of 1 kilopound weight. |
| |
| @item GSL_CONST_MKSA_POUNDAL |
| The force of 1 poundal. |
| @end table |
| |
| |
| @node Thermal Energy and Power |
| @section Thermal Energy and Power |
| @cindex energy, units of |
| @cindex power, units of |
| @cindex thermal energy, units of |
| @table @code |
| @item GSL_CONST_MKSA_CALORIE |
| The energy of 1 calorie. |
| |
| @item GSL_CONST_MKSA_BTU |
| The energy of 1 British Thermal Unit, @math{btu}. |
| |
| @item GSL_CONST_MKSA_THERM |
| The energy of 1 Therm. |
| |
| @item GSL_CONST_MKSA_HORSEPOWER |
| The power of 1 horsepower. |
| @end table |
| |
| |
| @node Pressure |
| @section Pressure |
| @cindex pressure, units of |
| @table @code |
| @item GSL_CONST_MKSA_BAR |
| The pressure of 1 bar. |
| |
| @item GSL_CONST_MKSA_STD_ATMOSPHERE |
| The pressure of 1 standard atmosphere. |
| |
| @item GSL_CONST_MKSA_TORR |
| The pressure of 1 torr. |
| |
| @item GSL_CONST_MKSA_METER_OF_MERCURY |
| The pressure of 1 meter of mercury. |
| |
| @item GSL_CONST_MKSA_INCH_OF_MERCURY |
| The pressure of 1 inch of mercury. |
| |
| @item GSL_CONST_MKSA_INCH_OF_WATER |
| The pressure of 1 inch of water. |
| |
| @item GSL_CONST_MKSA_PSI |
| The pressure of 1 pound per square inch. |
| @end table |
| |
| @node Viscosity |
| @section Viscosity |
| @cindex viscosity, units of |
| @table @code |
| @item GSL_CONST_MKSA_POISE |
| The dynamic viscosity of 1 poise. |
| |
| @item GSL_CONST_MKSA_STOKES |
| The kinematic viscosity of 1 stokes. |
| @end table |
| |
| |
| @node Light and Illumination |
| @section Light and Illumination |
| @cindex light, units of |
| @cindex illumination, units of |
| |
| @table @code |
| @item GSL_CONST_MKSA_STILB |
| The luminance of 1 stilb. |
| |
| @item GSL_CONST_MKSA_LUMEN |
| The luminous flux of 1 lumen. |
| |
| @item GSL_CONST_MKSA_LUX |
| The illuminance of 1 lux. |
| |
| @item GSL_CONST_MKSA_PHOT |
| The illuminance of 1 phot. |
| |
| @item GSL_CONST_MKSA_FOOTCANDLE |
| The illuminance of 1 footcandle. |
| |
| @item GSL_CONST_MKSA_LAMBERT |
| The luminance of 1 lambert. |
| |
| @item GSL_CONST_MKSA_FOOTLAMBERT |
| The luminance of 1 footlambert. |
| @end table |
| |
| |
| @node Radioactivity |
| @section Radioactivity |
| @cindex radioactivity, units of |
| @table @code |
| @item GSL_CONST_MKSA_CURIE |
| The activity of 1 curie. |
| |
| @item GSL_CONST_MKSA_ROENTGEN |
| The exposure of 1 roentgen. |
| |
| @item GSL_CONST_MKSA_RAD |
| The absorbed dose of 1 rad. |
| @end table |
| |
| |
| @node Force and Energy |
| @section Force and Energy |
| @cindex force and energy, units of |
| @table @code |
| @item GSL_CONST_MKSA_NEWTON |
| The SI unit of force, 1 Newton. |
| |
| @item GSL_CONST_MKSA_DYNE |
| The force of 1 Dyne = @c{$10^{-5}$} |
| @math{10^-5} Newton. |
| |
| @item GSL_CONST_MKSA_JOULE |
| The SI unit of energy, 1 Joule. |
| |
| @item GSL_CONST_MKSA_ERG |
| The energy 1 erg = @c{$10^{-7}$} |
| @math{10^-7} Joule. |
| @end table |
| |
| |
| @node Prefixes |
| @section Prefixes |
| @cindex prefixes |
| @cindex constants, prefixes |
| |
| These constants are dimensionless scaling factors. |
| |
| @table @code |
| @item GSL_CONST_NUM_YOTTA |
| @c{$10^{24}$} |
| @math{10^24} |
| |
| @item GSL_CONST_NUM_ZETTA |
| @c{$10^{21}$} |
| @math{10^21} |
| |
| @item GSL_CONST_NUM_EXA |
| @c{$10^{18}$} |
| @math{10^18} |
| |
| @item GSL_CONST_NUM_PETA |
| @c{$10^{15}$} |
| @math{10^15} |
| |
| @item GSL_CONST_NUM_TERA |
| @c{$10^{12}$} |
| @math{10^12} |
| |
| @item GSL_CONST_NUM_GIGA |
| @math{10^9} |
| |
| @item GSL_CONST_NUM_MEGA |
| @math{10^6} |
| |
| @item GSL_CONST_NUM_KILO |
| @math{10^3} |
| |
| @item GSL_CONST_NUM_MILLI |
| @c{$10^{-3}$} |
| @math{10^-3} |
| |
| @item GSL_CONST_NUM_MICRO |
| @c{$10^{-6}$} |
| @math{10^-6} |
| |
| @item GSL_CONST_NUM_NANO |
| @c{$10^{-9}$} |
| @math{10^-9} |
| |
| @item GSL_CONST_NUM_PICO |
| @c{$10^{-12}$} |
| @math{10^-12} |
| |
| @item GSL_CONST_NUM_FEMTO |
| @c{$10^{-15}$} |
| @math{10^-15} |
| |
| @item GSL_CONST_NUM_ATTO |
| @c{$10^{-18}$} |
| @math{10^-18} |
| |
| @item GSL_CONST_NUM_ZEPTO |
| @c{$10^{-21}$} |
| @math{10^-21} |
| |
| @item GSL_CONST_NUM_YOCTO |
| @c{$10^{-24}$} |
| @math{10^-24} |
| @end table |
| |
| @node Physical Constant Examples |
| @section Examples |
| |
| The following program demonstrates the use of the physical constants in |
| a calculation. In this case, the goal is to calculate the range of |
| light-travel times from Earth to Mars. |
| |
| The required data is the average distance of each planet from the Sun in |
| astronomical units (the eccentricities and inclinations of the orbits |
| will be neglected for the purposes of this calculation). The average |
| radius of the orbit of Mars is 1.52 astronomical units, and for the |
| orbit of Earth it is 1 astronomical unit (by definition). These values |
| are combined with the MKSA values of the constants for the speed of |
| light and the length of an astronomical unit to produce a result for the |
| shortest and longest light-travel times in seconds. The figures are |
| converted into minutes before being displayed. |
| |
| @example |
| @verbatiminclude examples/const.c |
| @end example |
| |
| @noindent |
| Here is the output from the program, |
| |
| @example |
| @verbatiminclude examples/const.out |
| @end example |
| |
| @node Physical Constant References and Further Reading |
| @section References and Further Reading |
| |
| The authoritative sources for physical constants are the 2002 CODATA |
| recommended values, published in the articles below. Further information |
| on the values of physical constants is also available from the cited |
| articles and the NIST website. |
| |
| @itemize @asis |
| @item Journal of Physical and Chemical Reference Data, 28(6), 1713-1852, 1999 |
| @item Reviews of Modern Physics, 72(2), 351-495, 2000 |
| @item @uref{http://www.physics.nist.gov/cuu/Constants/index.html} |
| @item @uref{http://physics.nist.gov/Pubs/SP811/appenB9.html} |
| @end itemize |
| |