.. index:: single: physical constants single: constants, physical single: conversion of units single: units, conversion of ****************** Physical Constants ****************** 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`. The full list of constants is described briefly below. Consult the header files themselves for the values of the constants used in the library. .. index:: single: fundamental constants single: constants, fundamental Fundamental Constants ===================== .. macro:: GSL_CONST_MKSA_SPEED_OF_LIGHT The speed of light in vacuum, :math:`c`. .. macro:: GSL_CONST_MKSA_VACUUM_PERMEABILITY The permeability of free space, :math:`\mu_0`. This constant is defined in the MKSA system only. .. macro:: GSL_CONST_MKSA_VACUUM_PERMITTIVITY The permittivity of free space, :math:`\epsilon_0`. This constant is defined in the MKSA system only. .. macro:: GSL_CONST_MKSA_PLANCKS_CONSTANT_H Planck's constant, :math:`h`. .. macro:: GSL_CONST_MKSA_PLANCKS_CONSTANT_HBAR Planck's constant divided by :math:`2\pi`, :math:`\hbar`. .. macro:: GSL_CONST_NUM_AVOGADRO Avogadro's number, :math:`N_a`. .. macro:: GSL_CONST_MKSA_FARADAY The molar charge of 1 Faraday. .. macro:: GSL_CONST_MKSA_BOLTZMANN The Boltzmann constant, :math:`k`. .. macro:: GSL_CONST_MKSA_MOLAR_GAS The molar gas constant, :math:`R_0`. .. macro:: GSL_CONST_MKSA_STANDARD_GAS_VOLUME The standard gas volume, :math:`V_0`. .. macro:: GSL_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT The Stefan-Boltzmann radiation constant, :math:`\sigma`. .. macro:: GSL_CONST_MKSA_GAUSS The magnetic field of 1 Gauss. .. index:: astronomical constants Astronomy and Astrophysics ========================== .. macro:: GSL_CONST_MKSA_ASTRONOMICAL_UNIT The length of 1 astronomical unit (mean earth-sun distance), :math:`au`. .. macro:: GSL_CONST_MKSA_GRAVITATIONAL_CONSTANT The gravitational constant, :math:`G`. .. macro:: GSL_CONST_MKSA_LIGHT_YEAR The distance of 1 light-year, :math:`ly`. .. macro:: GSL_CONST_MKSA_PARSEC The distance of 1 parsec, :math:`pc`. .. macro:: GSL_CONST_MKSA_GRAV_ACCEL The standard gravitational acceleration on Earth, :math:`g`. .. macro:: GSL_CONST_MKSA_SOLAR_MASS The mass of the Sun. .. index:: single: atomic physics, constants single: nuclear physics, constants Atomic and Nuclear Physics ========================== .. macro:: GSL_CONST_MKSA_ELECTRON_CHARGE The charge of the electron, :math:`e`. .. macro:: GSL_CONST_MKSA_ELECTRON_VOLT The energy of 1 electron volt, :math:`eV`. .. macro:: GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS The unified atomic mass, :math:`amu`. .. macro:: GSL_CONST_MKSA_MASS_ELECTRON The mass of the electron, :math:`m_e`. .. macro:: GSL_CONST_MKSA_MASS_MUON The mass of the muon, :math:`m_\mu`. .. macro:: GSL_CONST_MKSA_MASS_PROTON The mass of the proton, :math:`m_p`. .. macro:: GSL_CONST_MKSA_MASS_NEUTRON The mass of the neutron, :math:`m_n`. .. macro:: GSL_CONST_NUM_FINE_STRUCTURE The electromagnetic fine structure constant :math:`\alpha`. .. macro:: GSL_CONST_MKSA_RYDBERG The Rydberg constant, :math:`Ry`, in units of energy. This is related to the Rydberg inverse wavelength :math:`R_\infty` by :math:`Ry = h c R_\infty`. .. macro:: GSL_CONST_MKSA_BOHR_RADIUS The Bohr radius, :math:`a_0`. .. macro:: GSL_CONST_MKSA_ANGSTROM The length of 1 angstrom. .. macro:: GSL_CONST_MKSA_BARN The area of 1 barn. .. macro:: GSL_CONST_MKSA_BOHR_MAGNETON The Bohr Magneton, :math:`\mu_B`. .. macro:: GSL_CONST_MKSA_NUCLEAR_MAGNETON The Nuclear Magneton, :math:`\mu_N`. .. macro:: 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. .. macro:: GSL_CONST_MKSA_PROTON_MAGNETIC_MOMENT The magnetic moment of the proton, :math:`\mu_p`. .. macro:: GSL_CONST_MKSA_THOMSON_CROSS_SECTION The Thomson cross section, :math:`\sigma_T`. .. macro:: GSL_CONST_MKSA_DEBYE The electric dipole moment of 1 Debye, :math:`D`. .. index:: time units Measurement of Time =================== .. macro:: GSL_CONST_MKSA_MINUTE The number of seconds in 1 minute. .. macro:: GSL_CONST_MKSA_HOUR The number of seconds in 1 hour. .. macro:: GSL_CONST_MKSA_DAY The number of seconds in 1 day. .. macro:: GSL_CONST_MKSA_WEEK The number of seconds in 1 week. .. index:: single: imperial units single: units, imperial Imperial Units ============== .. macro:: GSL_CONST_MKSA_INCH The length of 1 inch. .. macro:: GSL_CONST_MKSA_FOOT The length of 1 foot. .. macro:: GSL_CONST_MKSA_YARD The length of 1 yard. .. macro:: GSL_CONST_MKSA_MILE The length of 1 mile. .. macro:: GSL_CONST_MKSA_MIL The length of 1 mil (1/1000th of an inch). .. index:: nautical units Speed and Nautical Units ======================== .. macro:: GSL_CONST_MKSA_KILOMETERS_PER_HOUR The speed of 1 kilometer per hour. .. macro:: GSL_CONST_MKSA_MILES_PER_HOUR The speed of 1 mile per hour. .. macro:: GSL_CONST_MKSA_NAUTICAL_MILE The length of 1 nautical mile. .. macro:: GSL_CONST_MKSA_FATHOM The length of 1 fathom. .. macro:: GSL_CONST_MKSA_KNOT The speed of 1 knot. .. index:: printers units Printers Units ============== .. macro:: GSL_CONST_MKSA_POINT The length of 1 printer's point (1/72 inch). .. macro:: GSL_CONST_MKSA_TEXPOINT The length of 1 TeX point (1/72.27 inch). .. index:: volume units Volume, Area and Length ======================= .. macro:: GSL_CONST_MKSA_MICRON The length of 1 micron. .. macro:: GSL_CONST_MKSA_HECTARE The area of 1 hectare. .. macro:: GSL_CONST_MKSA_ACRE The area of 1 acre. .. macro:: GSL_CONST_MKSA_LITER The volume of 1 liter. .. macro:: GSL_CONST_MKSA_US_GALLON The volume of 1 US gallon. .. macro:: GSL_CONST_MKSA_CANADIAN_GALLON The volume of 1 Canadian gallon. .. macro:: GSL_CONST_MKSA_UK_GALLON The volume of 1 UK gallon. .. macro:: GSL_CONST_MKSA_QUART The volume of 1 quart. .. macro:: GSL_CONST_MKSA_PINT The volume of 1 pint. .. @node Cookery .. @section Cookery .. @commentindex cookery units .. @table @commentode .. @item GSL_CONST_MKSA_CUP .. The volume of 1 cup. .. @item GSL_CONST_MKSA_FLUID_OUNCE .. The volume of 1 fluid ounce. .. @item GSL_CONST_MKSA_TABLESPOON .. The volume of 1 tablespoon. .. @item GSL_CONST_MKSA_TEASPOON .. The volume of 1 teaspoon. .. @end table .. index:: single: mass, units of single: weight, units of Mass and Weight =============== .. macro:: GSL_CONST_MKSA_POUND_MASS The mass of 1 pound. .. macro:: GSL_CONST_MKSA_OUNCE_MASS The mass of 1 ounce. .. macro:: GSL_CONST_MKSA_TON The mass of 1 ton. .. macro:: GSL_CONST_MKSA_METRIC_TON The mass of 1 metric ton (1000 kg). .. macro:: GSL_CONST_MKSA_UK_TON The mass of 1 UK ton. .. macro:: GSL_CONST_MKSA_TROY_OUNCE The mass of 1 troy ounce. .. macro:: GSL_CONST_MKSA_CARAT The mass of 1 carat. .. macro:: GSL_CONST_MKSA_GRAM_FORCE The force of 1 gram weight. .. macro:: GSL_CONST_MKSA_POUND_FORCE The force of 1 pound weight. .. macro:: GSL_CONST_MKSA_KILOPOUND_FORCE The force of 1 kilopound weight. .. macro:: GSL_CONST_MKSA_POUNDAL The force of 1 poundal. .. index:: single: energy, units of single: power, units of single: thermal energy, units of Thermal Energy and Power ======================== .. macro:: GSL_CONST_MKSA_CALORIE The energy of 1 calorie. .. macro:: GSL_CONST_MKSA_BTU The energy of 1 British Thermal Unit, :math:`btu`. .. macro:: GSL_CONST_MKSA_THERM The energy of 1 Therm. .. macro:: GSL_CONST_MKSA_HORSEPOWER The power of 1 horsepower. .. index:: pressure, units of Pressure ======== .. macro:: GSL_CONST_MKSA_BAR The pressure of 1 bar. .. macro:: GSL_CONST_MKSA_STD_ATMOSPHERE The pressure of 1 standard atmosphere. .. macro:: GSL_CONST_MKSA_TORR The pressure of 1 torr. .. macro:: GSL_CONST_MKSA_METER_OF_MERCURY The pressure of 1 meter of mercury. .. macro:: GSL_CONST_MKSA_INCH_OF_MERCURY The pressure of 1 inch of mercury. .. macro:: GSL_CONST_MKSA_INCH_OF_WATER The pressure of 1 inch of water. .. macro:: GSL_CONST_MKSA_PSI The pressure of 1 pound per square inch. .. index:: viscosity, units of Viscosity ========= .. macro:: GSL_CONST_MKSA_POISE The dynamic viscosity of 1 poise. .. macro:: GSL_CONST_MKSA_STOKES The kinematic viscosity of 1 stokes. .. index:: single: light, units of single: illumination, units of Light and Illumination ====================== .. macro:: GSL_CONST_MKSA_STILB The luminance of 1 stilb. .. macro:: GSL_CONST_MKSA_LUMEN The luminous flux of 1 lumen. .. macro:: GSL_CONST_MKSA_LUX The illuminance of 1 lux. .. macro:: GSL_CONST_MKSA_PHOT The illuminance of 1 phot. .. macro:: GSL_CONST_MKSA_FOOTCANDLE The illuminance of 1 footcandle. .. macro:: GSL_CONST_MKSA_LAMBERT The luminance of 1 lambert. .. macro:: GSL_CONST_MKSA_FOOTLAMBERT The luminance of 1 footlambert. .. index:: radioactivity, units of Radioactivity ============= .. macro:: GSL_CONST_MKSA_CURIE The activity of 1 curie. .. macro:: GSL_CONST_MKSA_ROENTGEN The exposure of 1 roentgen. .. macro:: GSL_CONST_MKSA_RAD The absorbed dose of 1 rad. .. index:: force and energy, units of Force and Energy ================ .. macro:: GSL_CONST_MKSA_NEWTON The SI unit of force, 1 Newton. .. macro:: GSL_CONST_MKSA_DYNE The force of 1 Dyne = :math:`10^{-5}` Newton. .. macro:: GSL_CONST_MKSA_JOULE The SI unit of energy, 1 Joule. .. macro:: GSL_CONST_MKSA_ERG The energy 1 erg = :math:`10^{-7}` Joule. .. index:: single: prefixes single: constants, prefixes Prefixes ======== These constants are dimensionless scaling factors. .. macro:: GSL_CONST_NUM_YOTTA :math:`10^{24}` .. macro:: GSL_CONST_NUM_ZETTA :math:`10^{21}` .. macro:: GSL_CONST_NUM_EXA :math:`10^{18}` .. macro:: GSL_CONST_NUM_PETA :math:`10^{15}` .. macro:: GSL_CONST_NUM_TERA :math:`10^{12}` .. macro:: GSL_CONST_NUM_GIGA :math:`10^9` .. macro:: GSL_CONST_NUM_MEGA :math:`10^6` .. macro:: GSL_CONST_NUM_KILO :math:`10^3` .. macro:: GSL_CONST_NUM_MILLI :math:`10^{-3}` .. macro:: GSL_CONST_NUM_MICRO :math:`10^{-6}` .. macro:: GSL_CONST_NUM_NANO :math:`10^{-9}` .. macro:: GSL_CONST_NUM_PICO :math:`10^{-12}` .. macro:: GSL_CONST_NUM_FEMTO :math:`10^{-15}` .. macro:: GSL_CONST_NUM_ATTO :math:`10^{-18}` .. macro:: GSL_CONST_NUM_ZEPTO :math:`10^{-21}` .. macro:: GSL_CONST_NUM_YOCTO :math:`10^{-24}` 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. .. include:: examples/const.c :code: Here is the output from the program, .. include:: examples/const.txt :code: References and Further Reading ============================== The authoritative sources for physical constants are the 2006 CODATA recommended values, published in the article below. Further information on the values of physical constants is also available from the NIST website. * P.J. Mohr, B.N. Taylor, D.B. Newell, "CODATA Recommended Values of the Fundamental Physical Constants: 2006", Reviews of Modern Physics, 80(2), pp. 633--730 (2008). * http://www.physics.nist.gov/cuu/Constants/index.html * http://physics.nist.gov/Pubs/SP811/appenB9.html