This chapter describes macros for the values of physical constants, such as the speed of light, c, and gravitational constant, 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 gsl_const_mksa.h.  The constants in the CGSM system are defined in gsl_const_cgsm.h.  Dimensionless constants, such as the fine structure constant, which are pure numbers are defined in 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.

Fundamental Constants
=====================

GSL_CONST_MKSA_SPEED_OF_LIGHT
     The speed of light in vacuum, c.

GSL_CONST_MKSA_VACUUM_PERMEABILITY
     The permeability of free space, \mu_0. This constant is defined in the MKSA system only.

GSL_CONST_MKSA_VACUUM_PERMITTIVITY
     The permittivity of free space, \epsilon_0.  This constant is defined in the MKSA system only.

GSL_CONST_MKSA_PLANCKS_CONSTANT_H
     Planck's constant, h.

GSL_CONST_MKSA_PLANCKS_CONSTANT_HBAR
     Planck's constant divided by 2\pi, \hbar.

GSL_CONST_NUM_AVOGADRO
     Avogadro's number, N_a.

GSL_CONST_MKSA_FARADAY
     The molar charge of 1 Faraday.

GSL_CONST_MKSA_BOLTZMANN
     The Boltzmann constant, k.

GSL_CONST_MKSA_MOLAR_GAS
     The molar gas constant, R_0.

GSL_CONST_MKSA_STANDARD_GAS_VOLUME
     The standard gas volume, V_0.

GSL_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT
     The Stefan-Boltzmann radiation constant, \sigma.

GSL_CONST_MKSA_GAUSS
     The magnetic field of 1 Gauss.

Astronomy and Astrophysics
==========================

GSL_CONST_MKSA_ASTRONOMICAL_UNIT
     The length of 1 astronomical unit (mean earth-sun distance), au.

GSL_CONST_MKSA_GRAVITATIONAL_CONSTANT
     The gravitational constant, G.

GSL_CONST_MKSA_LIGHT_YEAR
     The distance of 1 light-year, ly.

GSL_CONST_MKSA_PARSEC
     The distance of 1 parsec, pc.

GSL_CONST_MKSA_GRAV_ACCEL
     The standard gravitational acceleration on Earth, g.

GSL_CONST_MKSA_SOLAR_MASS
     The mass of the Sun.

Atomic and Nuclear Physics
==========================

GSL_CONST_MKSA_ELECTRON_CHARGE
     The charge of the electron, e.

GSL_CONST_MKSA_ELECTRON_VOLT
     The energy of 1 electron volt, eV.

GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS
     The unified atomic mass, amu.

GSL_CONST_MKSA_MASS_ELECTRON
     The mass of the electron, m_e.

GSL_CONST_MKSA_MASS_MUON
     The mass of the muon, m_\mu.

GSL_CONST_MKSA_MASS_PROTON
     The mass of the proton, m_p.

GSL_CONST_MKSA_MASS_NEUTRON
     The mass of the neutron, m_n.

GSL_CONST_NUM_FINE_STRUCTURE
     The electromagnetic fine structure constant \alpha.

GSL_CONST_MKSA_RYDBERG
     The Rydberg constant, Ry, in units of energy.  This is related to the Rydberg inverse wavelength R by Ry = h c R.

GSL_CONST_MKSA_BOHR_RADIUS
     The Bohr radius, a_0.

GSL_CONST_MKSA_ANGSTROM
     The length of 1 angstrom.

GSL_CONST_MKSA_BARN
     The area of 1 barn.

GSL_CONST_MKSA_BOHR_MAGNETON
     The Bohr Magneton, \mu_B.

GSL_CONST_MKSA_NUCLEAR_MAGNETON
     The Nuclear Magneton, \mu_N.

GSL_CONST_MKSA_ELECTRON_MAGNETIC_MOMENT
     The absolute value of the magnetic moment of the electron, \mu_e. The physical magnetic moment of the electron is negative.

GSL_CONST_MKSA_PROTON_MAGNETIC_MOMENT
     The magnetic moment of the proton, \mu_p.

GSL_CONST_MKSA_THOMSON_CROSS_SECTION
     The Thomson cross section, \sigma_T.

GSL_CONST_MKSA_DEBYE
     The electric dipole moment of 1 Debye, D.

Measurement of Time
===================

GSL_CONST_MKSA_MINUTE
     The number of seconds in 1 minute.

GSL_CONST_MKSA_HOUR
     The number of seconds in 1 hour.

GSL_CONST_MKSA_DAY
     The number of seconds in 1 day.

GSL_CONST_MKSA_WEEK
     The number of seconds in 1 week.

Imperial Units
==============

GSL_CONST_MKSA_INCH
     The length of 1 inch.

GSL_CONST_MKSA_FOOT
     The length of 1 foot.

GSL_CONST_MKSA_YARD
     The length of 1 yard.

GSL_CONST_MKSA_MILE
     The length of 1 mile.

GSL_CONST_MKSA_MIL
     The length of 1 mil (1/1000th of an inch).

Speed and Nautical Units
========================

GSL_CONST_MKSA_KILOMETERS_PER_HOUR
     The speed of 1 kilometer per hour.

GSL_CONST_MKSA_MILES_PER_HOUR
     The speed of 1 mile per hour.

GSL_CONST_MKSA_NAUTICAL_MILE
     The length of 1 nautical mile.

GSL_CONST_MKSA_FATHOM
     The length of 1 fathom.

GSL_CONST_MKSA_KNOT
     The speed of 1 knot.

Printers Units
==============

GSL_CONST_MKSA_POINT
     The length of 1 printer's point (1/72 inch).

GSL_CONST_MKSA_TEXPOINT
     The length of 1 TeX point (1/72.27 inch).

Volume, Area and Length
=======================

GSL_CONST_MKSA_MICRON
     The length of 1 micron.

GSL_CONST_MKSA_HECTARE
     The area of 1 hectare.

GSL_CONST_MKSA_ACRE
     The area of 1 acre.

GSL_CONST_MKSA_LITER
     The volume of 1 liter.

GSL_CONST_MKSA_US_GALLON
     The volume of 1 US gallon.

GSL_CONST_MKSA_CANADIAN_GALLON
     The volume of 1 Canadian gallon.

GSL_CONST_MKSA_UK_GALLON
     The volume of 1 UK gallon.

GSL_CONST_MKSA_QUART
     The volume of 1 quart.

GSL_CONST_MKSA_PINT
     The volume of 1 pint.

Mass and Weight
===============

GSL_CONST_MKSA_POUND_MASS
     The mass of 1 pound.

GSL_CONST_MKSA_OUNCE_MASS
     The mass of 1 ounce.

GSL_CONST_MKSA_TON
     The mass of 1 ton.

GSL_CONST_MKSA_METRIC_TON
     The mass of 1 metric ton (1000 kg).

GSL_CONST_MKSA_UK_TON
     The mass of 1 UK ton.

GSL_CONST_MKSA_TROY_OUNCE
     The mass of 1 troy ounce.

GSL_CONST_MKSA_CARAT
     The mass of 1 carat.

GSL_CONST_MKSA_GRAM_FORCE
     The force of 1 gram weight.

GSL_CONST_MKSA_POUND_FORCE
     The force of 1 pound weight.

GSL_CONST_MKSA_KILOPOUND_FORCE
     The force of 1 kilopound weight.

GSL_CONST_MKSA_POUNDAL
     The force of 1 poundal.

Thermal Energy and Power
========================

GSL_CONST_MKSA_CALORIE
     The energy of 1 calorie.

GSL_CONST_MKSA_BTU
     The energy of 1 British Thermal Unit, btu.

GSL_CONST_MKSA_THERM
     The energy of 1 Therm.

GSL_CONST_MKSA_HORSEPOWER
     The power of 1 horsepower.

Pressure
========

GSL_CONST_MKSA_BAR
     The pressure of 1 bar.

GSL_CONST_MKSA_STD_ATMOSPHERE
     The pressure of 1 standard atmosphere.

GSL_CONST_MKSA_TORR
     The pressure of 1 torr.

GSL_CONST_MKSA_METER_OF_MERCURY
     The pressure of 1 meter of mercury.

GSL_CONST_MKSA_INCH_OF_MERCURY
     The pressure of 1 inch of mercury.

GSL_CONST_MKSA_INCH_OF_WATER
     The pressure of 1 inch of water.

GSL_CONST_MKSA_PSI
     The pressure of 1 pound per square inch.

Viscosity
=========

GSL_CONST_MKSA_POISE
     The dynamic viscosity of 1 poise.

GSL_CONST_MKSA_STOKES
     The kinematic viscosity of 1 stokes.

Light and Illumination
======================

GSL_CONST_MKSA_STILB
     The luminance of 1 stilb.

GSL_CONST_MKSA_LUMEN
     The luminous flux of 1 lumen.

GSL_CONST_MKSA_LUX
     The illuminance of 1 lux.

GSL_CONST_MKSA_PHOT
     The illuminance of 1 phot.

GSL_CONST_MKSA_FOOTCANDLE
     The illuminance of 1 footcandle.

GSL_CONST_MKSA_LAMBERT
     The luminance of 1 lambert.

GSL_CONST_MKSA_FOOTLAMBERT
     The luminance of 1 footlambert.

Radioactivity
=============

GSL_CONST_MKSA_CURIE
     The activity of 1 curie.

GSL_CONST_MKSA_ROENTGEN
     The exposure of 1 roentgen.

GSL_CONST_MKSA_RAD
     The absorbed dose of 1 rad.

Force and Energy
================

GSL_CONST_MKSA_NEWTON
     The SI unit of force, 1 Newton.

GSL_CONST_MKSA_DYNE
     The force of 1 Dyne = $10^-5$ 10^-5 Newton.

GSL_CONST_MKSA_JOULE
     The SI unit of energy, 1 Joule.

GSL_CONST_MKSA_ERG
     The energy 1 erg = $10^-7$ 10^-7 Joule.

Prefixes
========

These constants are dimensionless scaling factors.

GSL_CONST_NUM_YOTTA
     $10^24$ 10^24

GSL_CONST_NUM_ZETTA
     $10^21$ 10^21

GSL_CONST_NUM_EXA
     $10^18$ 10^18

GSL_CONST_NUM_PETA
     $10^15$ 10^15

GSL_CONST_NUM_TERA
     $10^12$ 10^12

GSL_CONST_NUM_GIGA
     10^9

GSL_CONST_NUM_MEGA
     10^6

GSL_CONST_NUM_KILO
     10^3

GSL_CONST_NUM_MILLI
     $10^-3$ 10^-3

GSL_CONST_NUM_MICRO
     $10^-6$ 10^-6

GSL_CONST_NUM_NANO
     $10^-9$ 10^-9

GSL_CONST_NUM_PICO
     $10^-12$ 10^-12

GSL_CONST_NUM_FEMTO
     $10^-15$ 10^-15

GSL_CONST_NUM_ATTO
     $10^-18$ 10^-18

GSL_CONST_NUM_ZEPTO
     $10^-21$ 10^-21

GSL_CONST_NUM_YOCTO
     $10^-24$ 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.

          [file const.c not included]

Here is the output from the program,

          [file const.out not included]

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.

  Journal of Physical and Chemical Reference Data, 28(6), 1713-1852, 1999

  Reviews of Modern Physics, 72(2), 351-495, 2000

  http://www.physics.nist.gov/cuu/Constants/index.html

  http://physics.nist.gov/Pubs/SP811/appenB9.html