@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 MKS system (meters, kilograms, seconds) and the CGS system
(centimeters, grams, seconds), which is commonly used in Astronomy.

The definitions of constants in the MKS system are available in the file
@file{gsl_const_mks.h}.  The constants in the CGS system are defined in
@file{gsl_const_cgs.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 ::             
* Nautical Units::              
* Printers Units::              
* Volume::                      
* 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_MKS_SPEED_OF_LIGHT
The speed of light in vacuum, @math{c}.

@item GSL_CONST_MKS_VACUUM_PERMEABILITY
The permeability of free space, @math{\mu_0}

@item GSL_CONST_MKS_VACUUM_PERMITTIVITY
The permittivity of free space, @math{\epsilon_0}.

@item GSL_CONST_NUM_AVOGADRO
Avogadro's number, @math{N_a}.

@item GSL_CONST_MKS_FARADAY
The molar charge of 1 Faraday.

@item GSL_CONST_MKS_BOLTZMANN
The Boltzmann constant, @math{k}.

@item GSL_CONST_MKS_MOLAR_GAS
The molar gas constant, @math{R_0}.

@item GSL_CONST_MKS_STANDARD_GAS_VOLUME
The standard gas volume, @math{V_0}.

@item GSL_CONST_MKS_GAUSS
The magnetic field of 1 Gauss.

@item GSL_CONST_MKS_MICRON
The length of 1 micron.

@item GSL_CONST_MKS_HECTARE
The area of 1 hectare.

@item GSL_CONST_MKS_MILES_PER_HOUR
The speed of 1 mile per hour.

@item GSL_CONST_MKS_KILOMETERS_PER_HOUR
The speed of 1 kilometer per hour.
@end table

@node Astronomy and Astrophysics
@section Astronomy and Astrophysics
@cindex astronomical constants
@table @code
@item GSL_CONST_MKS_ASTRONOMICAL_UNIT
The length of 1 astronomical unit (mean earth-sun distance), @math{au}.

@item GSL_CONST_MKS_GRAVITATIONAL_CONSTANT
The gravitational constant, @math{G}.

@item GSL_CONST_MKS_LIGHT_YEAR
The distance of 1 light-year, @math{ly}.

@item GSL_CONST_MKS_PARSEC
The distance of 1 parsec, @math{pc}.

@item GSL_CONST_MKS_GRAV_ACCEL
The standard gravitational acceleration on Earth, @math{g}.

@item GSL_CONST_MKS_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_MKS_ELECTRON_CHARGE
The charge of the electron, @math{e}.

@item GSL_CONST_MKS_ELECTRON_VOLT
The energy of 1 electron volt, @math{eV}.

@item GSL_CONST_MKS_UNIFIED_ATOMIC_MASS
The unified atomic mass, @math{amu}.

@item GSL_CONST_MKS_MASS_ELECTRON
The mass of the electron, @math{m_e}.

@item GSL_CONST_MKS_MASS_MUON
The mass of the muon, @math{m_\mu}.

@item GSL_CONST_MKS_MASS_PROTON
The mass of the proton, @math{m_p}.

@item GSL_CONST_MKS_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_MKS_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_MKS_BOHR_RADIUS
The Bohr radius, @math{a_0}.

@item GSL_CONST_MKS_ANGSTROM
The length of 1 angstrom.

@item GSL_CONST_MKS_BARN
The area of 1 barn.

@item GSL_CONST_MKS_BOHR_MAGNETON
The Bohr Magneton, @math{\mu_B}.

@item GSL_CONST_MKS_NUCLEAR_MAGNETON
The Nuclear Magneton, @math{\mu_N}.

@item GSL_CONST_MKS_ELECTRON_MAGNETIC_MOMENT
The absolute value of the magnetic moment of the electron, @math{\mu_e}.
The physical magnetic moment of the election is negative.

@item GSL_CONST_MKS_PROTON_MAGNETIC_MOMENT
The magnetic moment of the proton, @math{\mu_p}.
@end table


@node Measurement of Time
@section Measurement of Time
@cindex time units
@table @code
@item GSL_CONST_MKS_MINUTE
The number of seconds in 1 minute.

@item GSL_CONST_MKS_HOUR
The number of seconds in 1 hour.

@item GSL_CONST_MKS_DAY
The number of seconds in 1 day.

@item GSL_CONST_MKS_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_MKS_INCH
The length of 1 inch.

@item GSL_CONST_MKS_FOOT
The length of 1 foot.

@item GSL_CONST_MKS_YARD
The length of 1 yard.

@item GSL_CONST_MKS_MILE
The length of 1 mile.

@item GSL_CONST_MKS_MIL
The length of 1 mil (1/1000th of an inch).
@end table


@node Nautical Units
@section Nautical Units
@cindex nautical units

@table @code
@item GSL_CONST_MKS_NAUTICAL_MILE
The length of 1 nautical mile.

@item GSL_CONST_MKS_FATHOM
The length of 1 fathom.

@item GSL_CONST_MKS_KNOT
The speed of 1 knot.
@end table


@node Printers Units
@section Printers Units
@cindex printers units

@table @code
@item GSL_CONST_MKS_POINT
The length of 1 printer's point (1/72 inch).

@item GSL_CONST_MKS_TEXPOINT
The length of 1 TeX point (1/72.27 inch).
@end table


@node Volume
@section Volume
@cindex volume units

@table @code
@item GSL_CONST_MKS_ACRE
The area of 1 acre.

@item GSL_CONST_MKS_LITER
The volume of 1 liter.

@item GSL_CONST_MKS_US_GALLON
The volume of 1 US gallon.

@item GSL_CONST_MKS_CANADIAN_GALLON
The volume of 1 Canadian gallon.

@item GSL_CONST_MKS_UK_GALLON
The volume of 1 UK gallon.

@item GSL_CONST_MKS_QUART
The volume of 1 quart.

@item GSL_CONST_MKS_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_MKS_CUP
@comment The volume of 1 cup.

@comment @item GSL_CONST_MKS_FLUID_OUNCE
@comment The volume of 1 fluid ounce.

@comment @item GSL_CONST_MKS_TABLESPOON
@comment The volume of 1 tablespoon.

@comment @item GSL_CONST_MKS_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_MKS_POUND_MASS
The mass of 1 pound.

@item GSL_CONST_MKS_OUNCE_MASS
The mass of 1 ounce.

@item GSL_CONST_MKS_TON
The mass of 1 ton.

@item GSL_CONST_MKS_METRIC_TON
The mass of 1 metric ton (1000 kg).

@item GSL_CONST_MKS_UK_TON
The mass of 1 UK ton.

@item GSL_CONST_MKS_TROY_OUNCE
The mass of 1 troy ounce.

@item GSL_CONST_MKS_CARAT
The mass of 1 carat.

@item GSL_CONST_MKS_GRAM_FORCE
The force of 1 gram weight.

@item GSL_CONST_MKS_POUND_FORCE
The force of 1 pound weight.

@item GSL_CONST_MKS_KILOPOUND_FORCE
The force of 1 kilopound weight.

@item GSL_CONST_MKS_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_MKS_CALORIE
The energy of 1 calorie.

@item GSL_CONST_MKS_BTU
The energy of 1 British Thermal Unit, @math{btu}.

@item GSL_CONST_MKS_THERM
The energy of 1 Therm.

@item GSL_CONST_MKS_HORSEPOWER
The power of 1 horsepower.
@end table


@node Pressure
@section Pressure
@cindex pressure, units of
@table @code
@item GSL_CONST_MKS_BAR
The pressure of 1 bar.

@item GSL_CONST_MKS_STD_ATMOSPHERE
The pressure of 1 standard atmosphere.

@item GSL_CONST_MKS_TORR
The pressure of 1 torr.

@item GSL_CONST_MKS_METER_OF_MERCURY
The pressure of 1 meter of mercury.

@item GSL_CONST_MKS_INCH_OF_MERCURY
The pressure of 1 inch of mercury.

@item GSL_CONST_MKS_INCH_OF_WATER
The pressure of 1 inch of water.

@item GSL_CONST_MKS_PSI
The pressure of 1 pound per square inch.
@end table

@node Viscosity
@section Viscosity
@cindex viscosity, units of
@table @code
@item GSL_CONST_MKS_POISE
The dynamic viscosity of 1 poise.

@item GSL_CONST_MKS_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_MKS_STILB
The luminance of 1 stilb.

@item GSL_CONST_MKS_LUMEN
The luminous flux of 1 lumen.

@item GSL_CONST_MKS_LUX
The illuminance of 1 lux.

@item GSL_CONST_MKS_PHOT
The illuminance of 1 phot.

@item GSL_CONST_MKS_FOOTCANDLE
The illuminance of 1 footcandle.

@item GSL_CONST_MKS_LAMBERT
The luminance of 1 lambert.

@item GSL_CONST_MKS_FOOTLAMBERT
The luminance of 1 footlambert.
@end table


@node Radioactivity
@section Radioactivity
@cindex radioactivity, units of
@table @code
@item GSL_CONST_MKS_CURIE
The activity of 1 curie.

@item GSL_CONST_MKS_ROENTGEN
The exposure of 1 roentgen.

@item GSL_CONST_MKS_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_MKS_NEWTON
The SI unit of force, 1 Newton.

@item GSL_CONST_MKS_DYNE
The force of 1 Dyne = @c{$10^{-5}$}
@math{10^-5} Newton.

@item GSL_CONST_MKS_JOULE
The SI unit of energy, 1 Joule.

@item GSL_CONST_MKS_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 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
MKS 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
#include <stdio.h>
#include <gsl/gsl_const_mks.h>

int
main (void)
@{
  double c  = GSL_CONST_MKS_SPEED_OF_LIGHT;
  double au = GSL_CONST_MKS_ASTRONOMICAL_UNIT;
  double minutes = GSL_CONST_MKS_MINUTE;

  /* distance stored in meters */
  double r_earth = 1.00 * au;  
  double r_mars  = 1.52 * au;

  double t_min, t_max;

  t_min = (r_mars - r_earth) / c;
  t_max = (r_mars + r_earth) / c;

  printf("light travel time from Earth to Mars:\n");
  printf("minimum = %.1f minutes\n", t_min / minutes);
  printf("maximum = %.1f minutes\n", t_max / minutes);

  return 0;
@}
@end example
@noindent
Here is the output from the program,

@example
light travel time from Earth to Mars:
minimum = 4.3 minutes
maximum = 21.0 minutes
@end example

@node Physical Constant References and Further Reading
@section References and Further Reading
@noindent
Further information on the values of physical constants is available
from the NIST website,

@itemize @asis
@item
@url{http://www.physics.nist.gov/cuu/Constants/index.html}
@end itemize
