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39. Physical Constants

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’.

39.1 Fundamental Constants  
39.2 Astronomy and Astrophysics  
39.3 Atomic and Nuclear Physics  
39.4 Measurement of Time  
39.5 Imperial Units  
39.6 Speed and Nautical Units  
39.7 Printers Units  
39.8 Volume, Area and Length  
39.9 Mass and Weight  
39.10 Thermal Energy and Power  
39.11 Pressure  
39.12 Viscosity  
39.13 Light and Illumination  
39.14 Radioactivity  
39.15 Force and Energy  
39.16 Prefixes  
39.17 Examples  
39.18 References and Further Reading  

The full list of constants is described briefly below. Consult the header files themselves for the values of the constants used in the library.

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39.1 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.

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39.2 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.

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39.3 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, $D$.

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39.4 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.

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39.5 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).

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39.6 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.

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39.7 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).

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39.8 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.

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39.9 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.

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39.10 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.

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39.11 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.

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39.12 Viscosity

GSL_CONST_MKSA_POISE

The dynamic viscosity of 1 poise.

GSL_CONST_MKSA_STOKES

The kinematic viscosity of 1 stokes.

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39.13 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.

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39.14 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.

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39.15 Force and Energy

GSL_CONST_MKSA_NEWTON

The SI unit of force, 1 Newton.

GSL_CONST_MKSA_DYNE

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

GSL_CONST_MKSA_JOULE

The SI unit of energy, 1 Joule.

GSL_CONST_MKSA_ERG

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

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39.16 Prefixes

These constants are dimensionless scaling factors.

GSL_CONST_NUM_YOTTA

$10^24$

GSL_CONST_NUM_ZETTA

$10^21$

GSL_CONST_NUM_EXA

$10^18$

GSL_CONST_NUM_PETA

$10^15$

GSL_CONST_NUM_TERA

$10^12$

GSL_CONST_NUM_GIGA

$10^9$

GSL_CONST_NUM_MEGA

$10^6$

GSL_CONST_NUM_KILO

$10^3$

GSL_CONST_NUM_MILLI

$10^-3$

GSL_CONST_NUM_MICRO

$10^-6$

GSL_CONST_NUM_NANO

$10^-9$

GSL_CONST_NUM_PICO

$10^-12$

GSL_CONST_NUM_FEMTO

$10^-15$

GSL_CONST_NUM_ATTO

$10^-18$

GSL_CONST_NUM_ZEPTO

$10^-21$

GSL_CONST_NUM_YOCTO

$10^-24$

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39.17 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 <stdio.h>
#include <gsl/gsl_const_mksa.h>

int
main (void)
{
  double c  = GSL_CONST_MKSA_SPEED_OF_LIGHT;
  double au = GSL_CONST_MKSA_ASTRONOMICAL_UNIT;
  double minutes = GSL_CONST_MKSA_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;
}

Here is the output from the program,

 
light travel time from Earth to Mars:
minimum = 4.3 minutes
maximum = 21.0 minutes
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39.18 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.

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