Physical Constants

# Title: Physical Constants

The GSL physical constants are defined as Ruby constants under the modules

- `GSL::CONST::MKSA` (MKSA unit)
- `GSL::CONST:CGSM` (CGSM unit)
- `GSL::CONST:NUM` (Dimension-less constants)

For example, the GSL C constant `GSL_CONST_MKSA_SPEED_OF_LIGHT` is represented by a Ruby constant,

    GSL_CONST_MKSA_SPEED_OF_LIGHT  ---> GSL::CONST::MKSA::SPEED_OF_LIGHT

The following lists a part of the constants. Most of the constants are defined both in the modules `GSL::CONST::MKSA` and `GSL::CONST::CGSM`. See also the GSL reference

## 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 (not defined in GSL::CONST::CGSM).
`GSL::CONST::MKSA::VACUUM_PERMITTIVITY`
  The permittivity of free space, \epsilon_0 (not defined in GSL::CONST::CGSM).
`GSL::CONST::NUM::AVOGADRO`
  Avogadro's number
`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::GAUSS`
  The magnetic field of 1 Gauss.

## 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.

## 3 Atomic and Nuclear Physics

`GSL::CONST::MKSA::ELECTRON_CHARGE`
  The charge of the electron, e.
`GSL::CONST::CGSM::ELECTRON_CHARGE_ESU`
  The charge of the electron, e, in esu unit (not defined in GSL::CONST::MKSA).
`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 proton, 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.

## 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.

## 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).

## 6 Nautical Units

`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.

## 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).

## 8 Volume

`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.

## 9 Mass and Weigth

`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.

## 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.

## 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.

## 12 Viscosity

`GSL::CONST::MKSA::POISE`
  The dynamic viscosity of 1 poise.
`GSL::CONST::MKSA::STOKES`
  The kinematic viscosity of 1 stokes.

## 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.

## 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.

## 15 Force and Energy

`GSL::CONST::MKSA::NEWTON`
  The SI unit of force, 1 Newton.
`GSL::CONST::MKSA::DYNE`
  he 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.

## 16 Prefixes

`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

### 16.1 Example

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.

    require("gsl")
    include GSL::CONST::MKSA

    puts("In MKSA unit")

    c  = SPEED_OF_LIGHT;
    au = ASTRONOMICAL_UNIT;
    minutes = MINUTE;

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

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

    printf("light travel time from Earth to Mars:\n");
    printf("c = %e [m/s]\n", c)
    printf("AU = %e [m]\n", au)
    printf("minutes = %e [s]\n", minutes)
    printf("minimum = %.1f minutes\n", t_min / minutes);
    printf("maximum = %.1f minutes\n\n", t_max / minutes);

back