On this page:
13.1 Fundamental Constants
cgs-speed-of-light
cgsm-speed-of-light
mksa-speed-of-light
mks-speed-of-light
mksa-vacuum-permeability
mks-vacuum-permeability
mksa-vacuum-permittivity
mks-vacuum-permittivity
cgs-plancks-constant-h
cgsm-plancks-constant-h
mksa-plancks-constant-h
mks-plancks-constant-h
cgs-plancks-constant-hbar
cgsm-plancks-constant-hbar
mksa-plancks-constant-hbar
mks-plancks-constant-hbar
num-avogadro
cgsm-faraday
mksa-faraday
mks-faraday
cgs-boltzmann
cgsm-boltzmann
mksa-boltzmann
mks-boltzmann
cgs-molar-gas
cgsm-molar-gas
mksa-molar-gas
mks-molar-gas
cgs-standard-gas-volume
cgsm-standard-gas-volume
mksa-standard-gas-volume
mks-standard-gas-volume
cgs-stefan-boltzmann-constant
cgsm-stefan-boltzmann-constant
mksa-stefan-boltzmann-constant
mks-stefan-boltzmann-constant
mksa-gauss
mks-gauss
13.2 Astronomy and Astrophysics
cgs-astronomical-unit
cgsm-astronomical-unit
mksa-astronomical-unit
mks-astronomical-unit
cgs-gravitational-constant
cgsm-gravitational-constant
mksa-gravitational-constant
mks-gravitational-constant
cgs-light-year
cgsm-light-year
mksa-light-year
mks-light-year
cgs-parsec
cgsm-parsec
mksa-parsec
mks-parsec
cgs-grav-accel
cgsm-grav-accel
mksa-grav-accel
mks-grav-accel
cgs-solar-mass
cgsm-solar-mass
mksa-solar-mass
mks-solar-mass
13.3 Atomic and Nuclear Physics
cgsm-electron-charge
mksa-electron-charge
mks-electron-charge
cgs-electron-volt
cgsm-electron-volt
mksa-electron-volt
mks-electron-volt
cgs-unified-atomic-mass
cgsm-unified-atomic-mass
mksa-unified-atomic-mass
mks-unified-atomic-mass
cgs-mass-electron
cgsm-mass-electron
mksa-mass-electron
mks-mass-electron
cgs-mass-muon
cgsm-mass-muon
mksa-mass-muon
mks-mass-muon
cgs-mass-proton
cgsm-mass-proton
mksa-mass-proton
mks-mass-proton
cgs-mass-neutron
cgsm-mass-neutron
mksa-mass-neutron
mks-mass-neutron
num-fine-structure
cgs-rydberg
cgsm-rydberg
mksa-rydberg
mks-rydberg
cgs-bohr-radius
cgsm-bohr-radius
mksa-bohr-radius
mks-bohr-radius
cgs-angstrom
cgsm-angstrom
mksa-angstrom
mks-angstrom
cgs-barn
cgsm-barn
mksa-barn
mks-barn
cgsm-bohr-magneton
mksa-bohr-magneton
mks-bohr-magneton
cgsm-nuclear-magneton
mksa-nuclear-magneton
mks-nuclear-magneton
cgsm-electron-magnetic-moment
mksa-electron-magnetic-moment
mks-electron-magnetic-moment
cgsm-proton-magnetic-moment
mksa-proton-magnetic-moment
mks-proton-magnetic-moment
cgs-thomson-cross-section
cgsm-thomson-cross-section
mksa-thomson-cross-section
mks-thomson-cross-section
mksa-debye
mks-debye
13.4 Measurements of Time
cgs-minute
cgsm-minute
mksa-minute
mks-minute
cgs-hour
cgsm-hour
mksa-hour
mks-hour
cgs-day
cgsm-day
mksa-day
mks-day
cgs-week
cgsm-week
mksa-week
mks-week
13.5 Imperial Units
cgs-inch
cgsm-inch
mksa-inch
mks-inch
cgs-foot
cgsm-foot
mksa-foot
mks-foot
cgs-yard
cgsm-yard
mksa-yard
mks-yard
cgs-mile
cgsm-mile
mksa-mile
mks-mile
cgs-mil
cgsm-mil
mksa-mil
mks-mil
13.6 Speed and Nautical Units
cgs-kilometers-per-hour
cgsm-kilometers-per-hour
mksa-kilometers-per-hour
mks-kilometers-per-hour
cgs-miles-per-hour
cgsm-miles-per-hour
mksa-miles-per-hour
mks-miles-per-hour
cgs-nautical-mile
cgsm-nautical-mile
mksa-nautical-mile
mks-nautical-mile
cgs-fathom
cgsm-fathom
mksa-fathom
mks-fathom
cgs-knot
cgsm-knot
mksa-knot
mks-knot
13.7 Printers Units
cgs-point
cgsm-point
mksa-point
mks-point
cgs-texpoint
cgsm-texpoint
mksa-texpoint
mks-texpoint
13.8 Volume, Area and Length
cgs-micron
cgsm-micron
mksa-micron
mks-micron
cgs-hectare
cgsm-hectare
mksa-hectare
mks-hectare
cgs-acre
cgsm-acre
mksa-acre
mks-acre
cgs-liter
cgsm-liter
mksa-liter
mks-liter
cgs-us-gallon
cgsm-us-gallon
mksa-us-gallon
mks-us-gallon
cgs-canadian-gallon
cgsm-canadian-gallon
mksa-canadian-gallon
mks-canadian-gallon
cgs-uk-gallon
cgsm-uk-gallon
mksa-uk-gallon
mks-uk-gallon
cgs-quart
cgsm-quart
mksa-quart
mks-quart
cgs-pint
cgsm-pint
mksa-pint
mks-pint
13.9 Mass and Weight
cgs-pound-mass
cgsm-pound-mass
mksa-pound-mass
mks-pound-mass
cgs-ounce-mass
cgsm-ounce-mass
mksa-ounce-mass
mks-ounce-mass
cgs-ton
cgsm-ton
mksa-tons
mks-ton
cgs-metric-ton
cgsm-metric-ton
mksa-metric-ton
mks-metric-ton
cgs-uk-ton
cgsm-uk-ton
mksa-uk-ton
mks-uk-ton
cgs-troy-ounce
cgsm-troy-ounce
mksa-troy-ounce
mks-troy-ounce
cgs-carat
cgsm-carat
mksa-carat
mks-carat
cgs-gram-force
cgsm-gram-force
mksa-gram-force
mks-gram-force
cgs-pound-force
cgsm-pound-force
mksa-pound-force
mks-pound-force
cgs-kilopound-force
cgsm-kilopound-force
mksa-kilopound-force
mks-kilopound-force
cgs-poundal
cgsm-poundal
mksa-poundal
mks-poundal
13.10 Thermal Energy and Power
cgs-calorie
cgsm-calorie
mksa-calorie
mks-calorie
cgs-btu
cgsm-btu
mksa-btu
mks-btu
cgs-therm
cgsm-therm
mksa-therm
mks-therm
cgs-horsepower
cgsm-horsepower
mksa-horsepower
mks-horsepower
13.11 Pressure
cgs-bar
cgsm-bar
mksa-bar
mks-bar
cgs-std-atmosphere
cgsm-std-atmosphere
mksa-std-atmosphere
mks-std-atmosphere
cgs-torr
cgsm-torr
mksa-torr
mks-torr
cgs-meter-of-mercury
cgsm-meter-of-mercury
mksa-meter-of-mercury
mks-meter-of-mercury
cgs-inch-of-mercury
cgsm-inch-of-mercury
mksa-inch-of-mercury
mks-inch-of-mercury
cgs-inch-of-water
cgsm-inch-of-water
mksa-inch-of-water
mks-inch-of-water
cgs-psi
cgsm-psi
mksa-psi
mks-psi
13.12 Viscosity
cgs-poise
cgsm-poise
mksa-poise
mks-poise
cgs-stokes
cgsm-stokes
mksa-stokes
mks-stokes
13.13 Light and Illumination
cgs-stilb
cgsm-stilb
mksa-stilb
mks-stilb
cgs-lumen
cgsm-lumen
mksa-lumen
mks-lumen
cgs-lux
cgsm-lux
mksa-lux
mks-lux
cgs-phot
cgsm-phot
mksa-phot
mks-phot
cgs-footcandle
cgsm-footcandle
mksa-footcandle
mks-footcandle
cgs-lambert
cgsm-lambert
mksa-lambert
mks-lambert
cgs-footlambert
cgsm-footlambert
mksa-footlambert
mks-footlambert
13.14 Radioactivity
cgs-curie
cgsm-curie
mksa-curie
mks-curie
cgs-roentgen
cgsm-roentgen
mksa-roentgen
mks-roentgen
cgs-rad
cgsm-rad
mksa-rad
mks-rad
13.15 Force and Energy
cgs-newton
cgsm-newton
mksa-newton
mks-newton
cgs-dyne
cgsm-dyne
mksa-dyne
mks-dyne
cgs-joule
cgsm-joule
mksa-joule
mks-joule
cgs-erg
cgsm-erg
mksa-erg
mks-erg
13.16 Prefixes
num-yotta
num-zetta
num-exa
num-peta
num-tera
num-giga
num-mega
num-kilo
num-milli
num-micro
num-nano
num-pico
num-femto
num-atto
num-zepto
num-yacto
13.17 Physical Constants Example

13 Physical Constants

    13.1 Fundamental Constants

    13.2 Astronomy and Astrophysics

    13.3 Atomic and Nuclear Physics

    13.4 Measurements of Time

    13.5 Imperial Units

    13.6 Speed and Nautical Units

    13.7 Printers Units

    13.8 Volume, Area and Length

    13.9 Mass and Weight

    13.10 Thermal Energy and Power

    13.11 Pressure

    13.12 Viscosity

    13.13 Light and Illumination

    13.14 Radioactivity

    13.15 Force and Energy

    13.16 Prefixes

    13.17 Physical Constants Example

This chapter describes the physical constants, such as the speed of light, c, and gravitational constant, G, provided by the Science Collection. The values are available in different unit systems, including the standard MKSA system (meters, kilograms, secomds, amperes) and the CGSM system (centimeters, grams, seconds, gauss), which is commonly used in Astronomy.

The constants described in this chapter are defined in the constants sub-collection of the Science Collection. All of the modules on the constants sub-collection can be made available using the form:

 (require (planet williams/science/constants))

The individual modules in the constants sub-collection can also be made available using any of the following forms:

(require (planet williams/science/constants/cgs-constants))

(require (planet williams/science/constants/cgms-constants))

(require (planet williams/science/constants/mksa-constants))

(require (planet williams/science/constants/mks-constants))

(require (planet williams/science/constants/num-constants))

13.1 Fundamental Constants

The speed of light in vacuum, c.

The permeability of free space, μ0.

The permittivity of free space, ε0.

Plancks’s constant, h.

Plancks’s constant divided by 2π, ћ.

Avogadro’s number, Na.

The molar charge of 1 Faraday.

Boltzmann’s constant, k.

The molar gas constant, R0.

The standard gas volume, V0.

The Stefan-Boltzmann radiation constant, σ.

The magnetic field of 1 Gauss.

13.2 Astronomy and Astrophysics

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

The gravitational constant, G.

The distance of 1 light-year, ly.

The distance of 1 parsec, pc.

The standard gravitational acceleration on Earth, g.

The mass of the Sun.

13.3 Atomic and Nuclear Physics

The charge of the electron, e.

The energy of 1 electron volt, eV.

The unified atomic mass, amu.

The mass of the electron, me.

The mass of the muon, m_μ.

The mass of the proton, mp.

The mass of the neutron, mn.

The electromagnetic fine structure constant, α.

The Rydberg constant, Ry, in units of energy. This is related to the Rydberg inverse wavelength by .

The Bohr radius, a0.

The length of 1 angstrom.

The area of 1 barn.

The Bohr magneton, μB.

The nuclear magneton, μN.

The absolute value of the magnetic mement of the electron, μe. The physical magnetic moment of the electron is negative.

The absolute value of the magnetic mement of the proton, μp.

The Thomson cross section, σT.

The electric dipole moment of 1 Debye, D.

13.4 Measurements of Time

The number of seconds in 1 minute.

The number of seconds in 1 hour.

The number of seconds in 1 day.

The number of seconds in 1 week.

13.5 Imperial Units

The length of 1 inch.

The length of 1 foot.

The length of 1 yard.

The length of 1 mile.

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

13.6 Speed and Nautical Units

The speed of 1 kilometer per hour.

The speed of 1 mile per hour.

The length of 1 nautical mile.

The length of 1 fathom.

The speed of 1 knot.

13.7 Printers Units

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

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

13.8 Volume, Area and Length

The length of 1 micron.

The area of 1 hectare.

The area of 1 acre.

The volume of 1 liter.

The volume of 1 US gallon.

The volume of 1 Canadian gallon.

The volume of 1 UK gallon.

The volume of 1 quart.

The volume of 1 pint.

13.9 Mass and Weight

The mass of 1 pound.

The mass of 1 ounce.

The mass of 1 ton.

The mass of 1 metric ton (1000 kg).

The mass of 1 UK ton.

The mass of 1 troy ounce.

The mass of 1 carat.

The force of 1 gram weight.

The force of 1 pound weight.

The force of 1 kilopound weight.

The force of 1 poundal.

13.10 Thermal Energy and Power

The energy of 1 calorie.

The energy of 1 British Thermal Unit, btu.

The energy of 1 therm.

The energy of 1 horsepower.

13.11 Pressure

The pressure of 1 bar.

The pressure of 1 standard atmosphere.

The pressure of 1 torr.

The pressure of 1 meter of mercury.

The pressure of 1 inch of mercury.

The pressure of 1 inch of water.

The pressure of 1 pound per square inch.

13.12 Viscosity

The dynamic viscosity of 1 poise.

The kinematic viscosity of 1 stokes.

13.13 Light and Illumination

The luminance of 1 stilb.

The lunimous flux of 1 lumen.

The illuminance of 1 lux.

The illuminance of 1 phot.

The illuminance of 1 footcandle.

The luminance of 1 lambert.

The luminance of 1 footlambert.

13.14 Radioactivity

The activity of 1 curie.

The exposure of 1 roentgen.

The absorbed dose of 1 rad.

13.15 Force and Energy

The SI unit of force, 1 Newton.

The force of 1 dyne = 10^-5 Newton.

The SI unit of energy, 1 Joule.

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

13.16 Prefixes

The constants are dimensionless scaling factors.

1024
1021
1018
1015
1012
109
106
103
10^-3
10^-6
10^-9
10^-12
10^-15
10^-18
10^-21
10^-24

13.17 Physical Constants 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 tracel times from Earth to Mars.

The required data is the average distance of each planet from the Sun in asttonomical units (the eccentricities and inclinations of the orbots will be neglected for the purpose 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 for the constants for the speed of light (m/s) and the length of an astronomical unit (m) to produve a result for the shortest and longest light travel time in seconds. The figures are converted into minutes before being displayed.

#lang racket
(require (planet williams/science/constants/mksa-constants))
 
(define c mksa-speed-of-light) ; m/s
(define au mksa-astronomical-unit) ; m
(define minutes mksa-minute) ; s
 
; Orbit radii in meters
(define r-earth (* 1.0 au)) ; m
(define r-mars (* 1.52 au)) ; m
 
; Light travel times in seconds
(define t-min (/ (- r-mars r-earth) c)) ; s
(define t-max (/ (+ r-mars r-earth) c)) ; s
 
(printf "Light travel time from Earth to Mars:~n")
(printf "min = ~a minutes~n"
        (real->decimal-string (/ t-min minutes) 1))
(printf "max = ~a minutes~n"
        (real->decimal-string (/ t-max minutes) 1))

Here is the output from the program.

Light travel time from Earth to Mars:

min = 4.3 minutes

max = 21.0 minutes