Physical Constants

O2scl

Introduction

The constants from GSL are reworked with the type const double and placed in namespaces called o2scl_mks, o2scl_cgs, and o2scl_mksa The GSL MKSA constants are identical to the MKS constants and thus are not duplicated here. The numerical constants from gsl_num and some other additional constants are given in the namespace o2scl_const,

Some of the numerical values have been updated from recently released data. Electron, neutron, proton, and atomic mass have been updated with CODATA 2018 values. Also electron charge, gravitational constant, plancks_constant_hbar, are updated. The astronomical unit has been updated with the result from ref Luzum11 (and possibly other values need updating as well).

These physical constants are often used to create unit conversion factors, described in Unit Conversions.

Namespace o2scl_const

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namespace o2scl_const

Constants.

CODATA 2014 values were from [Mohr16] and previous versions contained constants from [Luzum11] and [Mohr12] .

CODATA 2018 values are from physics.nist.gov/constants. IAU 2015 values are the nominal values from arXiv:1510.07674 and arXiv:1605.09788 .

Squared electron charge

const double e2_gaussian = o2scl_const::hc_mev_fm * o2scl_const::fine_structure

Electron charge squared in Gaussian units (derived)

In Gaussian Units:

\[\begin{split}\begin{eqnarray*} &\vec{\nabla} \cdot \vec{E} = 4 \pi \rho \, , \quad \vec{E}=-\vec{\nabla} \Phi \, , \quad \nabla^2 \Phi = - 4 \pi \rho \, , &\\& F=\frac{q_1 q_2}{r^2} \, , \quad W=\frac{1}{2} \int \rho V d^3 x =\frac{1}{8 \pi} \int | \vec{E} |^2 d^3 x \, , \quad \alpha=\frac{e^2}{\hbar c}=\frac{1}{137}& \end{eqnarray*}\end{split}\]

const double e2_hlorentz = o2scl_const::fine_structure * 4.0 * pi

Electron charge sqaured in Heaviside-Lorentz units where \(\hbar=c=1\) (derived)

In Heaviside-Lorentz units:

\[\begin{split}\begin{eqnarray*} &\vec{\nabla} \cdot \vec{E} = \rho \, , \quad \vec{E}=-\vec{\nabla} \Phi \, , \quad \nabla^2 \Phi = - \rho \, , &\\& F=\frac{q_1 q_2}{4 \pi r^2} \, , \quad W=\frac{1}{2} \int \rho V d^3 x =\frac{1}{2} \int | \vec{E} |^2 d^3 x \, , \quad \alpha=\frac{e^2}{4 \pi}=\frac{1}{137}& \end{eqnarray*}\end{split}\]

const double e2_mks = o2scl_mks::electron_charge

Electron charge squared in SI(MKS) units (derived)

In MKS units:

\[\begin{split}\begin{eqnarray*} &\vec{\nabla} \cdot \vec{E} = \rho \, , \quad \vec{E}=-\vec{\nabla} \Phi \, , \quad \nabla^2 \Phi = - \rho \, , &\\& F=\frac{1}{4 \pi \varepsilon_0}\frac{q_1 q_2}{r^2} \, , \quad W=\frac{1}{2} \int \rho V d^3 x =\frac{\varepsilon_0}{2} \int | \vec{E} |^2 d^3 x \, , \quad \alpha=\frac{e^2}{4 \pi \varepsilon_0 \hbar c}=\frac{1}{137}& \end{eqnarray*}\end{split}\]

Note the conversion formulas

\[ q_HL=\sqrt{4 \pi} q_G = \frac{1}{\sqrt{\varepsilon_0}} q_{SI} \]
as mentioned, e.g. in pg. 13 of D. Griffiths Intro to Elem. Particles.

const double ec_gauss_fm2 = o2scl_mks::electron_charge * 1.0e-34 / o2scl_mks::plancks_constant_hbar

1 \(\mathrm{Gauss}\) times the electron charge in Gaussian units in \(\mathrm{fm}^{-2}\)

const double gauss2_fm4 = ec_gauss_fm2 * ec_gauss_fm2 / o2scl_const::fine_structure

Conversion factor from \( \mathrm{Gauss}^2 \) to \(\mathrm{fm}^{-4}\) in Gaussian units.

This is useful, e.g. in converting magnetic field squared to an energy density.

Particle masses from PDG (4/30/19)

const double mass_lambda_MeV = 1115.683

\( \Lambda \) hyperon mass in \( \mathrm{MeV} \)

const double mass_sigma_minus_MeV = 1197.449

\( \Sigma^{-} \) hyperon mass in \( \mathrm{MeV} \)

const double mass_sigma_zero_MeV = 1192.642

\( \Sigma^{0} \) hyperon mass in \( \mathrm{MeV} \)

const double mass_sigma_plus_MeV = 1189.37

\( \Sigma^{+} \) hyperon mass in \( \mathrm{MeV} \)

const double mass_cascade_zero_MeV = 1314.86

\( \Xi^{0} \) hyperon mass in \( \mathrm{MeV} \)

const double mass_cascade_minus_MeV = 1321.71

\( \Xi^{-} \) hyperon mass in \( \mathrm{MeV} \)

const double mass_up_MeV = 2.2

Up quark mass in \( \mathrm{MeV} \).

const double mass_down_MeV = 4.7

Down quark mass in \( \mathrm{MeV} \).

const double mass_strange_MeV = 95.0

Strange quark mass in \( \mathrm{MeV} \).

Functions

template<class fp_t>
fp_t planck_f(size_t system = o2scl_mks)

Planck constant.

template<class fp_t>
fp_t hbar_f(size_t system = o2scl_mks)

Reduced Planck constant.

template<class fp_t>
fp_t speed_of_light_f(size_t system = o2scl_mks)

Speed of light.

template<class fp_t>
fp_t boltzmann_f(size_t system = o2scl_mks)

Speed of light.

template<class fp_t>
fp_t hbarc_f(size_t system = o2scl_mks)

Reduced Planck’s constant times speed of light \( \hbar c \).

template<class fp_t>
fp_t elem_charge_f()

Elementary charge.

template<class fp_t>
fp_t hc_mev_fm_f()

Reduced Planck constant times speed of light in \( \mathrm{MeV}~\mathrm{fm} \).

Variables

const double yotta = 1e24
const double zetta = 1e21
const double exa = 1e18
const double peta = 1e15
const double tera = 1e12
const double giga = 1e9
const double mega = 1e6
const double kilo = 1e3
const double milli = 1e-3
const double micro = 1e-6
const double nano = 1e-9
const double pico = 1e-12
const double femto = 1e-15
const double atto = 1e-18
const double zepto = 1e-21
const double yocto = 1e-24
const double fine_structure = 7.2973525693e-3

Fine structure constant (CODATA 2018 value)

const double avogadro = 6.02214076e23

Avogadro’s number (CODATA 2018 value; exact)

const double pi = boost::math::constants::pi<double>()

\( \pi \)

const double pi2 = boost::math::constants::pi_sqr<double>()

\( \pi^2 \)

const double root_pi = boost::math::constants::root_pi<double>()

\( \sqrt{\pi} \)

const double zeta32 = 2.6123753486854883433

\( \zeta(3/2) \)

const double zeta2 = boost::math::constants::zeta_two<double>()

\( \zeta(2) \)

const double zeta52 = 1.3414872572509171798

\( \zeta(5/2) \)

const double zeta3 = boost::math::constants::zeta_three<double>()

\( \zeta(3) \)

const double zeta5 = 1.0369277551433699263

\( \zeta(5) \)

const double zeta7 = 1.0083492773819228268

\( \zeta(7) \)

const double sin2_theta_weak = 0.23122

\( \sin^2 \theta_W \) (PDG 2018 value)

const double gfermi_gev2 = 1.1663787e-5

Fermi coupling constant in \( \mathrm{GeV}^{-2} \) (CODATA 2018 value)

const size_t o2scl_mks = 1

MKS units.

const size_t o2scl_cgs = 2

CGS units.

const double hc_mev_fm = hc_mev_fm_f<double>()

\( \hbar c \) in MeV fm (exact)

const double hc_mev_cm = hc_mev_fm * 1.0e-13

\( \hbar c \) in MeV cm (exact)

Namespace o2scl_mks

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namespace o2scl_mks

Constants in MKS units.

Where possible, constants here are defined in terms of the values in o2scl_cgs, in order to make it easier to update these values. See also the documentation at o2scl_cgs .

Fundamental constants

const double speed_of_light = o2scl_cgs::speed_of_light / 1.0e2

Speed of light in m / s.

const double gravitational_constant = o2scl_cgs::gravitational_constant / 1.0e3

Newtonian constant of gravitation in m^3 / kg s^2.

const double plancks_constant_h = o2scl_cgs::plancks_constant_h / 1.0e7

Planck constant in kg m^2 / s.

const double plancks_constant_hbar = o2scl_cgs::plancks_constant_hbar / 1.0e7

Planck constant divided by 2 pi in kg m^2 / s.

const double electron_volt = o2scl_cgs::electron_volt / 1.0e7

Electron volt in kg m^2 / s^2.

const double boltzmann = o2scl_cgs::boltzmann / 1.0e7

Boltzmann constant in kg m^2 / K s^2.

const double bohr_radius = o2scl_cgs::bohr_radius / 1.0e2

Bohr radius in m.

const double stefan_boltzmann_constant = o2scl_cgs::stefan_boltzmann_constant / 1.0e3

Stefan-Boltzmann constant in kg / K^4 s^3.

const double thomson_cross_section = o2scl_cgs::thomson_cross_section / 1.0e4

Thomson cross section in m^2.

const double gfermi = o2scl_cgs::gfermi * 1.0e14

Fermi coupling constant in s^4 / m^4 kg^2.

Solar system properties

const double solar_mass_parameter = o2scl_cgs::solar_mass_parameter

Solar mass times gravitational constant in km^3 / s^2.

const double solar_mass = o2scl_cgs::solar_mass / 1.0e3

Mass of the sun in kg.

const double solar_radius = o2scl_cgs::solar_radius / 1.0e2

Radius of the sun in m.

const double solar_temperature = o2scl_cgs::solar_temperature

Temperature of the sun’s photosphere in K.

const double solar_luminosity = o2scl_cgs::solar_luminosity

Luminosity of sun in erg/s.

const double earth_mass_parameter = o2scl_cgs::earth_mass_parameter

Earth mass times gravitational constant in m^3 / s^2.

const double earth_mass = o2scl_cgs::earth_mass / 1.0e3

Mass of the earth in kg.

const double earth_radius_equatorial = o2scl_cgs::earth_radius_equatorial / 1.0e2

Equatorial radius of earth in m.

const double earth_radius_polar = o2scl_cgs::earth_radius_polar / 1.0e2

Polar radius of earth in m.

const double jupiter_mass_parameter = o2scl_cgs::jupiter_mass_parameter

Jupter mass times gravitational constant in m^3 / s^2.

const double jupiter_mass = o2scl_cgs::jupiter_mass / 1.0e3 / 1.0e2

Mass of jupiter in kg.

const double jupiter_radius_equatorial = o2scl_cgs::jupiter_radius_equatorial

Equatorial radius of jupiter in m.

const double jupiter_radius_polar = o2scl_cgs::jupiter_radius_polar / 1.0e2

Polar radius of jupiter in m.

const double mercury_mass = o2scl_cgs::mercury_mass / 1.0e3

Mass of mercury in kg.

const double mercury_radius = o2scl_cgs::mercury_radius / 1.0e2

Radius of mercury in m.

const double venus_mass = o2scl_cgs::venus_mass / 1.0e3

Mass of venus in kg.

const double venus_radius = o2scl_cgs::venus_radius / 1.0e2

Radius of venus in m.

const double mars_mass = o2scl_cgs::mars_mass / 1.0e3

Mass of mars in kg.

const double mars_radius_equatorial = o2scl_cgs::mars_radius_equatorial / 1.0e2

Equatorial radius of mars in m.

const double mars_radius_polar = o2scl_cgs::mars_radius_polar / 1.0e2

Polar radius of mars in m.

const double saturn_mass = o2scl_cgs::saturn_mass / 1.0e3

Mass of saturn in kg.

const double saturn_radius_equatorial = o2scl_cgs::saturn_radius_equatorial / 1.0e2

Equatorial radius of saturn in m.

const double saturn_radius_polar = o2scl_cgs::saturn_radius_polar / 1.0e2

Polar radius of saturn in m.

const double uranus_mass = o2scl_cgs::uranus_mass / 1.0e3

Mass of uranus in kg.

const double uranus_radius_equatorial = o2scl_cgs::uranus_radius_equatorial / 1.0e2

Equatorial radius of uranus in m.

const double uranus_radius_polar = o2scl_cgs::uranus_radius_polar / 1.0e2

Polar radius of uranus in m.

const double neptune_mass = o2scl_cgs::neptune_mass / 1.0e3

Mass of neptune in kg.

const double neptune_radius_equatorial = o2scl_cgs::neptune_radius_equatorial / 1.0e2

Equatorial radius of neptune in m.

const double neptune_radius_polar = o2scl_cgs::neptune_radius_polar / 1.0e2

Polar radius of neptune in m.

const double pluto_mass = o2scl_cgs::pluto_mass / 1.0e3

Mass of pluto in kg.

const double pluto_radius = o2scl_cgs::pluto_radius / 1.0e2

Radius of pluto in m.

Astrophysical constants

const double astronomical_unit = o2scl_cgs::astronomical_unit / 1.0e2

Astronomical unit in m.

const double parsec = o2scl_cgs::parsec / 1.0e2

Parsec in \( \mathrm{m} \).

const double grav_accel = o2scl_cgs::grav_accel / 1.0e2

Acccleration due to gravity in m / s^2.

const double schwarzchild_radius = o2scl_cgs::schwarzchild_radius / 1.0e2

Schwarzchild radius in m.

const double sidereal_year = o2scl_cgs::sidereal_year

Sidereal year in s.

const double tropical_year = o2scl_cgs::tropical_year

Tropical year in s.

const double julian_year = o2scl_cgs::julian_year

Julian year in s.

const double light_year = o2scl_cgs::light_year / 1.0e2

Light year in \( \mathrm{m} \).

Particle masses

const double mass_electron = o2scl_cgs::mass_electron / 1.0e3

Electron mass in kg.

const double mass_muon = o2scl_cgs::mass_muon / 1.0e3

Muon mass in kg.

const double mass_tau = o2scl_cgs::mass_tau / 1.0e3

Muon mass in kg.

const double mass_proton = o2scl_cgs::mass_proton / 1.0e3

Proton mass in kg.

const double mass_neutron = o2scl_cgs::mass_neutron / 1.0e3

Neutron mass in kg.

Nuclear masses

const double mass_deuteron = o2scl_cgs::mass_deuteron / 1.0e3

Deuteron mass in kg.

const double mass_triton = o2scl_cgs::mass_triton / 1.0e3

Triton mass in kg.

const double mass_helion = o2scl_cgs::mass_helion / 1.0e3

Helion mass in kg.

const double mass_alpha = o2scl_cgs::mass_alpha / 1.0e3

Alpha particle mass in kg.

const double unified_atomic_mass = o2scl_cgs::unified_atomic_mass / 1.0e3

Atomic mass constant in kg.

Chemical constants

const double rydberg = o2scl_cgs::rydberg / 1.0e7

Rydberg constant in kg m^2 / s^2.

const double molar_gas = o2scl_cgs::molar_gas / 1.0e7

kg m^2 / K mol s^2

const double standard_gas_volume = o2scl_cgs::standard_gas_volume / 1.0e6

m^3 / mol

Unit conversions

const double minute = o2scl_cgs::minute

s

const double hour = o2scl_cgs::hour

s

const double day = o2scl_cgs::day

s

const double week = o2scl_cgs::week

s

const double inch = o2scl_cgs::inch * 1.0e-2

m

const double foot = o2scl_cgs::foot * 1.0e-2

m

const double yard = o2scl_cgs::yard * 1.0e-2

m

const double mile = o2scl_cgs::mile * 1.0e-2

m

const double nautical_mile = o2scl_cgs::nautical_mile * 1.0e-2

m

const double fathom = o2scl_cgs::fathom * 1.0e-2

m

const double mil = o2scl_cgs::mil * 1.0e-2

m

const double point = o2scl_cgs::point * 1.0e-2

m

const double texpoint = o2scl_cgs::texpoint * 1.0e-2

m

const double micron = o2scl_cgs::micron * 1.0e-2

m

const double angstrom = o2scl_cgs::angstrom * 1.0e-2

m

const double hectare = o2scl_cgs::hectare * 1.0e-4

m^2

const double acre = o2scl_cgs::acre * 1.0e-4

m^2

const double barn = o2scl_cgs::barn * 1.0e-4

m^2

const double liter = o2scl_cgs::liter * 1.0e-6

m^3

const double us_gallon = o2scl_cgs::us_gallon * 1.0e-6

m^3

const double quart = o2scl_cgs::quart * 1.0e-6

m^3

const double pint = o2scl_cgs::pint * 1.0e-6

m^3

const double cup = o2scl_cgs::cup * 1.0e-6

m^3

const double fluid_ounce = o2scl_cgs::fluid_ounce * 1.0e-6

m^3

const double tablespoon = o2scl_cgs::tablespoon * 1.0e-6

m^3

const double teaspoon = o2scl_cgs::teaspoon * 1.0e-6

m^3

const double canadian_gallon = o2scl_cgs::canadian_gallon * 1.0e-6

m^3

const double uk_gallon = o2scl_cgs::uk_gallon * 1.0e-6

m^3

const double miles_per_hour = o2scl_cgs::miles_per_hour * 1.0e-2

m / s

const double kilometers_per_hour = o2scl_cgs::kilometers_per_hour * 1.0e-2

m / s

const double knot = o2scl_cgs::knot * 1.0e-2

m / s

const double pound_mass = o2scl_cgs::pound_mass * 1.0e-3

kg

const double ounce_mass = o2scl_cgs::ounce_mass * 1.0e-3

kg

const double ton = o2scl_cgs::ton * 1.0e-3

kg

const double metric_ton = o2scl_cgs::metric_ton * 1.0e-3

kg

const double uk_ton = o2scl_cgs::uk_ton * 1.0e-3

kg

const double troy_ounce = o2scl_cgs::troy_ounce * 1.0e-3

kg

const double carat = o2scl_cgs::carat * 1.0e-3

kg

const double gram_force = o2scl_cgs::gram_force * 1.0e-5

kg m / s^2

const double pound_force = o2scl_cgs::pound_force * 1.0e-5

kg m / s^2

const double kilopound_force = o2scl_cgs::kilopound_force * 1.0e-5

kg m / s^2

const double poundal = o2scl_cgs::poundal * 1.0e-5

kg m / s^2

const double calorie = o2scl_cgs::calorie * 1.0e-7

kg m^2 / s^2

const double btu = o2scl_cgs::btu * 1.0e-7

kg m^2 / s^2

const double therm = o2scl_cgs::therm * 1.0e-7

kg m^2 / s^2

const double horsepower = o2scl_cgs::horsepower * 1.0e-7

kg m^2 / s^3

const double bar = o2scl_cgs::bar * 1.0e-1

kg / m s^2

const double std_atmosphere = o2scl_cgs::std_atmosphere * 1.0e-1

kg / m s^2

const double torr = o2scl_cgs::torr * 1.0e-1

kg / m s^2

const double meter_of_mercury = o2scl_cgs::meter_of_mercury * 1.0e-1

kg / m s^2

const double inch_of_mercury = o2scl_cgs::inch_of_mercury * 1.0e-1

kg / m s^2

const double inch_of_water = o2scl_cgs::inch_of_water * 1.0e-1

kg / m s^2

const double psi = o2scl_cgs::psi * 1.0e-1

kg / m s^2

const double poise = o2scl_cgs::poise * 1.0e-1

kg m^-1 s^-1

const double stokes = o2scl_cgs::stokes * 1.0e-4

m^2 / s

const double gauss = 1.0e-4

kg / A s^2

const double stilb = o2scl_cgs::stilb * 1.0e4

cd / m^2

const double lumen = o2scl_cgs::lumen

cd sr

const double lux = o2scl_cgs::lux * 1.0e4

cd sr / m^2

const double phot = o2scl_cgs::phot * 1.0e4

cd sr / m^2

const double footcandle = o2scl_cgs::footcandle * 1.0e4

cd sr / m^2

const double lambert = o2scl_cgs::lambert * 1.0e4

cd sr / m^2

const double footlambert = o2scl_cgs::footlambert * 1.0e4

cd sr / m^2

const double curie = o2scl_cgs::curie

1 / s

const double rad = o2scl_cgs::rad * 1.0e-4

m^2 / s^2

const double newton = o2scl_cgs::newton * 1.0e-5

kg m / s^2

const double dyne = o2scl_cgs::dyne * 1.0e-5

kg m / s^2

const double joule = o2scl_cgs::joule * 1.0e-7

kg m^2 / s^2

const double erg = o2scl_cgs::erg * 1.0e-7

kg m^2 / s^2

ELectromagnetic constants

const double electron_magnetic_moment = o2scl_cgsm::electron_magnetic_moment / 1.0e3

A m^2.

const double proton_magnetic_moment = o2scl_cgsm::proton_magnetic_moment / 1.0e3

A m^2.

const double roentgen = o2scl_cgs::roentgen * 1.0e3

A s / kg.

const double bohr_magneton = o2scl_cgsm::bohr_magneton / 1.0e3

Bohr magneton in A m^2.

const double nuclear_magneton = o2scl_cgsm::nuclear_magneton / 1.0e3

A m^2.

const double vacuum_permittivity = 1.0 / o2scl_mks::speed_of_light / o2scl_mks::speed_of_light / 4.0e-7 / o2scl_const::pi

A^2 s^4 / kg m^3 (derived)

const double vacuum_permeability = 4.0 * o2scl_const::pi * 1.00000000082e-7

Vacuum permeability in kg m / A^2 s^2 (being redefined as of 5/20, this value is from Wikipedia)

const double faraday = o2scl_cgsm::faraday * 10.0

A s / mol.

const double electron_charge = o2scl_cgsm::electron_charge * 1.0e1

A s (derived)

Namespace o2scl_cgs

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namespace o2scl_cgs

Constants in CGS units.

CODATA 2014 values were from Mohr16. CODATA 2018 values are from physics.nist.gov/constants. IAU 2015 values are the nominal values from arXiv:1510.07674 and arXiv:1605.09788 .

Fundamental constants

const double speed_of_light = 2.99792458e10

Speed of light in \( \mathrm{cm}/\mathrm{s} \) (exact)

const double gravitational_constant = 6.67430e-8

Newtonian constant of gravitation in cm^3 / g s^2 (CODATA 2018 value)

const double plancks_constant_h = 6.62607015e-27

Planck constant in g cm^2 / s (CODATA 2018 value; exact)

const double plancks_constant_hbar = o2scl_cgs::plancks_constant_h / 2.0 / o2scl_const::pi

Planck constant divided by 2 pi in g cm^2 / s (derived)

const double electron_volt = 1.602176634e-12

Electron volt in g cm^2 / s^2 (CODATA 2018; exact)

const double boltzmann = 1.380649e-16

Boltzmann constant in g cm^2 / K s^2 (CODATA 2018; exact)

const double bohr_radius = 5.29177210903e-9

Bohr radius in cm (CODATA 2018 value)

const double stefan_boltzmann_constant = o2scl_const::pi * o2scl_const::pi * o2scl_cgs::boltzmann * o2scl_cgs::boltzmann * o2scl_cgs::boltzmann * o2scl_cgs::boltzmann / 60.0 / o2scl_cgs::plancks_constant_hbar / o2scl_cgs::plancks_constant_hbar / o2scl_cgs::plancks_constant_hbar / o2scl_cgs::speed_of_light / o2scl_cgs::speed_of_light

Stefan-Boltzmann constant in g / K^4 s^3 (CODATA 2018; derived; exact)

const double thomson_cross_section = 6.6524587321e-25

Thomson cross section in cm^2 (CODATA 2018 value)

const double gfermi = o2scl_const::gfermi_gev2 * 1.0e-18 / o2scl_cgs::electron_volt / o2scl_cgs::electron_volt

Fermi coupling constant in s^4 / cm^4 g^2 (derived from CODATA 2018 value)

Solar system properties

const double solar_mass_parameter = 1.3271244e26

Solar mass times gravitational constant in cm^3 / s^2 (IAU 2015 value)

Note that this value differs slightly in Barycentric Coordinate Time and Barycentric Dynamical Time. This is the IAU’s nominal value.

const double solar_mass = solar_mass_parameter / gravitational_constant

Mass of the sun in g (derived)

const double solar_radius = 6.957e10

Radius of the sun in cm (IAU 2015 value)

const double solar_temperature = 5772.0

Temperature of the sun’s photosphere in K (IAU 2015 value)

const double solar_luminosity = 3.828e40

Luminosity of sun in erg/s (IAU 2015 value)

const double earth_mass_parameter = 3.986004e20

Earth mass times gravitational constant in cm^3 / s^2 (IAU 2015 value)

const double earth_mass = earth_mass_parameter / gravitational_constant

Mass of the earth in g (derived)

const double earth_radius_equatorial = 6.3781e8

Equatorial radius of earth in cm (IAU 2015 value)

const double earth_radius_polar = 6.3568e8

Polar radius of earth in cm (IAU 2015 value)

const double jupiter_mass_parameter = 1.2668653e23

Jupter mass times gravitational constant in cm^3 / s^2 (IAU 2015 value)

const double jupiter_mass = jupiter_mass_parameter / gravitational_constant

Mass of jupiter in g (derived)

const double jupiter_radius_equatorial = 7.1492e9

Equatorial radius of jupiter in cm (IAU 2015 value)

const double jupiter_radius_polar = 6.6854e9

Polar radius of jupiter in cm (IAU 2015 value)

const double mercury_mass = 3.3011e26

Mass of mercury in g.

const double mercury_radius = 2.4397e8

Radius of mercury in cm.

const double venus_mass = 7.8675e27

Mass of venus in g.

const double venus_radius = 6.0518e8

Radius of venus in cm.

const double mars_mass = 6.4171e26

Mass of mars in g.

const double mars_radius_equatorial = 3.3962e8

Equatorial radius of mars in cm.

const double mars_radius_polar = 3.3762e8

Polar radius of mars in cm.

const double saturn_mass = 5.6834e29

Mass of saturn in g.

const double saturn_radius_equatorial = 6.0268e9

Equatorial radius of saturn in cm.

const double saturn_radius_polar = 5.4364e9

Polar radius of saturn in cm.

const double uranus_mass = 8.6810e28

Mass of uranus in g.

const double uranus_radius_equatorial = 2.5559e9

Equatorial radius of uranus in cm.

const double uranus_radius_polar = 2.4973e9

Polar radius of uranus in cm.

const double neptune_mass = 1.02413e29

Mass of neptune in g.

const double neptune_radius_equatorial = 2.4764e9

Equatorial radius of neptune in cm.

const double neptune_radius_polar = 2.4341e9

Polar radius of neptune in cm.

const double pluto_mass = 1.303e25

Mass of pluto in g.

const double pluto_radius = 1.1883e8

Radius of pluto in cm.

Astrophysical constants

const double astronomical_unit = 1.495978707e13

Astronomical unit in cm (IAU 2009 value; now exact)

const double parsec = o2scl_cgs::astronomical_unit * 648000.0 / o2scl_const::pi

Parsec in \( \mathrm{cm} \) (derived; exact)

const double grav_accel = 9.80665e2

Acccleration due to gravity in cm / s^2 (CODATA 2018; now exact)

const double schwarzchild_radius = 2.0 * o2scl_cgs::solar_mass_parameter / o2scl_cgs::speed_of_light / o2scl_cgs::speed_of_light

Schwarzchild radius in cm (derived)

const double sidereal_year = 365.256363004 * 8.64e4

Sidereal year in s (from http://hpiers.obspm.fr/eop-pc/models/constants.html)

const double tropical_year = 365.242190402 * 8.64e4

Tropical year in s (from http://hpiers.obspm.fr/eop-pc/models/constants.html)

const double julian_year = 365.25 * 8.64e4

Julian year in s (exact)

const double light_year = o2scl_cgs::julian_year * o2scl_cgs::speed_of_light

Light year in \( \mathrm{cm} \) (derived; exact)

Particle masses

const double mass_electron = 9.1093837015e-28

Electron mass in g (CODATA 2018 value)

const double mass_muon = 1.883531627e-25

Muon mass in g (CODATA 2018 value)

const double mass_tau = 3.16754e-24

Muon mass in g (CODATA 2018 value)

const double mass_proton = 1.67262192369e-24

Proton mass in g (CODATA 2018 value)

const double mass_neutron = 1.67492749804e-24

Neutron mass in g (CODATA 2018 value)

Nuclear masses

const double mass_deuteron = 3.3435837724e-24

Deuteron mass in kg (CODATA 2018 value)

const double mass_triton = 5.0073567446e-24

Triton mass in kg (CODATA 2018 value)

const double mass_helion = 5.0064127796e-24

Helion mass in kg (CODATA 2018 value)

const double mass_alpha = 6.6446573357e-24

Alpha particle mass in kg (CODATA 2018 value)

const double unified_atomic_mass = 1.6605390666e-24

Atomic mass constant in g (CODATA 2018 value)

Chemical constants

const double rydberg = 2.1798723611035e-11

Rydberg constant in g cm^2 / s^2 (CODATA 2018 value)

const double molar_gas = o2scl_const::avogadro * o2scl_cgs::boltzmann

Molar gas constant, “R”, in g cm^2 / K mol s^2 (CODATA 2018; exact; derived)

const double standard_gas_volume = 2.271095464e4

Molar volume of ideal gas at standard T and P in cm^3 / mol (CODATA 2018 value)

Unit conversions

const double minute = 6e1

s

const double hour = 3.6e3

s

const double day = 8.64e4

s

const double week = 6.048e5

s

const double inch = 2.54e0

cm

const double foot = 3.048e1

cm

const double yard = 9.144e1

cm

const double mile = 1.609344e5

cm

const double nautical_mile = 1.852e5

cm

const double fathom = 1.8288e2

cm

const double mil = 2.54e-3

cm

const double point = 3175.0 / 90000.0

cm

const double texpoint = 3.51459803515e-2

cm

const double micron = 1e-4

cm

const double angstrom = 1e-8

cm

const double hectare = 1e8

cm^2

const double acre = 4.04685642241e7

cm^2

const double barn = 1e-24

cm^2

const double liter = 1e3

cm^3

const double us_gallon = 3.78541178402e3

cm^3

const double quart = 9.46352946004e2

cm^3

const double pint = 4.73176473002e2

cm^3

const double cup = 2.36588236501e2

cm^3

const double fluid_ounce = 2.95735295626e1

cm^3

const double tablespoon = 1.47867647813e1

cm^3

const double teaspoon = 4.92892159375e0

cm^3

const double canadian_gallon = 4.54609e3

cm^3

const double uk_gallon = 4.546092e3

cm^3

const double miles_per_hour = 4.4704e1

cm / s

const double kilometers_per_hour = 250.0 / 9.0

cm / s

const double knot = 463.0 / 9.0

cm / s

const double pound_mass = 4.5359237e2

g

const double ounce_mass = 2.8349523125e1

g

const double ton = 9.0718474e5

g

const double metric_ton = 1e6

g

const double uk_ton = 1.0160469088e6

g

const double troy_ounce = 3.1103475e1

g

const double carat = 2e-1

g

const double gram_force = 9.80665e2

cm g / s^2

const double pound_force = 4.44822161526e5

cm g / s^2

const double kilopound_force = 4.44822161526e8

cm g / s^2

const double poundal = 1.38255e4

cm g / s^2

const double calorie = 4.1868e7

g cm^2 / s^2

const double btu = 1.05505585262e10

g cm^2 / s^2

const double therm = 1.05506e15

g cm^2 / s^2

const double horsepower = 7.457e9

g cm^2 / s^3

const double bar = 1e6

g / cm s^2

const double std_atmosphere = 1.01325e6

g / cm s^2

const double torr = 1.33322368421e3

g / cm s^2

const double meter_of_mercury = 1.33322368421e6

g / cm s^2

const double inch_of_mercury = 3.38638815789e4

g / cm s^2

const double inch_of_water = 2.490889e3

g / cm s^2

const double psi = 6.89475729317e4

g / cm s^2

const double poise = 1e0

g / cm s

const double stokes = 1e0

cm^2 / s

const double stilb = 1e0

cd / cm^2

const double lumen = 1e0

cd sr

const double lux = 1e-4

cd sr / cm^2

const double phot = 1e0

cd sr / cm^2

const double footcandle = 1.076e-3

cd sr / cm^2

const double lambert = 1e0

cd sr / cm^2

const double footlambert = 1.07639104e-3

cd sr / cm^2

const double curie = 3.7e10

1 / s

const double rad = 1e2

cm^2 / s^2

const double newton = 1e5

cm g / s^2

const double dyne = 1e0

cm g / s^2

const double joule = 1e7

g cm^2 / s^2

const double erg = 1e0

g cm^2 / s^2

Electromagnetic constants

const double roentgen = 2.58e-7

A s / g.

Namespace o2scl_cgsm

Top

namespace o2scl_cgsm

Constants in CGSM units.

Where possible, constants here are defined in terms of the values in o2scl_cgs, in order to make it easier to update these values. See also the documentation at o2scl_cgs .

Fundamental constants

const double speed_of_light = o2scl_cgs::speed_of_light

Speed of light in cm / s.

const double gravitational_constant = o2scl_cgs::gravitational_constant

Newtonian constant of gravitation in cm^3 / g s^2.

const double plancks_constant_h = o2scl_cgs::plancks_constant_h

Planck constant in g cm^2 / s.

const double plancks_constant_hbar = o2scl_cgs::plancks_constant_hbar

Planck constant divided by 2 pi in g cm^2 / s.

const double electron_volt = o2scl_cgs::electron_volt

Electron volt in g cm^2 / s^2.

const double boltzmann = o2scl_cgs::boltzmann

Boltzmann constant in g cm^2 / K s^2.

const double bohr_radius = o2scl_cgs::bohr_radius

Bohr radius in cm.

const double stefan_boltzmann_constant = o2scl_cgs::stefan_boltzmann_constant

Stefan-Boltzmann constant in g / K^4 s^3.

const double thomson_cross_section = o2scl_cgs::thomson_cross_section

Thomson cross section in cm^2.

const double gfermi = o2scl_cgs::gfermi

Fermi coupling constant in s^4 / cm^4 g^2.

Solar system properties

const double solar_mass_parameter = o2scl_cgs::solar_mass_parameter

Solar mass times gravitational constant in cm^3 / s^2 (IAU 2015 value)

Note that this value differs slightly in Barycentric Coordinate Time and Barycentric Dynamical Time. This is the IAU’s nominal value.

const double solar_mass = o2scl_cgs::solar_mass

Mass of the sun in g (derived)

const double solar_radius = o2scl_cgs::solar_radius

Radius of the sun in cm (IAU 2015 value)

const double solar_temperature = o2scl_cgs::solar_temperature

Temperature of the sun’s photosphere in K (IAU 2015 value)

const double solar_luminosity = o2scl_cgs::solar_luminosity

Luminosity of sun in erg/s (IAU 2015 value)

const double earth_mass_parameter = o2scl_cgs::earth_mass_parameter

Earth mass times gravitational constant in cm^3 / s^2 (IAU 2015 value)

const double earth_mass = o2scl_cgs::earth_mass

Mass of the earth in g (derived)

const double earth_radius_equatorial = o2scl_cgs::earth_radius_equatorial

Equatorial radius of earth in cm (IAU 2015 value)

const double earth_radius_polar = o2scl_cgs::earth_radius_polar

Polar radius of earth in cm (IAU 2015 value)

const double jupiter_mass_parameter = o2scl_cgs::jupiter_mass_parameter

Jupter mass times gravitational constant in cm^3 / s^2 (IAU 2015 value)

const double jupiter_mass = o2scl_cgs::jupiter_mass

Mass of jupiter in g (derived)

const double jupiter_radius_equatorial = o2scl_cgs::jupiter_radius_equatorial

Equatorial radius of jupiter in cm (IAU 2015 value)

const double jupiter_radius_polar = o2scl_cgs::jupiter_radius_polar

Polar radius of jupiter in cm (IAU 2015 value)

const double mercury_mass = o2scl_cgs::mercury_mass

Mass of mercury in g.

const double mercury_radius = o2scl_cgs::mercury_radius

Radius of mercury in cm.

const double venus_mass = o2scl_cgs::venus_mass

Mass of venus in g.

const double venus_radius = o2scl_cgs::venus_radius

Radius of venus in cm.

const double mars_mass = o2scl_cgs::mars_mass

Mass of mars in g.

const double mars_radius_equatorial = o2scl_cgs::mars_radius_equatorial

Equatorial radius of mars in cm.

const double mars_radius_polar = o2scl_cgs::mars_radius_polar

Polar radius of mars in cm.

const double saturn_mass = o2scl_cgs::saturn_mass

Mass of saturn in g.

const double saturn_radius_equatorial = o2scl_cgs::saturn_radius_equatorial

Equatorial radius of saturn in cm.

const double saturn_radius_polar = o2scl_cgs::saturn_radius_polar

Polar radius of saturn in cm.

const double uranus_mass = o2scl_cgs::uranus_mass

Mass of uranus in g.

const double uranus_radius_equatorial = o2scl_cgs::uranus_radius_equatorial

Equatorial radius of uranus in cm.

const double uranus_radius_polar = o2scl_cgs::uranus_radius_polar

Polar radius of uranus in cm.

const double neptune_mass = o2scl_cgs::neptune_mass

Mass of neptune in g.

const double neptune_radius_equatorial = o2scl_cgs::neptune_radius_equatorial

Equatorial radius of neptune in cm.

const double neptune_radius_polar = o2scl_cgs::neptune_radius_polar

Polar radius of neptune in cm.

const double pluto_mass = o2scl_cgs::pluto_mass

Mass of pluto in g.

const double pluto_radius = o2scl_cgs::pluto_radius

Radius of pluto in cm.

Astrophysical constants

const double astronomical_unit = o2scl_cgs::astronomical_unit

Astronomical unit in cm (IAU 2009 value; now exact)

const double parsec = o2scl_cgs::parsec

Parsec in \( \mathrm{cm} \) (derived; exact)

const double grav_accel = o2scl_cgs::grav_accel

Acccleration due to gravity in cm / s^2 (CODATA 2018; now exact)

const double schwarzchild_radius = o2scl_cgs::schwarzchild_radius

Schwarzchild radius in cm (derived)

const double sidereal_year = o2scl_cgs::sidereal_year

Sidereal year in s (from http://hpiers.obspm.fr/eop-pc/models/constants.html)

const double tropical_year = o2scl_cgs::tropical_year

Tropical year in s (from http://hpiers.obspm.fr/eop-pc/models/constants.html)

const double julian_year = o2scl_cgs::julian_year

Julian year in s (exact)

const double light_year = o2scl_cgs::light_year

Light year in \( \mathrm{cm} \) (derived; exact)

Particle masses

const double mass_electron = o2scl_cgs::mass_electron

Electron mass in g.

const double mass_muon = o2scl_cgs::mass_muon

Muon mass in g.

const double mass_tau = o2scl_cgs::mass_tau

Muon mass in g.

const double mass_proton = o2scl_cgs::mass_proton

Proton mass in g.

const double mass_neutron = o2scl_cgs::mass_neutron

Neutron mass in g.

Nuclear masses

const double mass_deuteron = o2scl_cgs::mass_deuteron

Deuteron mass in g.

const double mass_triton = o2scl_cgs::mass_triton

Triton mass in g.

const double mass_helion = o2scl_cgs::mass_helion

Helion mass in g.

const double mass_alpha = o2scl_cgs::mass_alpha

Alpha particle mass in g.

const double unified_atomic_mass = o2scl_cgs::unified_atomic_mass

Atomic mass constant in g.

Chemical constants

const double rydberg = o2scl_cgs::rydberg

Rydberg constant in g cm^2 / s^2.

const double molar_gas = o2scl_cgs::molar_gas

Molar gas constant, “R”, in g cm^2 / K mol s^2.

const double standard_gas_volume = o2scl_cgs::standard_gas_volume

Molar volume of ideal gas at standard T and P in cm^3 / mol.

Unit conversions

const double minute = o2scl_cgs::minute

s

const double hour = o2scl_cgs::hour

s

const double day = o2scl_cgs::day

s

const double week = o2scl_cgs::week

s

const double inch = o2scl_cgs::inch

cm

const double foot = o2scl_cgs::foot

cm

const double yard = o2scl_cgs::yard

cm

const double mile = o2scl_cgs::mile

cm

const double nautical_mile = o2scl_cgs::nautical_mile

cm

const double fathom = o2scl_cgs::fathom

cm

const double mil = o2scl_cgs::mil

cm

const double point = o2scl_cgs::point

cm

const double texpoint = o2scl_cgs::texpoint

cm

const double micron = o2scl_cgs::micron

cm

const double angstrom = o2scl_cgs::angstrom

cm

const double hectare = o2scl_cgs::hectare

cm^2

const double acre = o2scl_cgs::acre

cm^2

const double barn = o2scl_cgs::barn

cm^2

const double liter = o2scl_cgs::liter

cm^3

const double us_gallon = o2scl_cgs::us_gallon

cm^3

const double quart = o2scl_cgs::quart

cm^3

const double pint = o2scl_cgs::pint

cm^3

const double cup = o2scl_cgs::cup

cm^3

const double fluid_ounce = o2scl_cgs::fluid_ounce

cm^3

const double tablespoon = o2scl_cgs::tablespoon

cm^3

const double teaspoon = o2scl_cgs::teaspoon

cm^3

const double canadian_gallon = o2scl_cgs::canadian_gallon

cm^3

const double uk_gallon = o2scl_cgs::uk_gallon

cm^3

const double miles_per_hour = o2scl_cgs::miles_per_hour

cm / s

const double kilometers_per_hour = o2scl_cgs::kilometers_per_hour

cm / s

const double knot = o2scl_cgs::knot

cm / s

const double pound_mass = o2scl_cgs::pound_mass

g

const double ounce_mass = o2scl_cgs::ounce_mass

g

const double ton = o2scl_cgs::ton

g

const double metric_ton = o2scl_cgs::metric_ton

g

const double uk_ton = o2scl_cgs::uk_ton

g

const double troy_ounce = o2scl_cgs::troy_ounce

g

const double carat = o2scl_cgs::carat

g

const double gram_force = o2scl_cgs::gram_force

cm g / s^2

const double pound_force = o2scl_cgs::pound_force

cm g / s^2

const double kilopound_force = o2scl_cgs::kilopound_force

cm g / s^2

const double poundal = o2scl_cgs::poundal

cm g / s^2

const double calorie = o2scl_cgs::calorie

g cm^2 / s^2

const double btu = o2scl_cgs::btu

g cm^2 / s^2

const double therm = o2scl_cgs::therm

g cm^2 / s^2

const double horsepower = o2scl_cgs::horsepower

g cm^2 / s^3

const double bar = o2scl_cgs::bar

g / cm s^2

const double std_atmosphere = o2scl_cgs::std_atmosphere

g / cm s^2

const double torr = o2scl_cgs::torr

g / cm s^2

const double meter_of_mercury = o2scl_cgs::meter_of_mercury

g / cm s^2

const double inch_of_mercury = o2scl_cgs::inch_of_mercury

g / cm s^2

const double inch_of_water = o2scl_cgs::inch_of_water

g / cm s^2

const double psi = o2scl_cgs::psi

g / cm s^2

const double poise = o2scl_cgs::poise

g / cm s

const double stokes = o2scl_cgs::stokes

cm^2 / s

const double stilb = o2scl_cgs::stilb

cd / cm^2

const double lumen = o2scl_cgs::lumen

cd sr

const double lux = o2scl_cgs::lux

cd sr / cm^2

const double phot = o2scl_cgs::phot

cd sr / cm^2

const double footcandle = o2scl_cgs::footcandle

cd sr / cm^2

const double lambert = o2scl_cgs::lambert

cd sr / cm^2

const double footlambert = o2scl_cgs::footlambert

cd sr / cm^2

const double curie = o2scl_cgs::curie

1 / s

const double rad = o2scl_cgs::rad

cm^2 / s^2

const double newton = o2scl_cgs::newton

cm g / s^2

const double dyne = o2scl_cgs::dyne

cm g / s^2

const double joule = o2scl_cgs::joule

g cm^2 / s^2

const double erg = o2scl_cgs::erg

g cm^2 / s^2

Electromagnetic constants

const double electron_magnetic_moment = 9.2847647043e-21

Electron magnetic moment in abamp cm^2 (CODATA 2018 value)

const double proton_magnetic_moment = 1.41060679736e-23

Proton magnetic moment in abamp cm^2 (CODATA 2018 value)

const double roentgen = o2scl_cgs::roentgen / 10.0

Roentgen abamp s / g.

const double bohr_magneton = 9.2740100783e-21

Bohr magneton in abamp cm^2 (CODATA 2018 value)

const double nuclear_magneton = 5.0507837461e-24

Nuclear magneton in abamp cm^2 (CODATA 2018 value)

const double faraday = o2scl_const::avogadro * o2scl_cgs::electron_volt / 1.0e8

Faraday constant in abamp s / mol (CODATA 2018 value; derived; exact)

const double electron_charge = electron_volt * 1.0e-8

Electron charge in abamp s (derived)