Constants of physical expressions as constexpr. More...

#include <numbers>
#include "arts_constexpr_math.h"
#include "matpack_concepts.h"

Namespaces
namespace	Constant
	Namespace containing several constants, physical and mathematical.

Variables
constexpr Numeric	Constant::pi = std::numbers::pi
	The following mathematical constants are generated in python Decimal package by the code:

constexpr Numeric	Constant::inv_pi = std::numbers::inv_pi
	Inverse of pi.

constexpr Numeric	Constant::two_pi = 2 * pi
	Two times pi.

constexpr Numeric	Constant::inv_two_pi = 0.5 * inv_pi
	Inverse of two pi.

constexpr Numeric	Constant::sqrt_pi = 1.0/std::numbers::inv_sqrtpi
	Square root of pi.

constexpr Numeric	Constant::inv_sqrt_pi = std::numbers::inv_sqrtpi
	Inverse of the square root of pi.

constexpr Numeric	Constant::euler = std::numbers::e
	Euler's number.

constexpr Numeric	Constant::inv_euler = 1.0 / euler
	Inverse of Euler's number.

constexpr Numeric	Constant::log10_euler = std::numbers::log10e
	Ten's logarithm of Euler's number.

constexpr Numeric	Constant::ln_10 = std::numbers::ln10
	Natural logarithm of 10.

constexpr Numeric	Constant::sqrt_2 = std::numbers::sqrt2
	Square root of 2.

constexpr Numeric	Constant::inv_sqrt_2 = 1.0 / sqrt_2
	Inverse of the square root of 2.

constexpr Numeric	Constant::ln_2 = std::numbers::ln2
	Natural logarithm of 2.

constexpr Numeric	Constant::inv_ln_2 = 1.0 / ln_2
	Inverse of the natural logarithm of 2.

constexpr Numeric	Constant::sqrt_ln_2
	Square root of natural logarithm of 2.

constexpr Numeric	Constant::inv_sqrt_ln_2
	Inverse of the square root of the natural logarithm of 2.

constexpr Numeric	Constant::Delta_nu_Cs = 9192631770
	Cesium-133 Unperturbed ground-state hyperfine transition frequency [Hz] From: https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units Date: 2019-04-01.

constexpr Numeric	Constant::speed_of_light = 299792458
	Speed of light [m/s] From: https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units Date: 2019-04-01.

constexpr Numeric	Constant::c = speed_of_light
	Speed of light convenience name [m/s].

constexpr Numeric	Constant::planck_constant = 6.62607015e-34
	Planck constant [J s] From: https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units Date: 2019-04-01.

constexpr Numeric	Constant::h = planck_constant
	Planck constant convenience name [J s].

constexpr Numeric	Constant::reduced_planck_constant = h * inv_two_pi
	Reduced planck constant [J s].

constexpr Numeric	Constant::h_bar = reduced_planck_constant
	Reduced planck constant convenience name [J s].

constexpr Numeric	Constant::elementary_charge = 1.602176634e-19
	Elementary charge [C] From: https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units Date: 2019-04-01.

constexpr Numeric	Constant::e = elementary_charge
	Elementary charge convenience name [C].

constexpr Numeric	Constant::boltzmann_constant = 1.380649e-23
	Boltzmann constant [J/K] From: https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units Date: 2019-04-01.

constexpr Numeric	Constant::k = boltzmann_constant
	Boltzmann constant convenience name [J/K].

constexpr Numeric	Constant::avogadro_constant = 6.02214076e23
	Avogadro constant [1/mol] From: https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units Date: 2019-04-01.

constexpr Numeric	Constant::NA = avogadro_constant
	Avogadro constant convenience name [1/mol].

constexpr Numeric	Constant::K_cd = 683
	Luminous efficacy of monochromatic 540 THz radiation [lm / W] From: https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units Date: 2019-04-01.

constexpr Numeric	Constant::fine_structure_constant = 7.2973525693e-3
	Fine structure constant [-] From: https://physics.nist.gov/cgi-bin/cuu/Value?alph Date: 2019-06-18 Reported error: (11)

constexpr Numeric	Constant::alpha = fine_structure_constant
	Fine structure constant convenience name [-].

constexpr Numeric	Constant::rydberg_constant = 10973731.568160
	Rydberg constant [1/m] From: https://physics.nist.gov/cgi-bin/cuu/Value?ryd Date: 2016-06-18 Reported error: (21)

constexpr Numeric	Constant::R_inf = rydberg_constant
	Rydberg constant convenience name [1/m].

constexpr Numeric	Constant::magnetic_constant = 2 * h * alpha / (c * Math::pow2(e))
	Magnetic constant [H/m].

constexpr Numeric	Constant::mu_0 = magnetic_constant
	Magnetic constant convenience name [H/m].

constexpr Numeric	Constant::vacuum_permittivity = Math::pow2(e) / (2 * h * c * alpha)
	Vacuum permittivity [F/m].

constexpr Numeric	Constant::epsilon_0 = vacuum_permittivity
	Vacuum permittivity convenience name [F/m].

constexpr Numeric	Constant::electron_mass = 2 * h * R_inf / (c * Math::pow2(alpha))
	Mass of resting electron [kg].

constexpr Numeric	Constant::m_e = electron_mass
	Mass of resting electron convenience name [kg].

constexpr Numeric	Constant::unified_atomic_mass_unit = 1.66053906660e-27
	Unified atomic mass unit [kg] From: https://physics.nist.gov/cgi-bin/cuu/Value?ukg Date: 2020-02-18 Reported error: (50)

constexpr Numeric	Constant::m_u = unified_atomic_mass_unit
	Unified atomic mass unit convenience name [kg].

constexpr Numeric	Constant::mass_ratio_electrons_per_proton = 1'836.152'673'43
	Mass ratio of electrons to protons [-] From: https://physics.nist.gov/cgi-bin/cuu/Value?mpsme Date: 2020-01-08 Reported error: (11)

constexpr Numeric	Constant::proton_mass
	Mass of a proton [kg].

constexpr Numeric	Constant::mass_ratio_electrons_per_neutron = 1'838.683'661'73
	Mass ratio of electrons to protons [-] From: https://physics.nist.gov/cgi-bin/cuu/Value?mnsme Date: 2020-01-08 Reported error: (89)

constexpr Numeric	Constant::neutron_mass
	Mass of a neutron [kg].

constexpr Numeric	Constant::bohr_magneton = e * h_bar / (2 * m_e)
	Bohr magneton [J/T].

constexpr Numeric	Constant::ideal_gas_constant = k * NA
	Ideal gas constant [J/mol K].

constexpr Numeric	Constant::R = ideal_gas_constant
	Ideal gas constant convenience name [J/mol K].

constexpr Numeric	Constant::doppler_broadening_const_squared = 2'000 * R / Math::pow2(c)
	Doppler broadening constant squared [kg/T]^2.

constexpr Numeric	Constant::one_degree_in_radians = pi / 180
	One degree in radians.

constexpr Numeric	Constant::stefan_boltzmann_constant
	Stefan-Boltzmann constant [W/(K^4*m^2)].

constexpr Numeric	Constant::sigma = stefan_boltzmann_constant
	Stefan-Boltzmann constant convenience name [W/(K^4*m^2)].

constexpr Numeric	Constant::density_of_ice_at_0c = 0.9167e3
	Global constant, Density of water ice at 0C [kg/m3] source: http://en.wikipedia.org/wiki/Ice.

constexpr Numeric	Constant::denity_of_water_at_4c = 1e3
	Global constant, Density of liquid water +4C [kg/m3] source: http://en.wikipedia.org/wiki/Water.

constexpr Numeric	Constant::cosmic_microwave_background_temperature = 2.735
	Global constant, Planck temperature for cosmic background radiation [K].

constexpr Numeric	Constant::earth_radius = 6.3781e6
	Global constant, the radius of the Earth [m].

constexpr Numeric	Constant::temperature_at_0c = 273.15
	Global constant, Temperature in Celsius of 0 Kelvin.

Detailed Description

Constants of physical expressions as constexpr.

Following May 2019 reported SI unit updates, several previously important constant are proper constants and not derived constants.

This file contains the intended May 2019 constants update meaning that the Planck constant, Boltzmann constant, elementary charge, Avogadro number, the definition of a luminosity, the frequency of Cesium, and the speed of light have been given constant values.

All other values are derived. To be internally consistent in ARTS, the adaptation of these rules below take the approach that only the fine structure constant and the Rydberg constant are 'measurable' quantities. All other quantities are derived by their formal relationships. As an example, the resting mass of an electron is defined as 2 h R_inf / c alpha^2. This means that they should be constant in their internal relationships to the level permitted by the select floating point accuracy.

Note 1: The constants below contains both named and a few convenience variables

Note 2: Derived constants of convenience, such as the Doppler broadening constant, should also go into here if they have a clear name.

Note 3: The PrintPhysicalConstants convenience function is part of the global ARTS namespace. Please update this if and when new constants are added to this namespace.

Author: Richard Larsson

Date: 2019-04-01

Definition in file arts_constants.h.

Namespaces

Variables

Detailed Description