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Mathematical and Physical Constants in Cosmology and micro physics (updated SI CIPM CODATA 2019)

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LaGuer/MathPhysicalConstants.jl

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Purpose

MathPhysicalConstants is a Julia package which has the values of a range of mathematical and physical constants updated with most recent available dataset from BIPM in 2018. CurrentlyMKS andCGS units andInternational System of Units. Updated CODATA 2017 and redefinition of SI base units followingISU, BIPM, CGPM, CIPM approved resolutions and scheduled to come into force on 20 May 2019.Seehttps://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units

Installation

The package can be installed directly from itsgithub repository:

Pkg.clone("https://github.com/LaGuer/MathPhysicalConstants.jl")

Usage

Usage is pretty straightforward. Start off by loading the package.

julia> using MathPhysicalConstants

Query and retrieve the Planck Constant using the most updated International System of Units (SI)

julia> MathPhysicalConstants.SI.PlanckConstantH6.62607015e-34julia> big(MathPhysicalConstants.SI.PlanckConstantH)6.62606895999999960651234296395253273824527450725424150396117674176417443843193e-34

Let's have a look athttps://en.wikipedia.org/wiki/Compton_wavelength ƛe ≡ ħ/m_e.c the reduced Compton electron wavelength radius formula. Try it with BigFloat and Measurement

julia> big(MathPhysicalConstants.SI.PlanckConstantHbar)/(big(MathPhysicalConstants.SI.MassElectron)*big(MathPhysicalConstants.SI.SpeedOfLight))2.42631027637202010003687587191357482878156204816578736228540160944126721996979e-12

Now let's have a look athttps://en.m.wikipedia.org/wiki/Age_of_the_universe determined with the following equation: R_H = 2ħ^2/(G.m_e.m_p.m_n) as described inhttps://fr.wikipedia.org/wiki/Analyse_dimensionnelle#Cosmologie:_Rayon_de_Hubble

julia> R3mn=(2*SI.PlanckConstantHbar^2)/(SI.SanchezGravitationalConstant*SI.MassElectron*SI.MassProton*SI.MassNeutron)1.3056254088279212e26

One converts the result in Gly with SI.GigaLightYear:

julia> 1.3056254088279212e26/SI.GigaLightYear13.800754843601865

Other examples of MathPhysicalConstantsLet's switch to Earth's gravitational acceleration in MKS units.

julia> MathPhysicalConstants.MKS.GravAccel9.80665

Or in CGS units.

julia> MathPhysicalConstants.CGS.GravAccel980.665

last but not least in International System of Units (SI)

julia> MathPhysicalConstants.SI.GravAccel9.80665

SI Constant List

SymbolNameFormulaDimensionValueUnit
πpi--3.1415926535897932pure number
eEuler's number--2.7182817284590452pure number
γeuler_gamma--0.5772156649015329pure number
TSSGP26 sporadic group Productexp(841.2869278)-2.3241836455143e365pure number
HFPHappy Family productexp(674.5210288)-8.7249055755086e292pure number
O_MMonster Group Cardinal--8.080174248 × 10^53pure number
O_BBaby Monster Group Cardinal--4.15478148 × 10^33pure number
cSpeed of light in vacuum--2.99792458e8m.s^-1
ħReduced Planck constant$\hbar=h/2\pi$-1.054571800e-34m^2 kg s^-1
G'constant of gravitation CODATA2019-M^-1L^3T^-26.67408(31)e-11m^3 kg^-1 s^-2
GF.M.Sanchez constant of gravitation$F_{gr}=Gmm'/ d^{2}$M^-1L^3T^-26.675453818e-11m^3 kg^-1 s^-2
aElectric constant$F_{qq}=\hbarc/ad^{2}$dimensionless137.035999139^-1pure number
R_UUniverse Hubble radius (F.M.Sanchez)$R_U=2G.M_{U}/c)^{2}$L1.3065e26m
G_FFermi Coupling Constant(F.M.Sanchez)$G_F=(ħc)^3/E_{F}^{2}$ML^5T^-21.4358509(7)e-62J.m^3
a_GGravit Sanchez Coupling Constant$a_G=ħc/Gm_pm_H$-1.691936465e38pure number
M_UUniverse Sanchez Mass$M_U=(ħc/G)^2/m_e.m_p.m_H$M8.7936e52kg
t_ccKotov Cosmic Periodicity-s9600.061(2)s
r_H(0)Bare Hydrogen radius$a\hbar/m_{e}c$L5.291772103e-11m
HHydrogen-electron mass ratio$m_H/m_e$dimensionless1837.152645m_e
pProton-electron mass ratio$m_p/m_e$dimensionless1836.152672m_e
nNeutron-electron mass ratio$m_n/m_e$dimensionless1838.683659m_e
m_eelectron mass-M9.10938356(11)e-31kg
μ'Muon electron mass ratio CODATA2019-dimensionless206.7682826(41)m_e
μMuon mass F.M.Sanchez-dimensionless206.7682869m_e
f'Strg Nuc Coupling Constant CODATA2019-dimensionless1/0.1181(11)pure number
fStrg Nuc Coupling Constant C.Bizouard$F^{2}/2\pi(pH)^{3}/2$dimensionless8.434502892pure number
F'Fermi Constant reduced mass CODAT2019$E_{F}/m_{e}c^{2}$dimensionless573007.33(25)pure number
FFermi Constant reduc mass F.M.Sanchez-dimensionless573007.3652pure number
d_eelectron magnetic moment excess-dimensionless1.00115965218091(26)pure number
θ'CMB Temperature CODATA2019--2.7255(6) KK
θCMB Temperature F.M.Sanchez--2.725820831 KK
k_BBoltzman Energy-temperature Convers°--1.3806488e10-23J K^-1
WIntermed vector boson Red. Mass-dimensionless157298(23)pure number
W_sIn vector boson Red. Mass F.M.Sanchez-dimensionless157340pure number
ZIntermediate vector boson Red. Mass-dimensionless178450.0(41)pure number
Z_sIn vector boson Red. Mass F.M.Sanchez-dimensionless178452pure number
Π±Pion / Pi Meson Reduced Mass-dimensionless273.13203(68)pure number
Π0Pion / Pi Meson Reduced Mass-dimensionless264.1426(18)pure number

License

TheMathPhysicalConstants.jl package is licensed under the MIT "Expat" License. Theoriginal author is La Guer.

Please, cite this paper (http://vixra.org/pdf/1811.0146v8.pdf) if youemploy this package in your research work.

DOI

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