generalized Weather with UnitSystem

Project.toml

@@ -1,7 +1,7 @@
 name = "Geophysics"
 uuid = "74efdf00-b554-44e1-bd21-abb9281d951c"
 authors = ["Michael Reed"]
-version = "0.3.1"
+version = "0.3.2"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

docs/src/constants.md

@@ -0,0 +1,306 @@
+# Physics Constants
+
+```@contents
+Pages = ["units.md","constants.md","convert.md"]
+```
+
+The following are fundamental constants of physics:
+
+```math
+\alpha = \frac{\lambda e^2}{4\pi\varepsilon_0\hbar c} = 
+\frac{\lambda c\mu_0 (e\alpha_L)^2}{4\pi\hbar} = 
+\frac{e^2k_e}{\hbar c} = 
+\frac{\lambda e^2}{2\mu_0ch} = 
+\frac{\lambda c\mu_0\alpha_L^2}{2R_K} = 
+\frac{e^2Z_0}{2h}
+```
+
+There exists a deep relationship between the fundamental constants, which also makes them very suitable as a basis for `UnitSystem` dimensional analysis. All of the formulas on this page are part of the `Test` suite to guarantee their universal correctness.
+
+```math
+\mu_{eu} = \frac{m_e}{m_u}, \qquad
+\mu_{pu} = \frac{m_p}{m_u}, \qquad
+\mu_{pe} = \frac{m_p}{m_e}, \qquad
+\alpha_\text{inv} = \frac{1}{\alpha}, \qquad
+\alpha_G = \left(\frac{m_e}{m_P}\right)^2
+```
+
+```@docs
+αinv
+```
+
+## Fundamental Constants
+
+```math
+\Delta\nu_{\text{Cs}} = \Delta\tilde\nu_{\text{Cs}}c = \frac{\Delta\omega_{\text{Cs}}}{2\pi}  = \frac{c}{\Delta\lambda_{\text{Cs}}} = \frac{\Delta E_{\text{Cs}}}{h}
+```
+
+```@docs
+hyperfine
+```
+
+```math
+c = \frac1{\alpha_L\sqrt{\mu_0\varepsilon_0}} = \frac{1}{\alpha}\sqrt{\frac{E_h}{m_e}} = \frac{\hbar\alpha}{m_e r_e}  = \frac{e^2k_e}{\hbar\alpha} = \frac{m_e^2G}{\hbar\alpha_G}
+```
+```@docs
+lightspeed
+```
+
+```math
+h = 2\pi\hbar = \frac{2e\alpha_L}{K_J} = \frac{8\alpha}{\lambda c\mu_0K_J^2} = \frac{4\alpha_L^2}{K_J^2R_K}
+```
+```@docs
+planck
+```
+
+```math
+\hbar = \frac{h}{2\pi} = \frac{e\alpha_L}{\pi K_J} = \frac{4\alpha}{\pi\lambda c\mu_0K_J^2} = \frac{2\alpha_L}{\pi K_J^2R_K}
+```
+```@docs
+planckreduced
+```
+
+```math
+m_P = \sqrt{\frac{\hbar c}{G}} = \frac{m_e}{\sqrt{\alpha_G}} = \frac{2R_\infty h}{c\alpha^2\sqrt{\alpha_G}}
+```
+```@docs
+planckmass
+```
+
+```math
+G = \frac{\hbar c}{m_P^2} = \frac{\hbar c\alpha_G}{m_e^2} = \frac{c^3\alpha^4\alpha_G}{8\pi R_\infty^2 h} = \frac{\kappa c^4}{8\pi}
+```
+```@docs
+newton
+```
+
+```math
+\kappa = \frac{8\pi G}{c^4} = \frac{8\pi\hbar}{c^3m_P^2} = \frac{8\pi\hbar\alpha_G}{c^3m_e^2} = \frac{\alpha^4\alpha_G}{R_\infty^2 h c}
+```
+```@docs
+einstein
+```
+
+## Atomic Constants
+
+```math
+m_u = \frac{M_u}{N_A} = \frac{m_e}{\mu_{eu}} = \frac{m_p}{\mu_{pu}} = \frac{2R_\infty h}{\mu_{eu}c\alpha^2} = \frac{m_P}{\mu_{eu}}\sqrt{\alpha_G}
+```
+```@docs
+atomicmass
+```
+
+```math
+m_p = \mu_{pu} m_u = \mu_{pu}\frac{M_u}{N_A} = \mu_{pe}m_e = \mu_{pe}\frac{2R_\infty h}{c\alpha^2} = m_P\mu_{pe}\sqrt{\alpha_G}
+```
+```@docs
+protonmass
+```
+
+```math
+m_e = \mu_{eu}m_u = \mu_{eu}\frac{M_u}{N_A} = \frac{m_p}{\mu_{pe}} = \frac{2R_\infty h}{c\alpha^2} = m_P\sqrt{\alpha_G}
+```
+```@docs
+electronmass
+```
+
+```math
+E_h = m_e(c\alpha)^2 = \frac{\hbar c\alpha}{a_0} = \frac{\hbar^2}{m_ea_0^2} = 2R_\infty hc = m_P\sqrt{\alpha_G}(c\alpha)^2
+```
+```@docs
+hartree
+```
+
+```math
+R_\infty = \frac{E_h}{2hc} = \frac{m_e c\alpha^2}{2h} = \frac{\alpha}{4\pi a_0} = \frac{m_e r_e c}{2ha_0} = \frac{\alpha^2m_ec}{4\pi\hbar}  = \frac{m_Pc\alpha^2\sqrt{\alpha_G}}{2h}
+```
+```@docs
+rydberg
+```
+
+```math
+a_0 = \frac{\hbar}{m_ec\alpha} = \frac{\hbar^2}{k_e m_ee^2} = \frac{\mu_{pe}a_0^*}{\mu_{pe}+1} = \frac{r_e}{\alpha^2} = \frac{\alpha}{4\pi R_\infty}
+```
+```@docs
+bohr
+```
+
+```math
+a_0^* = \left(1+\frac{1}{\mu_{pe}}\right)a_0
+```
+```@docs
+bohrreduced
+```
+
+```math
+r_e = \frac{\hbar\alpha}{m_ec} = \alpha^2a_0 = \frac{e^2 k_e}{m_ec^2} = \frac{2hR_\infty a_0}{m_ec} = \frac{\alpha^3}{4\pi R_\infty}
+```
+```@docs
+electronradius
+```
+
+## Thermodynamic Constants
+
+```math
+M_u = m_uN_A = N_A\frac{m_e}{\mu_{eu}} = N_A\frac{m_p}{\mu_{pu}} = N_A\frac{2R_\infty h}{\mu_{eu}c\alpha^2}
+```
+```@docs
+molarmass
+```
+
+```math
+N_A = \frac{R_u}{k_B} = \frac{M_u}{m_u} = M_u\frac{\mu_{eu}}{m_e} = M_u\frac{\mu_{eu}c\alpha^2}{2R_\infty h}
+```
+```@docs
+avogadro
+```
+
+```math
+k_B = \frac{R_u}{N_A} = m_u\frac{R_u}{M_u} = \frac{m_e R_u}{\mu_{eu}M_u} = \frac{2R_uR_\infty h}{M_u \mu_{eu}c\alpha^2}
+```
+```@docs
+boltzmann
+```
+
+```math
+R_u = k_B N_A = k_B\frac{M_u}{m_u} = k_BM_u\frac{\mu_{eu}}{m_e} = k_BM_u\frac{\mu_{eu}c\alpha^2}{2hR_\infty}
+```
+```@docs
+universal
+```
+
+```math
+\sigma = \frac{2\pi^5 k_B^4}{15h^3c^2} = \frac{\pi^2 k_B^4}{60\hbar^3c^2} = \frac{32\pi^5 h}{15c^6\alpha^8} \left(\frac{R_uR_\infty}{\mu_{eu}M_u}\right)^4
+```
+```@docs
+stefan
+```
+
+```math
+a = 4\frac{\sigma}{c} = \frac{8\pi^5 k_B^4}{15h^3c^3} = \frac{\pi^2 k_B^4}{15\hbar^3c^3} = \frac{2^7\pi^5 h}{15c^7\alpha^8} \left(\frac{R_uR_\infty}{\mu_{eu}M_u}\right)^4
+```
+```@docs
+radiationdensity
+```
+
+```math
+K_{\text{cd}} = \frac{I_v}{\int_0^\infty \bar{y}(\lambda)\cdot\frac{dI_e}{d\lambda}d\lambda}, \qquad 
+\bar{y}\left(\frac{c}{540\times 10^{12}}\right)\cdot I_e = 1
+```
+```@docs
+luminousefficacy
+```
+
+## Electromagnetic Constants
+
+```math
+\lambda = \frac{4\pi\alpha_B}{\mu_0\alpha_L} = 4\pi k_e\varepsilon_0 = Z_0\varepsilon_0c
+```
+```@docs
+rationalization
+```
+
+```math
+\mu_0 = \frac{1}{\varepsilon_0 (c\alpha_L)^2} = \frac{4\pi k_e}{\lambda (c\alpha_L)^2} = \frac{2h\alpha}{\lambda c(e\alpha_L)^2} = \frac{2R_K\alpha}{\lambda c\alpha_L^2}
+```
+```@docs
+permeability
+```
+
+```math
+\varepsilon_0 = \frac{1}{\mu_0(c\alpha_L)^2} = \frac{\lambda}{4\pi k_e} = \frac{\lambda e^2}{2\alpha hc} = \frac{\lambda}{2R_K\alpha c}
+```
+```@docs
+permittivity
+```
+
+```math
+k_e = \frac{\lambda}{4\pi\varepsilon_0} = \frac{\mu_0\lambda (c\alpha_L)^2}{4\pi} = \frac{\alpha \hbar c}{e^2} = \frac{R_K\alpha c}{2\pi} = \frac{\alpha_B}{\alpha_L\mu_0\varepsilon_0} = k_mc^2
+```
+```@docs
+coulomb
+```
+
+```math
+k_m = \alpha_L\alpha_B = \mu_0\alpha_L^2\frac{\lambda}{4\pi} = \frac{k_e}{c^2} = \frac{\alpha \hbar}{ce^2} = \frac{R_K\alpha}{2\pi c}
+```
+```@docs
+ampere
+```
+
+```math
+\alpha_L = \frac{1}{c\sqrt{\mu_0\varepsilon_0}} = \frac{\alpha_B}{\mu_0\varepsilon_0k_e} = \frac{4\pi \alpha_B}{\lambda\mu_0} = \frac{k_m}{\alpha_B}
+```
+```@docs
+lorentz
+```
+
+```math
+\alpha_B = \mu_0\alpha_L\frac{\lambda}{4\pi} = \alpha_L\mu_0\varepsilon_0k_e = \frac{k_m}{\alpha_L} = \frac{k_e}{c}\sqrt{\mu_0\varepsilon_0}
+```
+```@docs
+biotsavart
+```
+
+```math
+e = \sqrt{\frac{2h\alpha}{Z_0}} = \frac{2\alpha_L}{K_JR_K} = \sqrt{\frac{h}{R_K}} = \frac{hK_J}{2\alpha_L} = \frac{F}{N_A}
+```
+```@docs
+charge
+```
+
+```math
+F = eN_A = N_A\sqrt{\frac{2h\alpha}{Z_0}} = \frac{2N_A\alpha_L}{K_JR_K} = N_A\sqrt{\frac{h}{R_K}} = \frac{hK_JN_A}{2\alpha_L}
+```
+```@docs
+faraday
+```
+
+```math
+Z_0 = \mu_0\lambda c\alpha_L^2 = \frac{\lambda}{\varepsilon_0 c} = \lambda\alpha_L\sqrt{\frac{\mu_0}{\varepsilon_0}} = \frac{2h\alpha}{e^2} = 2R_K\alpha
+```
+```@docs
+impedance
+```
+
+```math
+G_0 = \frac{2e^2}{h} = \frac{4\alpha}{Z_0} = \frac{2}{R_K} = \frac{hK_J^2}{2\alpha_L^2} = \frac{2F^2}{hN_A^2}
+```
+```@docs
+conductance
+```
+
+```math
+R_K = \frac{h}{e^2} = \frac{Z_0}{2\alpha} = \frac{2}{G_0} = \frac{4\alpha_L^2}{hK_J^2} = h\frac{N_A^2}{F^2}
+```
+```@docs
+klitzing
+```
+
+```math
+K_J = \frac{2e\alpha_L}{h} = \alpha_L\sqrt{\frac{8\alpha}{hZ_0}} = \alpha_L\sqrt{\frac{4}{hR_K}} = \frac{1}{\Phi_0} = \frac{2F\alpha_L}{hN_A}
+```
+```@docs
+josephson
+```
+
+```math
+\Phi_0 = \frac{h}{2e\alpha_L} = \frac{1}{\alpha_L}\sqrt{\frac{hZ_0}{8\alpha}} = \frac{1}{\alpha_L}\sqrt{\frac{hR_K}{4}} = \frac{1}{K_J} = \frac{hN_A}{2F\alpha_L}
+```
+```@docs
+magneticflux
+```
+
+```math
+\mu_B = \frac{e\hbar\alpha_L}{2m_e} = \frac{\hbar\alpha_L^2}{m_eK_JR_K} = \frac{h^2K_J}{8\pi m_e} = \frac{\alpha_L\hbar F}{2m_e N_A} = \frac{ec\alpha^2\alpha_L}{8\pi R_\infty}
+```
+```@docs
+magneton
+```
+
+## Constants Index
+
+```@index
+Pages = ["constants.md","units.md"]
+```
+