numbat/modules/physics/constants.nbt

use units::si

### Physics constants

# The speed of light in vacuum
let speed_of_light: Speed = 299_792_458 m / s

# The Newtonian constant of gravitation
let gravitational_constant: Force × Length^2 / Mass^2 =  6.67430e-11 m³ / (kg s²)

# Standard acceleration of gravity on earth
let gravity: Acceleration = 9.80665 m / s²

# The Planck constant
let planck_constant = 6.62607015e-34 J / Hz

# The reduced Planck constant
let ℏ = planck_constant / 2π

# Mass of the electron
let electron_mass: Mass = 9.1093837015e-31 kg

# Elementary charge (charge of the electron)
let elementary_charge: Charge =  1.602176634e-19 C
let electron_charge: Charge = elementary_charge

# Magnetic constant (vacuum magnetic permeability)
let µ0: Force / Current^2 =  1.25663706212e-6 N / A²
let mu0 = µ0

# Electric constant ( vacuum electric permittivity)
let ε0: Capacitance / Length = 8.8541878128e-12 F / m
let eps0 = ε0

# Bohr magneton
let µ_B: Energy / MagneticFluxDensity = 9.2740100783e-24 J / T

# Fine structure constant
let α: Scalar = 7.2973525693e-3

# Proton mass
let proton_mass: Mass =  1.67262192369e-27 kg

# Avogadro constant
let N_A: 1 / AmountOfSubstance = 6.02214076e23 / mol

# Boltzmann constant
let k_B: Energy / Temperature = 1.380649e-23 J / K

# Ideal gas constant
let R: Energy / (AmountOfSubstance × Temperature) = 8.31446261815324 J / (K mol)

# Planck length
let planck_length: Length = sqrt(ℏ gravitational_constant / speed_of_light^3) -> m

# Planck mass
let planck_mass: Mass = sqrt(ℏ speed_of_light / gravitational_constant) -> kg

# Planck time
let planck_time: Time = sqrt(ℏ gravitational_constant / speed_of_light^5) -> s

# Planck temperature
let planck_temperature: Temperature = sqrt(ℏ speed_of_light^5 / (gravitational_constant * k_B^2)) -> K

# Planck energy
let planck_energy: Energy = sqrt(ℏ speed_of_light^5 / gravitational_constant) -> J

# Bohr radius
let a0: Length = 4 pi ε0 ℏ^2 / (electron_charge^2 electron_mass)