Crate metrology 

metrology

The physical constants the physica crates share, defined once: the exact SI defining constants, the CODATA 2018 values of G, α, μ₀, ε₀ and the particle masses, the flux quanta, standard gravity, and the astronomical units of mass, distance and time; plus the one-line laws of radioactive decay.

Install

cargo add metrology

Example

use metrology::{C, G, HBAR, SOLAR_MASS};

// The Schwarzschild radius of the Sun, 2GM/c²: about 2.95 km.
let r = 2.0 * G * SOLAR_MASS / (C * C);
assert!((r / 2953.3 - 1.0).abs() < 1e-3);

// The Planck length, √(ħG/c³).
assert!(((HBAR * G / C.powi(3)).sqrt() / metrology::PLANCK_LENGTH - 1.0).abs() < 1e-5);

What is inside

Group	Constants	Source
SI defining constants (exact)	C, H, HBAR, E_CHARGE, K_B, N_A, R_GAS	SI Brochure 2019
Measured	G, ALPHA, MU_0, EPS_0, M_E, M_P, AMU, M_H, MU_B, MU_N, GAMMA_P, PLANCK_LENGTH	CODATA 2018
Flux quanta (exact)	FLUX_QUANTUM (h/2e), JOSEPHSON_CONSTANT (2e/h), DIRAC_FLUX (h/e, one Dirac monopole)	SI Brochure 2019; PDG monopole review
Energy	EV, KEV, MEV, GEV
Molecular binding	WATER_DIMER_D0 (one hydrogen bond, 13.22 kJ/mol)	Rocher-Casterline et al. 2011
decay	activity, activity_step_after_suppression, ec_half_life_shift, CURIE	the decay law; Pommé et al. 2016 and Ohtsuki et al. 2004 for the tests
Derived couplings	EINSTEIN_KAPPA (8πG/c⁴)	Einstein field equations
Earth and astronomy	G0, GM_EARTH, EARTH_ROTATION, MOON_EARTH_MASS_RATIO, GM_MOON, WGS84_A, WGS84_F, GM_SUN, SOLAR_MASS, AU, PARSEC, MPC, YEAR	IERS Conventions 2010; IAU 2015 B3
Reference ellipsoids and potentials	GRS80_F, GRS80_GM, W0_IAU, W0_IHRS, L_G, L_B, EARTH_ANGULAR_MOMENTUM	Moritz 2000; IAU 2000 B1.9 and 2006 B3; IAG 2015 Resolution 1

Applications

Anywhere a calculation must agree with another: the crates in this family all take their constants from here, so a result computed through two of them matches to the last digit. Pin the version to pin the constants, which is what reproducing a published number needs.

How it is checked

A test checks that the derived constants agree with each other: ħ = h/2π, R = N_A k_B, μ₀ε₀c² = 1, α = e²/4πε₀ħc (ħ and R are the 2019 SI’s exact h/2π and N_A k_B, not CODATA’s truncated digits), the Planck length, the solar mass, both magnetons, and the flux quanta (h/e = 2Φ₀, and μ₀ times the Dirac charge 3.291×10⁻⁹ A m). The decay tests reproduce radium’s 0.988 Ci per gram, ⁶⁰Co’s 7.2×10⁻⁴ step after a two-day stop, and ⁷Be’s 0.83% half-life shift in C₆₀.

One of eight crates in physica: physica (all of them, plus cross-domain analogies) · metrology (constants) · geopotential (the gravity field) · gravimetry (missions and GRACE) · gravitational (waves) · gravitics (frontier gravity) · magnetics (magnetism and MHD) · plasmoid (fusion plasma).

Modules

decay

Radioactive decay: the one-line laws other crates share. A source in steady state, made as fast as it decays, has an activity equal to its production rate, so that case needs no function.

Constants

ALPHA

Fine-structure constant.

AMU

Atomic mass constant (one dalton), kg.

AU

Astronomical unit, m (exact, IAU 2012).

C

Speed of light in vacuum, m/s (exact).

DIRAC_FLUX

The flux h/e = 2Φ₀ of one Dirac magnetic monopole, Wb: μ₀ times the Dirac charge g_D = h/(μ₀e), so the monopole’s field μ₀g_D/(4πr²) is fixed by h and e alone.

EARTH_ANGULAR_MOMENTUM

Earth’s spin angular momentum Iω, kg m²/s: 5.86×10³³, the value the LAGEOS and LARES frame-dragging analyses use (Ciufolini & Pavlis 2004).

EARTH_ROTATION

Earth’s nominal mean angular velocity, rad/s (IERS Conventions 2010, Table 1.1; also the GRS80 and WGS84 defining value). GPS uses 7.292 115 146 7×10⁻⁵ (IS-GPS-200).

EINSTEIN_KAPPA

Einstein’s coupling constant 8πG/c⁴, s² kg⁻¹ m⁻¹: the stiffness of spacetime in G_μν = κT_μν. Its reciprocal, 4.8×10⁴² N, is why laboratory stress-energy curves spacetime so little.

EPS_0

Vacuum electric permittivity, F/m.

EV

One electronvolt, J.

E_CHARGE

Elementary charge, C (exact).

FLUX_QUANTUM

Superconducting flux quantum h/2e, Wb: the flux a Cooper-pair loop holds per quantum, and the period of the Aharonov–Bohm phase for paired charges.

G

Newtonian constant of gravitation, m³ kg⁻¹ s⁻² (uncertainty 22 ppm).

G0

Standard acceleration of gravity, m/s² (exact, conventional).

GAMMA_P

Proton gyromagnetic ratio, s⁻¹ T⁻¹ (γ_p/2π = 42.577 MHz/T, the MRI Larmor frequency).

GEV

One gigaelectronvolt, J.

GM_EARTH

Earth’s gravitational parameter GM (IERS 2010, including the atmosphere), m³/s².

GM_MOON

The Moon’s gravitational parameter, m³/s²: GM_EARTH × MOON_EARTH_MASS_RATIO, 4.902 800 2×10¹² and, like GM_EARTH, TT-compatible. The JPL DE430 ephemeris gives 4 902.800 066 km³/s² on its own time scale, 3×10⁻⁸ lower.

GM_SUN

Nominal solar mass parameter GM☉ (IAU 2015 Resolution B3), m³/s².

GRS80_F

GRS80 flattening (Moritz 2000), derived there from its defining J₂; it differs from WGS84’s in the ninth digit. GRS80’s semi-major axis and rotation rate are WGS84_A and EARTH_ROTATION.

GRS80_GM

GRS80’s geocentric gravitational constant (Moritz 2000), m³/s²: the 1980 value, 1.5×10⁻⁷ above GM_EARTH, and the μ of the GPS interface specification.

H

Planck constant, J s (exact).

HBAR

Reduced Planck constant h/2π, J s (exact; CODATA prints it truncated, 1.054 571 817…×10⁻³⁴).

JOSEPHSON_CONSTANT

Josephson constant 2e/h, Hz/V: a junction at voltage V oscillates at K_J·V (483.6 MHz/µV).

KEV

One kiloelectronvolt, J.

K_B

Boltzmann constant, J/K (exact).

L_B

L_B = 1 − dTDB/dTCB (IAU 2006 Resolution B3).

L_G

L_G = 1 − dTT/dTCG, the defining constant of Terrestrial Time (IAU 2000 Resolution B1.9): W0_IAU/c² to its ten digits.

MEV

One megaelectronvolt, J.

MOON_EARTH_MASS_RATIO

The Moon-to-Earth mass ratio (IERS Conventions 2010, Table 1.1).

MPC

Megaparsec, m.

MU_0

Vacuum magnetic permeability, N/A².

MU_B

Bohr magneton eħ/2m_e, J/T.

MU_N

Nuclear magneton eħ/2m_p, J/T.

M_E

Electron mass, kg.

M_H

Mass of a hydrogen atom, kg.

M_P

Proton mass, kg.

N_A

Avogadro constant, mol⁻¹ (exact).

PARSEC

Parsec, m.

PLANCK_LENGTH

Planck length √(ħG/c³), m.

R_GAS

Molar gas constant N_A k_B, J mol⁻¹ K⁻¹ (exact; 8.314 462 618…).

SOLAR_MASS

Solar mass GM☉/G, kg.

W0_IAU

The geoid potential W₀ that Terrestrial Time’s rate was defined from (IAU 2000 Resolution B1.9; IERS Conventions 2010, Table 1.1), m²/s². For time scales and clock rates.

W0_IHRS

The reference potential of the International Height Reference System (IAG 2015 Resolution 1), m²/s²: 2.6 m²/s², about 26 cm, below W0_IAU. For heights.

WATER_DIMER_D0

Dissociation energy D₀ of the water dimer, the energy of one hydrogen bond, J/mol: 1105 ± 10 cm⁻¹ = 13.22 kJ/mol (Rocher-Casterline et al. 2011).

WGS84_A

WGS84 ellipsoid semi-major axis, m.

WGS84_F

WGS84 ellipsoid flattening.

YEAR

Julian year, s.