Physics Constants Reference
CODATA values of fundamental constants, astronomical data, and practical notes on choosing unit systems and scaling constants for simulation.
Fundamental Constants (SI)
| Symbol | Name | Value | Unit | Notes |
|---|---|---|---|---|
| c | Speed of light in vacuum | 2.997 924 58 × 10⁸ | m/s | Exact (fixed by SI 2019) |
| h | Planck constant | 6.626 070 15 × 10⁻³⁴ | J·s | Exact (fixed by SI 2019) |
| ℏ | Reduced Planck constant | 1.054 571 817 × 10⁻³⁴ | J·s | ℏ = h / (2π) |
| G | Newtonian gravitational constant | 6.674 30 × 10⁻¹¹ | m³/(kg·s²) | Least precisely known. Rel. uncertainty: 2.2×10⁻⁵ |
| g | Standard gravity (Earth surface) | 9.806 65 | m/s² | Conventional; varies 9.764–9.834 by location |
| e | Elementary charge | 1.602 176 634 × 10⁻¹⁹ | C | Exact (fixed by SI 2019) |
| m_e | Electron rest mass | 9.109 383 70 × 10⁻³¹ | kg | = 0.511 MeV/c² |
| m_p | Proton rest mass | 1.672 621 924 × 10⁻²⁷ | kg | = 938.3 MeV/c² |
| N_A | Avogadro constant | 6.022 140 76 × 10²³ | mol⁻¹ | Exact (fixed by SI 2019) |
| k_B | Boltzmann constant | 1.380 649 × 10⁻²³ | J/K | Exact (fixed by SI 2019). Thermal energy at 300K: 25.9 meV |
| R | Gas constant | 8.314 462 618 | J/(mol·K) | R = k_B · N_A |
| ε₀ | Vacuum permittivity | 8.854 187 8128 × 10⁻¹² | F/m | ε₀ = 1/(μ₀c²) |
| μ₀ | Vacuum permeability | 1.256 637 062 × 10⁻⁶ | N/A² | μ₀ = 4π × 10⁻⁷ (approx) |
| k_e | Coulomb constant | 8.987 551 792 × 10⁹ | N·m²/C² | k_e = 1/(4πε₀) |
| σ | Stefan-Boltzmann constant | 5.670 374 419 × 10⁻⁸ | W/(m²·K⁴) | Blackbody radiation: P = σT⁴ |
| α | Fine-structure constant | 7.297 352 5693 × 10⁻³ | dimensionless | ≈ 1/137. Strength of EM coupling. |
Thermodynamic & Material Properties
| Quantity | Symbol / Value | Unit | Notes |
|---|---|---|---|
| Water density (20°C) | 998.2 | kg/m³ | SPH simulations typically use ρ₀ = 1000 |
| Water dynamic viscosity (20°C) | 1.002 × 10⁻³ | Pa·s | Low viscosity → turbulent flow at moderate Re |
| Water surface tension (20°C) | 0.0728 | N/m | Bubble simulations use simplified surface tension force |
| Air density (STP, 1 atm, 0°C) | 1.293 | kg/m³ | At 20°C: 1.204 kg/m³ |
| Air dynamic viscosity (20°C) | 1.81 × 10⁻⁵ | Pa·s | Used in drag coefficient calculations |
| Speed of sound (air, 20°C) | 343.2 | m/s | Mach number: M = v/343 |
| Sand bulk density (dry) | 1520–1680 | kg/m³ | Varies with grain size and packing |
| Young's modulus (steel) | 200 | GPa | Spring constant for structural FEM |
| Young's modulus (glass) | 70 | GPa | Lower stiffness per unit stress than steel |
| Poisson's ratio (steel) | 0.28–0.30 | dimensionless | Lateral contraction when stretched |
Astronomical Constants
| Symbol | Name | Value (SI) | Notes |
|---|---|---|---|
| AU | Astronomical Unit | 1.495 978 707 × 10¹¹ m | Mean Earth–Sun distance |
| ly | Light-year | 9.460 730 472 × 10¹⁵ m | Distance light travels in 1 Julian year |
| pc | Parsec | 3.085 677 581 × 10¹⁶ m | ≈ 3.26156 ly |
| M☉ | Solar mass | 1.989 × 10³⁰ kg | Reference mass for galaxy simulations |
| R☉ | Solar radius | 6.957 × 10⁸ m | ≈ 109 Earth radii |
| L☉ | Solar luminosity | 3.828 × 10²⁶ W | Energy output per second |
| M⊕ | Earth mass | 5.972 × 10²⁴ kg | Orbital mechanics reference |
| R⊕ | Earth radius (equatorial) | 6.378 137 × 10⁶ m | Tectonic & atmosphere simulations |
| Hubble constant (H₀) | 67–73 km/s/Mpc | Cosmological expansion rate (measure-dependent) |
Choosing Simulation Units
Never use raw SI units in simulations. Gravitational constant G = 6.67 × 10⁻¹¹ in SI will cause floating-point underflow; particle masses of 10⁻²⁷ kg disappear in accumulation errors. Choose a unit system where all quantities are O(1).
Length = AU (1.5×10¹¹ m), Mass = M☉ (2×10³⁰ kg), Time = years → G ≈ 4π² AU³/(M☉·yr²). All values near 1.
Length = particle spacing h₀ (e.g. 0.02 m), ρ₀ = 1000, pressure constant k tuned to speed of sound. Put all in [0,1]×[0,1] simulation box.
Use reduced units: σ (Lennard-Jones diameter) = 1, ε (LJ energy) = 1, m = 1. Temperature in ε/k_B. Avoids 10⁻¹⁰ m / 10⁻²⁷ kg / 10⁻²³ J.
Match units: if lengths in mm, forces in N, then stress in MPa (N/mm²) and E in MPa. Avoid mixing m and mm in same equation.
Non-dimensionalise via Reynolds number Re = ρvL/μ. Set ρ=1, L=1, v reference=1 → tune μ to desired Re. Physical Re maps to simulation directly.
Treat pixels as length unit. Set g ≈ 0.5–2 px/frame² for visible but not instantaneous gravity. Scale spring constants to canvas size.