临界密度计算器 — 公式

Critical Density of the Universe

The critical density is the dividing line between a universe that expands forever and one that eventually re-collapses.

Formula

rho_crit = 3 H0² / (8 pi G)

  • *H0* must be in SI units of 1/s (about 2.27 x 10⁻¹⁸ s⁻¹ for 70 km/s/Mpc)
  • *G* = 6.674 x 10⁻¹¹ N m² kg⁻²

    • The observed value is roughly 9.5 x 10⁻²⁷ kg/m³, equivalent to about 5.7 hydrogen atoms per cubic metre.

    计算示例

    Using H0 = 2.27e-18 s⁻¹ (≈ 70 km/s/Mpc).

    1. rho_crit = 3 H0² / (8 pi G)
    2. H0² = (2.27e-18)² = 5.153e-36
    3. 8 pi G = 1.676e-9
    4. rho_crit = 3 * 5.153e-36 / 1.676e-9
    5. rho_crit ≈ 9.22e-27 kg/m³