Calculateur de Densité Critique
Calculez la densité critique de l'univers.
Critical Density
0.000000000000000000000000009216 kg/m³
Critical Density vs Hubble Constant (H0)
Formule
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)
The observed value is roughly 9.5 x 10⁻²⁷ kg/m³, equivalent to about 5.7 hydrogen atoms per cubic metre.
Exemple Résolu
Using H0 = 2.27e-18 s⁻¹ (≈ 70 km/s/Mpc).
- 01rho_crit = 3 H0² / (8 pi G)
- 02H0² = (2.27e-18)² = 5.153e-36
- 038 pi G = 1.676e-9
- 04rho_crit = 3 * 5.153e-36 / 1.676e-9
- 05rho_crit ≈ 9.22e-27 kg/m³
Questions Fréquentes
Why is it called the critical density?
It is the precise density at which the universe is geometrically flat. Below it, the universe is open and expands forever (even without dark energy). Above it, the universe is closed.
How do I convert H0 from km/s/Mpc to 1/s?
Divide by 3.086e19 (the number of km in a Mpc). So 70 km/s/Mpc becomes 70 / 3.086e19 ≈ 2.27e-18 s⁻¹.
Is the observed density close to critical?
Yes. Observations indicate the total density is within about 0.4% of the critical value, meaning the universe is very nearly flat.