- #1
Orion1
- 973
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This is my equation for the Universe mass based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters in SI units.
Observable Universe mass composition:
[tex]H_0 = 2.32987690448613 \cdot 10^{- 18} \; \text{s}^{- 1}[/tex] - Hubble parameter (WMAP)
[tex]\Omega_b = 0.00444[/tex] - Baryon density
[tex]\Omega_{dm} = (\Omega_m - \Omega_b) = 0.2216[/tex] - dark matter density
[tex]dN_s = 10^{22}[/tex] - HST observable stellar number
[tex]dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3)[/tex] - HST observable stellar volume
[tex]M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg}[/tex] - solar mass
Observable Universe mass:
[tex]\boxed{M_u = \frac{4 \pi M_{\odot}}{3 \Omega_b} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}[/tex]
[tex]\boxed{M_u = 1.18029735794067 \cdot 10^{55} \; \text{kg}}[/tex]
Gravitationally observable dark matter mass:
[tex]\boxed{M_{dm} = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_{dm}}{\Omega_b} \right) \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}[/tex]
[tex]\boxed{M_{dm} = 2.61553894519654 \cdot 10^{54}}[/tex]
Hubble critical mass:
[tex]\boxed{M_c = \frac{c^3}{2 G H_0}}[/tex]
[tex]\boxed{M_c = 8.66352589042757 \cdot 10^{52} \; \text{kg}}[/tex]
Reference:
"[URL law - Wikipedia[/URL]
http://en.wikipedia.org/wiki/Lambda-CDM_model"
http://en.wikipedia.org/wiki/Universe"
http://en.wikipedia.org/wiki/Observable_universe"
http://en.wikipedia.org/wiki/Dark_matter"
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