Please comment on my assumptions and results, this has confused me for some time. Thanks(adsbygoogle = window.adsbygoogle || []).push({});

The following is an attempt to reconcile the critical density of the universe with the amount of observable matter as represented by number of stars.

Assumptions for critical density: Hubble constant (H) = 72 km/sec/Mpc or 2.34 x e-18/sec; volume of universe = 9.22 x e84 cm3; cosmological constant = 7.12 x e-30 (from Brian Greene’s Hidden Reality, page 337); and ratio of matter (baryonic) to dark matter is 1 to 5. majority of baryonic matter exists as stars.

Calculation of mass based on critical density : critical density = 3 x H2/(8 x pie x G) = 9.81 x e-30 gm/cm3; density of matter and dark matter = 2.69 x e-30 gm/cm3 (9.81 x e-30 minus 7.12 x e-30); density of matter = .45 x e-30 gm/cm3 (ratio of 1 to 5); mass of both matter and dark matter = 2.47 x e55gm (volume x density); mass of dark matter = 20.6 x e54 gm; and mass of matter = 4.1 x e54 gm.

Assumptions for number of stars: number of galaxies = e11; number of stars per galaxy = 5 x e10; average mass of star = .6 x e33 gm (.3 x sun’s mass).

Calculation of matter based on number of stars: matter = 5.4 x e54 gm.

Thus, using these assumptions the results are reasonably close, 4.1 to 5.4 x e54 gm for matter. When dark matter is included, 2.47 x e55 gm, the result is also close to the e55 gm, which is based on CMB splotches size (stated in Hidden Reality, page 275).

Jim Johnson, Jan 22, 2012

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# Critical density and observable mass

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