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jimjohnson
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Please comment on my assumptions and results, this has confused me for some time. Thanks
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
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