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Chapter 34: Q3CQ (page 1236)
Question: If the universe is infinite, does it have a center? Discuss.
Because there is always an equal amount of space surrounding every point and the universe expands uniformly, all points are equivalent and there is no centre.
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To get an idea of how empty deep space is on the average, perform the following calculations: (a) Find the volume our Sun would occupy if it had an average density equal to the critical density of\({\rm{1}}{{\rm{0}}^{{\rm{ - 26}}}}{\rm{kg/}}{{\rm{m}}^{\rm{3}}}\)thought necessary to halt the expansion of the universe. (b) Find the radius of a sphere of this volume in light years. (c) What would this radius be if the density were that of luminous matter, which is approximately\({\rm{5 \% }}\)that of the critical density? (d) Compare the radius found in part (c) with the\({\rm{4 - ly}}\)average separation of stars in the arms of the Milky Way.
The peak intensity of the CMBR occurs at a wavelength of\({\rm{1}}{\rm{.1 - mm}}\). (a) What is the energy in eV of a\({\rm{1}}{\rm{.1 - mm}}\)photon? (b) There are approximately\({\rm{1}}{{\rm{0}}^{\rm{9}}}\)photons for each massive particle in deep space. Calculate the energy of\({\rm{1}}{{\rm{0}}^{\rm{9}}}\)such photons. (c) If the average massive particle in space has a mass half that of a proton, what energy would be created by converting its mass to energy? (d) Does this imply that space is “matter dominated”? Explain briefly.
(a) Estimate the mass of the luminous matter in the known universe, given there are\({\rm{1}}{{\rm{0}}^{{\rm{11}}}}\)galaxies, each containing\({\rm{1}}{{\rm{0}}^{{\rm{11}}}}\)stars of average mass\({\rm{1}}{\rm{.5}}\)times that of our Sun. (b) How many protons (the most abundant nuclide) are there in this mass? (c) Estimate the total number of particles in the observable universe by multiplying the answer to (b) by two, since there is an electron for each proton, and then by\({\rm{1}}{{\rm{0}}^{\rm{9}}}\), since there are far more particles (such as photons and neutrinos) in space than in luminous matter.
Does observed gravitational lensing correspond to a converging or diverging lens? Explain briefly.
Another known cause of red shift in light is the source being in a high gravitational field. Discuss how this can be eliminated as the source of galactic red shifts, given that the shifts are proportional to distance and not to the size of the galaxy.
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