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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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The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, and so the neutron star spins rapidly. If the initial core radius is\({\rm{5 \times 1}}{{\rm{0}}^{\rm{5}}}{\rm{ km}}\)and it collapses to\({\rm{10}}{\rm{.0 km}}\), find the neutron star鈥檚 angular velocity in revolutions per second, given the core鈥檚 angular velocity was originally\({\rm{1}}\)revolution per\({\rm{30}}\)days.
Suppose you measure the red shifts of all the images produced by gravitational lensing, such as in figure below. You find that the central image has a red shift less than the outer images, and those all have the same red shift. Discuss how this not only shows that the images are of the same object, but also implies that the red shift is not affected by taking different paths through space. Does it imply that cosmological red shifts are not caused by traveling through space (light getting tired, perhaps)?
If some unknown cause of red shift鈥攕uch as light becoming 鈥渢ired鈥� from traveling long distances through empty space鈥攊s discovered, what effect would there be on cosmology?
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 鈥渕atter dominated鈥�? Explain briefly.
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.
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