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Chapter 34: Q1PE (page 1238)
Find the approximate mass of the luminous matter in the Milky Way galaxy, given it has approximately\({\rm{1}}{{\rm{0}}^{{\rm{11}}}}\)stars of average mass\({\rm{1}}{\rm{.5}}\)times that of our Sun.
The mass is obtained as: \({\rm{3 x 1}}{{\rm{0}}^{{\rm{41}}}}\).
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Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass\({\rm{1}}{\rm{.5 \times 1}}{{\rm{0}}^{{\rm{11}}}}\)times that of the Sun (or\({\rm{3 \times 1}}{{\rm{0}}^{{\rm{41}}}}{\rm{ kg}}\)), located\({\rm{30,000 ly}}\)away.
If there is no observable edge to the universe, can we determine where its centre of expansion is? Explain.
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.
Quantum gravity, if developed, would be an improvement on both general relativity and quantum mechanics, but more mathematically difficult. Under what circumstances would it be necessary to use quantum gravity? Similarly, under what circumstances could general relativity be used? When could special relativity, quantum mechanics, or classical physics be used?
(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.
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