(1) (235 points.) (a) (2 points.) What is Olbers's paradox and why is it puzzling? (b)...

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(1) (235 points.) (a) (2 points.) What is Olbers's paradox and why is it puzzling? (b) (3 points.) What are three possible resolutions of it? (2) (1+1+1 = 3 points.) State Hubble's law, explain its meaning, and argue that the Universe is expanding. (3) (3 points.) Explain how the "center" of the expansion of the Universe can be in an unobservable spatial dimension. (4) (1+1+1+1 = 4 points.) Can Hubble's law be used to determine the distance of (a) a Centauri and other stars relatively near the Sun, (b) the center of our Galaxy, (c) the Large Magellanic Cloud, a satellite of our Galaxy, and (d) a cluster of galaxies very far from the Local Group? (5) (2 points.) If the speed of light were infinite, would there still be a way for astronomers to look back at galaxies as they appeared long ago? (1) (235 points.) (a) (2 points.) What is Olbers's paradox and why is it puzzling? (b) (3 points.) What are three possible resolutions of it? (2) (1+1+1 = 3 points.) State Hubble's law, explain its meaning, and argue that the Universe is expanding. (3) (3 points.) Explain how the "center" of the expansion of the Universe can be in an unobservable spatial dimension. (4) (1+1+1+1 = 4 points.) Can Hubble's law be used to determine the distance of (a) a Centauri and other stars relatively near the Sun, (b) the center of our Galaxy, (c) the Large Magellanic Cloud, a satellite of our Galaxy, and (d) a cluster of galaxies very far from the Local Group? (5) (2 points.) If the speed of light were infinite, would there still be a way for astronomers to look back at galaxies as they appeared long ago?