Download Astronomy II (Astr 1020) Homework #6 - Prof. Richard Ignace and more Assignments Astronomy in PDF only on Docsity! Astronomy II (Astr 1020) Spring 2008 Prof Richard Ignace HOMEWORK #6 Notes: You will need a calculator, a pencil, and a standard scantron. Each question has one correct answer. Choose the best answer for each. Mark your answer on the scantron. This homework is due at the beginning of class on April 15. Late homeworks will not be accepted. 1. Olbers’ paradox is best summarized by which of the following? a) If the Universe has an infinite age, why hasn’t it collapsed? b) If the Universe is finite in space, does it have an edge? c) If the Universe is finite in time, what occured before the Big Bang? d) If the Universe began as a single “point,” how can it be infinite? e) Why is the night sky dark? 2. The Cosmological Principle implies which one of the following are valid: a) The Doppler effect and Euclidean geometry b) Newtonian mechanics and relativity c) Homogeneity and isotropy of the Universe d) Hubble’s Law and the curvature of the Universe e) Great taste and less filling 3. Why does the presence of quasars at great distances (and only at great distances) from our galaxy imply that the Perfect Cosmological Principle is not valid? a) The distances and radial velocities for the quasars violate the Hubble relation. b) They show that the Universe was generally different at an earlier time. c) The quasars are so bright that no known energy source can possibly power them. d) The great distances to the quasars allow us to observe gravitational lensing effects. e) There is no evidence that galaxies have formed at such great distances. 1 4. The Principle of Equivalence states that a) Before inflation, there was an epoch in which all four forces were combined into one. b) The Microwave Background Radiation has a temperature equivalent to that of a perfect radiator (“black body”) of 3 K temperature. c) Gravitational attraction and accelerated motion are equivalent. d) Light can be described both as a particle and as a wave. e) After inflation, our Universe evolved into a flat geometry. 5. One of the curious results of General Relativity and curved spacetime is gravitational redshift. When light is emitted by a star, its wavelength changes (gets longer) as it travels outward through space. The formula for this shift is ∆λ/λ0 = GM/Rc 2, where M is the mass of the star, R its radius, G the gravitational constant, and c is the speed of light. The new wavelength is λ = λ0 + ∆λ, for λ0 the original wavelength. (Like getting a raise in salary, where you have your old salary, your raise, and then your new salary is the sum.) Consider a neutron star of 2M and 10 km. If light of 3000 Å is emitted at the surface of the star, what wavelength will it have upon reaching the Earth? a) 900 Å b) 2110 Å c) 3000 Å d) 3900 Å 6. The fact that the Microwave Background Radiation has almost exactly the same spectrum in all directions in the sky is evidence that the Universe is: a) Isotropic b) Expanding c) Redshifted d) Filled with dust clouds e) Filled with stars 7. What observational fact is explained by inflation? a) The existence of black holes. b) The isotropy of our Universe. c) The primordial abundances of H and He. d) The formation of elliptical galaxies. 8. In Special Relativity observers moving at different speeds fail to agree on simultaneity. One of the consequences is a thing called time dilation: Moving clocks tick slower. Suppose you have a friend who is an astronaut. In a test flight, the astronaut reaches escape speed from the Earth at 11 km/s. Your friend’s watch ticks slower than yours by the factor Γ = √ 1 − v2/c2, where c is the speed of light, and v is the rocket speed. Determine the difference in these clock rates, 1 − Γ. (This means when 1 second passes on your watch, some fraction of a second Γ will pass on your friend’s watch. Find the difference between the two values.) a) 6.72× 10−10 seconds b) 1.34× 10−9 seconds c) 0.99999 seconds d) 0.5 seconds 2
