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# homework7 - Astronomy 362 Problem Set#6 Due Friday March 7...

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Astronomy 362 Problem Set #6 Due Friday, March 7 at 12 noon In the homework problems below, “C&O” refers to your textbook. I have selected the problems with the expectation that they will take up to 1 hour of hard thinking/calculating each. If you are taking longer than this, feel free to come by my office to hash out where you are stuck. Note on collaborating: You may work together on this problem set, but all work presented here must be your own. You must clearly acknowledge any people you collaborated with. ASSUMED READING: Please finish C&O Chapter 25 (Sections 3 and 4) for homework (if you haven’t already). 1. Explain (in words) how the virial theorem for gravitational systems 2 K + U = 0 allows you to use the redshift-measured velocities for galaxies in a galaxy cluster to determine the mass of the galaxy cluster. I am not asking you to actually do any derivations of an expression for the mass, rather, I want you to explain how you obtain K and U and how they are related to velocities and the masses. 2. [C&O 25.11 (tweaked)] Let’s consider the evidence for a supermassive black hole at the center of our neighbor, the Andromeda galaxy (aka M31). a. From the data shown i n F i g u r e 2 5 . 3 7 (reproduced here) for the stellar rotational velocities near the c e n t e r o f M 3 1 , estimate the amount of mass within 1” of the center of the g a l a x y ( i n s o l a r masses). Compare your answer with the value quoted in the Figure 25.37 The stellar velocity dispersion and rotational velocities of stars near the center of M31. measured along

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