Homework 6: The Milky Way Astro 201 Prof. Bechtold Due: Thursday, October 21, 2010 This homework is patterned after lab assignments from the University of Michigan, and University of Washington Astronomy web sites. Part 1. Estimates of the Sun s motion in the Milky Way Galaxy a. Thickness of the Milky Way. (1 point) The disk of the Milky Way is about 100,000 light years in diameter, and 1000 light years thick. What is the ratio of diameter to thickness of the Milky Way? b. Everyday analogy (4 points) Describe an everyday object that has the same diameter- to- thickness ratio as the Milky Way. Demonstrate that this is the case, using estimates for the size and thickness of the object. The object does not have to be perfectly circular. c. Motion of the Sun up and down in the disk of the Milky Way. (2 points) The Sun moves up and down in the disk of the Milky Way, covering a distance of about 2000 light years (1.9 x 10 16 kilometers) in 65 million years (2.1 x 10 15 seconds). What is the Sun s average speed in this motion (in km/sec)? Recall that speed v = distance traveled/ time
d. Motion of the Sun around the Center of the Milky Way. (3 points) In addition to moving up and down out of the disk of the Milky Way, the Sun orbits around the center of the Milky Way. The Sun is on average about 28,000 light years, or 2.65 x 10 17 km from the center of the Galaxy and orbits in a circle with a period of about 230 million years, or 7.25 x 10 15 seconds. That is, to go around once, the Sun takes 230 million years. Recalling that the circumference of a circle is 2*pi*R, what is the speed of the Sun in its orbit around the center of the Milky Way (in km/sec)? e. Compare your answers in part (c) and (d). (5 points) The Sun s motion in the galaxy is like a merry- go- round; it bobs up and down while orbiting around the center of the Galaxy. Based on the velocities you calculated in the previous two parts, which is the dominant motion? Is this merry- go- round smooth or bumpy?
Part 2. Map the Structure of the Milky Way using Globular Clusters. Harlow Shapley used RR Lyrae variable stars to measure the distance to globular clusters, and then he used the positions of globular clusters relative to the Sun to determine the position of the Sun in the Milky Way. This approach proved more successful than Herschel s earlier attempts, where he counted stars in the Milky Way Disk. The Milky Way disk has a lot of dust in between the stars, and it s difficult to see stars very far in the disk without using infrared cameras. Globular clusters, on the other hand, are distributed in the spherical halo of the Milky Way, and are not as affected by dust obscuration. In this part of the homework, you will plot the positions of the Milky Way globular clusters relative to the Sun, and determine where the center of the Milky Way is. 1. Using the polar graph in Figure 1, plot the galactic longitude versus distance for the globular clusters in Table 1. The Sun is at the center of this polar graph. The constellations in different directions from the Sun are noted: Auriga, Perseus, etc. In this polar plot, the galactic longitude in Table 1 is plotted around the center (zero to 360 degrees), and the distance is plotted by using the circles which are labeled 5, 10, 15, 20, 25 or 30 kiloparsecs. Note that the distance given is not the actual distance, since we have projected a 3-dimensional space onto a 2-dimensional piece of paper. The actual distances are greater than those given here. (10 points) 2. Estimate the center of the distribution of globular clusters, and mark it on the graph. Describe how you defined the center of the distribution. (5 points)
3. Using your graph, measure the distance of the Sun from the center of the Milky Way. (4 points) 4. Towards which constellation does the center of the Milky Way appear, as seen from the Sun? (1 point)
Figure 1: Polar plot of Distribution of Globular Clusters
Table 1. Data for Globular Clusters NGC # is the name of each Globular Cluster Gal. Long. is the Galactic Longitude, in degrees Projected Distance is the distance in kiloparsecs