Exercise 1 Using the data above in Table 1, make a plot of right ascension versus declination on your printed out Milky Way Globular Clusters Distribution Graph (Diagram 1-the top plot). RA is along the x-axis and goes from 0 to 24 hours, Dec is on the y-axis and goes from +90 to 0 to –90 degrees.) Insert the plot into your lab report with your signature and date. You will type your answers to the below questions in your lab report and then scan/photo your graph(s) and insert them into your lab document. Again, it would be helpful to review the Exploration from Module 1: “Math Primer for Astronomy” (note this contains link for a free online scientific calculator). There are also good math examples in the Appendix of our eText. Would you describe the distribution of clusters on the plot as random, or is there a pattern (explain your answer)? Now look at your plot and point in the direction in which you see most of the globular clusters. This is the general direction of the Galactic Center. Estimate the center of the distribution of the globular clusters. Also estimate (no calculation required — just an educated estimate) the accuracy of determining this center. You have now determined the rough center of our Galaxy! RA = ____________________ ± ________________ Dec = ____________________ ± ________________ Shapely was correct in thinking that the distribution of globular clusters could reveal something about the Galaxy as a whole. He went one step further. He used the locations of the globular clusters to determine the distance to the Galactic Center. His result was surprisingly accurate and differed from the modern value by less than 10%. So, let’s follow in his footsteps. The next step is to determine the distance to the clusters. Shapely did this by using RR Lyrae stars. These are variable stars, which have a relatively narrow range of luminosities. From the difference between the apparent magnitudes (measured from his photographic plates) and the absolute magnitudes (calculated from the luminosities), he calculated the distances in parsecs to the star (via: m - M = 5log10(d) + 5). So now we have the distances and the directions of the globular clusters and we can determine the 3-dimensional distributions of the globular clusters relative to us. However, we will use a different coordinate system that is based on galactic latitude and longitude rather than RA and Dec. The plane of the Galaxy is designated as “0 latitude”. Why would we want to do this? RA and Dec is a messy coordinate system that depends on our orientation in space and the earth’s rotation around its axis. The system based on galactic latitude and longitude is therefore simpler. However, it means that we have to transform the measured RA and DEC positions of the globular clusters and galactic latitude and longitude. To simplify things even further, let’s express the galactic latitude and longitude in terms of x, y, and z coordinates. The advantage of this is that x,.