Distance to the Center of the Milky Way

Adapted from Learning Astronomy by Doing Astronomy by Ana Larson

Summary

In this exercise, you will use the locations of globular clusters in the halo to estimate the distance of the Sun from the center of the Milky Way.

Background and Theory

In the not-too-distant past, astronomers though that the Sun was at the center of our galaxy, the Milky Way. Observations and determinations of distances were hampered by the lack of knowledge of interstellar dust, which blocks much of the starlight from distant parts of the galaxy (including the galactic center). It was not until the distances to globular clusters were determined using the RR Lyrae stars that a more accurate picture of the size and shape of our galaxy was constructed. By determining the distribution of the globular clusters, Harlow Shapley was able to determine the diameter of the galaxy, and the distanc to the galactic center.

Procedure
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. 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.

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.
3. Determine the distance from the Sun to the center of the distribution.
4. Determine the direction to the center of the distribution. This is the direction to the center of the galaxy.
5. In which constellation does the center of the galaxy lie?
6. At what time of year is this constellation most conspicuous? Hint: check a planisphere, or the textbook.
7. Why is the Milky Way Galaxy more spectacular in the summer than in the winter? (ignore weather conditions!)
8. Describe the two dimensional space distribution of the globular clusters.
9. How do we know the Sun is not at the center of this distribution?
10. During their long orbit around the center of the Milky Way Galaxy, each globular cluster will cross through the plane of the disk. Why do we find most globular clusters far out in the halo? (Hint: Do Kepler's laws apply to globular clusters?)

Figure 1: Polar Plot of the Distribution of Globular Clusters

Table 1: Globular Cluster Data
NGC # Gal.
Long.
Projected
Distance
(kpc)
NGC # Gal.
Long.
Projected
Distance
(kpc)
NGC # Gal.
Long.
Projected
Distance
(kpc)
NGC # Gal.
Long.
Projected
Distance
(kpc)
104 306 3.5   6273 357 7   288 147 0.3   6284 358 16.1
362 302 6.6   6287 0 16.6   1904 228 14.4   6293 357 9.7
2808 283 8.9   6333 5 12.6   Pal 4 202 30.9   6341 68 6.5
4147 251 4.2   6356 7 18.8   4590 299 11.2   6366 18 16.7
5024 333 3.4   6397 339 2.8   5053 335 3.1   6402 21 14.1
5139 309 5   6535 27 15.3   5272 42 2.2   6656 9 3
5634 342 17.6   6712 27 5.7   5694 331 27.4   6717 13 14.4
Pal 5 1 24.8   6723 0 7   5897 343 12.6   6752 337 4.8
5904 4 5.5   6760 36 8.4   6093 353 11.9   6779 62 10.4
6121 351 4.1   Pal 10 53 8.3   6541 349 3.9   6809 9 5.5
O 1276 22 25   Pal 11 32 27.2   6626 7 4.8   6838 56 2.6
6638 8 15.1   6864 20 31.5   6144 352 16.3   6934 52 17.3
6171 3 15.7   6981 35 17.7   6205 59 4.8   7078 65 9.4
6218 15 6.7   7089 54 9.9   6229 73 18.9   7099 27 9.1
6235 359 18.9   Pal 12 31 25.4   6254 15 5.7   7492 53 15.8
6266 353 11.6