Abstract
In an effort to provide additional opportunities for active and cooperative learning by students in introductory earth-science classes, I have developed an exercise on the use of globular clusters to determine the size of the Milky Way Galaxy and our position in it. The exercise has the added virtue of dealing with one of the fundamental astronomical questions of the twentieth century, namely the nature of the Milky Way Galaxy and Earth's position in the Galaxy. In the early years of this century, the most widely accepted model of the Milky Way Galaxy was that developed by J.C. Kapteyn who postulated that the Galaxy is a flattened ellipsoidal system of stars with a diameter of 50 to 60 thousand light years, with the earth located a bit above the plane of the system and only about 2 thousand light years from the center. It was the opinion of most astronomers at the time that the Milky Way Galaxy was the cosmos, the Universe. An alternative model was proposed by H. Shapley in the years 1915-17 on the basis of his studies of globular clusters, which are distinctive, highly luminous, spherical clusters of as many as a million stars. Shapley found that the globular clusters define a system with a diameter of approximately 325 thousand light years, with the earth located about 50 thousand light years from the center of the system. Subsequent work has substantially decreased Shapley's dimensions, but his picture of the Milky Way as based on the spatial distribution of the globular clusters, with Earth located well away from the center has stood the test of time. In this exercise, students can be given modern globular cluster data either as celestial coordinates and distances or as x, y, and z coordinates with Earth at the origin of the coordinate system. They are then asked to determine the size of the system as defined by the clusters and Earth's position in that system. The problem can be presented to the students in a variety of ways requiring various levels of mathematical and conceptual sophistication, and a variety of methods, ranging from the relatively simple to fairly complex (including computer plotting) can be used to develop solutions. Even the relatively simple methods lead to a picture that agrees spatially and dimensionally with the model almost universally accepted by astronomers.
