Astronomy is the scientific study of objects beyond Earth: planets, stars, galaxies, and the cosmos itself. Observations are made with ground-based and satellite-borne telescopes spanning the entire electromagnetic spectrum from radio through gamma rays. Data structures and scientific problems are diverse, so that many statistical techniques are needed to advance our understanding of cosmic objects and phenomena. Mixture models have played a significant role in such analyses, though not always under this name. The method is used for many purposes, ranging from the classification of objects in a multidimensional parameter space to the study of spatial clustering patterns of stars or galaxies. This second problem has attracted attention among statisticians. A galaxies data set (Postman et al., 1986), made up of recessional velocities of 83 galaxies in units of kilometers per second, has served as a challenging test case for estimating the number of components in a mixture model.