Final answer:
Globular clusters in a spiral galaxy like the Milky Way are found in the spherical halo that surrounds the galactic disk, where they orbit in long elliptical orbits and are mostly composed of old stars.
Step-by-step explanation:
In a spiral galaxy like the Milky Way, you would look for globular clusters in the halo of the galaxy, orbiting the galactic center in long elliptical orbits. According to Kepler's laws, these clusters would spend most of their time at the apogee of their orbits, where they move slowest. This is because Kepler's second law states that a body in orbit moves faster when it is near the object it is orbiting and slower when it is farther away. The halo region of the galaxy is quite extensive, and it contains a spherical distribution of very old faint stars, among which the globular clusters are found.
Globular clusters are long-lived and can be composed of some of the oldest stars in a galaxy. They are typically located in regions free of interstellar dust, allowing them to be visible at great distances. In contrast, open clusters are commonly found in the disk of the galaxy and are younger than globular clusters. The astronomer Harlow Shapley utilized the positions of globular clusters to map out the spherical volume they occupy and concluded that the center of this system coincides with the center of the Milky Way itself, near Sagittarius.