Question

the location of the center of our galaxy was first determined by observations of
the sun.
black holes.
globular clusters.
the motions of nearby stars.
the spiral arms.

Explanation:

Harlow Shapley used globular clusters to determine the location of the Milky Way's center. He assumed globular clusters form a spherical distribution around the galactic center. By mapping their positions, he found the center was not near the Sun (which was previously thought). Black holes (like Sagittarius A*) were discovered later. The Sun is just a star in the galaxy. The motions of nearby stars and spiral arms weren't the first - used methods for this specific determination.

Answer:

globular clusters.