Final answer:
William Herschel concluded the solar system was at the center of the Milky Way by counting stars in a flattened disc structure around the sky.
Step-by-step explanation:
In 1785, William Herschel concluded that the solar system was at the center of the Milky Way Galaxy after using a large reflecting telescope to observe the stars. Herschel and his sister Caroline counted stars in different directions and found that most stars lay within a flattened structure that encircled the sky, with roughly the same number of stars in any direction around this disc. He incorrectly assumed the Sun was near this hub due to his limited observation range, hindered by interstellar dust.
Thus, they inferred that the Sun must be near the 'hub' of this disc-shaped galaxy. However, since they were observing from within the galaxy, like trying to map New York City from Times Square instead of from a helicopter, Herschel's view was limited to the stars within about 6000 light-years due to the absorption of light by interstellar dust. Today, we know that we reside in just a small section of the galaxy's entire 100,000-light-year-diameter disc.