Final answer:
Exact dimensions for the Galaxy's disk are difficult to define due to factors such as the obscuring effects of interstellar dust, the absence of a sharp boundary, the variable thickness of the disk based on star populations, and the impracticality of scaled models.
Step-by-step explanation:
It is difficult to give exact dimensions for the Galaxy's disk because of several key challenges in observational astronomy. Firstly, the vast distances to stars and interstellar dust within the Galaxy transform straightforward apparent brightness measurements into complex tasks. For distant galaxies, individual stars are not resolvable, and the apparent brightness is dimmed not solely by distance but also by the interstellar medium—predominantly dust—which obscures and reddens the light of stars.
As a result, initial estimates based on apparent brightness alone led to underestimations of the Galaxy's size. Further complicating matters, the Galaxy does not have a sharp boundary, and its thickness varies depending on whether we observe younger or older star populations. Even the analogy of a scaled model is problematic, as representing the Earth as something tangible leads to an impractical scale for the Galaxy. Lastly, while we understand that the Galaxy consists of a circular disk approximately 100,000 light-years in diameter, complexities arise from factors such as the elliptical orbits of halo stars intersecting the disk. Considering the abovementioned factors and the varying thickness of the Galaxy's components, precise dimensional determination remains challenging.