This paper investigates the galaxy rotation curve problem while validating dark matter asthe primary solution. Standard Newtonian Dynamics show that stellar speeds decrease withradial distance from the central area of galaxies. Since the early 20th century, physicists have found flat rotation curves during observations, which demonstrate unidentified mass in galaxies that they have termed dark matter. The primary focus of this investigation delves into how welldark matter functions as an answer to resolve the galaxy rotation curve issue. The study evaluatesthe accuracy of dark matter models, particularly the NFW and Burkert profiles, by comparingmathematical model-generated rotation curves with experimental data obtained from the Gaiaand APOGEE databases. The first outcome shows that standard baryonic matter explanations donot duplicate observed rotation patterns, particularly in the Milky Way. The combination of NFWand Burkert profiles produces significant improvements in the match while analyzing older datapoints. Recently acquired data with elevated accuracy shows departures from current dark mattertheory to describe galaxy rotation curves. Current data requires evaluating alternative scientificmodels, including Modified Newtonian Dynamics (MOND) and revised models of dark matterdistributions. This paper indicates that dark matter remains the primary theory for unexplained observations, yet details that high-quality new datasets demand improved theoretical models. The research advances the ongoing astrophysical discussions about how galaxies function and shape dark matter patterns and potential modern physics theories beyond existing theoretical boundaries.