What governs the orbital paths of stars around the Milky Way's galactic center?

The massive gravitational pull exerted by the collective mass of the galaxy

Stars within the Milky Way galaxy are subject to immense gravitational forces generated by the combined mass of all the stars, gas, dust, and dark matter concentrated toward the galactic center. This collective gravity establishes a dominant inward pull. For a star to maintain a stable path rather than spiraling inward, it must possess a corresponding sideways motion, or orbital velocity, that perfectly balances this inward gravitational force. This dynamic equilibrium results in stars tracing established, curved paths, analogous to planets orbiting the Sun. If the star's velocity were too slow relative to the gravitational pull, it would fall toward the center; if too fast, it would fly out of the galaxy. This balance ensures their long-term, stable orbits over billions of years.