The topology of equatorial time-like circular orbits around quiescent black holes is a subject of significant interest in the realms of quantum mechanics and gravitational physics. Equatorial orbits in the vicinity of a quiescent black hole exhibit intricate geometrical properties that are crucial for understanding various phenomena, including gravitational lensing and the dynamics of accretion disks. This study delves into the characterization of the topological features of such orbits, shedding light on their stability, frequency, and potential implications for astrophysical observations.