Circular orbits around a Schwarzschild black hole integrated with PyGRO. The top panels display the resulting orbits on the equatorial plane, with the black circle representing the central black hole. The bottom panels show the effective potential in Eq. (12) computed with PyGRO for the distinct orbital configurations. We analyze: (left panels) an unstable circular orbit with a = 5M, thus lying on a maximum of the effective potential. The instability of the orbit manifests with the orbit falling into the black hole (gray dashed line) due to the accumulation of numerical errors when integrating for a long time interval. This example orbit is labeled as (2) in Table 1; (central panels) the case with a = 6M corresponding to the ISCO and thus a saddle point in the effective potential; (right panels) a normal stable circular orbit which can be realized for all a > 6M, corresponding to local minimums of the effective potential. This example orbit is labeled as (3) in Table 1.