In 2014, it was announced the discovery of two well-defined rings around the Centaur (10199) Chariklo. It was the first finding of such structures around a small body. In 2015, it was proposed that the Centaur (2060) Chiron may also have a ring. In a previous work, we analyzed how the close encounters with the giant planets would affect the rings of Chariklo. It was found that the most likely result is the survival of the rings. In the present work we broaden
our analysis to (2060) Chiron. Besides Chariklo, Chiron is, up to now, the only known Centaur with a presumed ring. Applying the same method of Araujo, Sfair & Winter (2016), we performed numerical integrations of a system composed by 729 clones of Chiron, the Sun and the giant planets. It was computed the number of close encounters that would disrupt the ring of Chiron along its half-life time. This number was then compared to the one of Chariklo. We found that the probability of Chiron lose its ring due to close encounters with the giant planets
is 5.5 higher than for Chariklo. Our analysis showed that, opposite to Chariklo, Chiron is more likely to stay in an orbit with relatively low inclination and high eccentricity. Thus, we found that Chiron-like orbits are much less favorable to the existence of rings than Chariklo-like orbits. Overall, for observational purposes of rings of Centaurs, we concluded that orbits with high inclinations and low eccentricity should be prioritized.