????\revised????\accepted????\shorttitleRingsandCloseEncounters\shortauthorsWoodetal. The field of ringed Centaurs is only a few years old. Since Centaurs are known to regularly encounter the giant planets, it is of interest to explore the effect of a close encounter between a ringed Centaur and a giant planet on the ring structure. The severity of such an encounter depends on quantities such as the small body mass; velocity at infinity, \(v_{inf}\); ring orbital radius, \(r\); and encounter distance. In this work, we derive a formula for a critical distance at which the radial force is zero on a collinear ring particle in the four-body, circular restricted, planar problem. Numerical simulations of close encounters with Jupiter or Uranus in the three-body planar problem are made to experimentally determine the largest encounter distance, \(R\), at which the effect on the ring is ”noticeable” using different values of small body mass, \(v_{inf}\), and \(r\). \(R\) values are compared to the critical distance. We find that \(R\) lies inside the critical distance for Centaurs with masses \(\ll\) the mass of Pluto but can lie beyond it for Centaurs with the mass of Pluto and ring structure analogous to Chariklo’s. Changing the mass by a factor of almost 4 changed \(R\) by \(\leq 0.2\) tidal disruption distance, \(R_{td}\). Effects on \(R\) due to changes in \(v_{inf}\), or \(r\) are found to be \(\leq\) 1.5\(R_{td}\). \(R\) values found using a four-body problem suggest that the critical distance might be useful as a first approximation of the constraint on \(R\).