Modeling Centaur orbits is difficult. From the abstract cited "...Here, we examined 17 multiple-opposition high-inclination Centaurs and the two polar trans-neptunian objects 2008 KV42 and (471325) 2011 KT19. The statistical distributions show that their orbits were nearly polar 4.5 Gyr in the past, and were located in the scattered disc and inner Oort cloud regions. Early polar inclinations cannot be accounted for by current Solar system formation theory as the early planetesimal system must have been nearly flat in order to explain the low-inclination asteroid and Kuiper belts. Furthermore, the early scattered disc and inner Oort cloud regions are believed to have been devoid of Solar system material as the planetesimal disc could not have extended far beyond Neptune’s current orbit in order to halt the planet’s outward migration. The nearly polar orbits of high-inclination Centaurs 4.5 Gyr in the past therefore indicate their probable early capture from the interstellar medium."
Centaur modeling showed a polar inclination orbit some 4.5 billion years ago, something not explained by the solar protoplanetary disk model, also something not observed in astronomy either for the present location of the Centaurs. Here is another link,
New discovery: First asteroid population from outside our solar system Table 1. in the report cited shows what time issues are involved. My note, the report attached in Table 1. shows what is taking place with the 19 Centaurs studied. Short orbital times when extrapolated over long periods, collisions and ejections take place.
"Table 1. Clone statistics at −4.5Gyr. Orbital inclination is denoted by I, eccentricity by e, semimajor axis by a, and perihelion by q. RGD stands for the relative generalized deviation of the Centaur’s orbit. T0 and Tm are the minimum and median lifetimes. Orbital elements are not given to nominal orbit precision to avoid an overcrowded table."
My comment, prograde Chiron is shown. Using the orbital elements provided and my trusty spreadsheet, Chiron has a period about 50.49 years. In a time span of 1E+9 years, Chiron could complete 19.8E+6 perihelion passages but will never survive this long as shown in the report and table calculations, most lifetimes < 100E+6 years in the solar system. Centaur present locations and their orbital stability over 4.5 billion years is the problem, this new model offers a possible solution. Other objects in the solar system like the ring age of Saturn, etc. are issues too in reconciling with the radiometric ages of meteorites used to establish the 4.5 billion years time line.
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