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Study of a Potential Relationship Between Two Long-Period Comets and Rapid Inward Drifting of Aphelion Due to Orbital-Cascade Resonance

We study a potential genetic relationship of comets C/1846 O1 and C/1973 D1, whose apparent orbital similarity was tested by Kresak (1982) only statistically, using the Southworth-Hawkins (1963) criterion D. Our orbit determination for C/1846 O1 shows its period was ~500 yr, ~30 times shorter than that of C/1973 D1. Formerly unrecognized, this incongruity makes the objects' common origin less likely. Long-term orbit integration suggests that, if related, the two comets would have to have separated far away from the Sun (probably ~700 AU) 21 millennia ago and, unlike C/1973 D1, C/1846 O1 would have to have been subjected to a complex orbital evolution. Given the chance of encountering Jupiter to ~0.6 AU some 400 days after perihelion, C/1846 O1 and C/1973 D1 may have been perturbed, during their return in the 15th millennium BCE, into orbits that were, respectively, smaller and larger than was the parent's, with a net difference of more than 0.002 (AU)^{-1} in 1/a. Whereas C/1973 D1 was on the way to its 1973 perihelion, C/1846 O1 should have been subjected to recurring encounters with Jupiter, during which the orbital period continued to shorten by integral multiples of the Jovian orbital period, a process called high-order orbital-cascade resonance. While the integrated perturbation effect of C/1846 O1 by Jupiter does not appear to reduce the comet's orbital period to below ~1200 yr by the mid-19th century, we find that orbital-cascade resonance offers an attractive mechanism for rapid inward drifting of aphelion especially among dynamically new comets.