Many cometary nuclei split, usually for no clear reason (Boehnhardt 2004, Di Sisto et al. 2009, Fernandez 2009). Most splitting events release small, short-lived fragments (Chen and Jewitt 1994). In some cases, though, two or more long-lived comets appear to have a joint origin. Carusi et al. 1985 noted that the Jupiter-family comets 42P and 53P had very similar orbits before 1850, when they had nearly simultaneous close approaches with Jupiter. Tancredi et al. (2000) suggested that 14P and 121P might have originated at the same time as 42P and 53P. Hui et al. (2017) argue that the Encke-type comets 332P and P/2010 B2 WISE have a common progenitor. 332P is undergoing cascading (i.e., multi-generational) fragmentation (e.g., Sekanina and Chodas 2007). We will use orbit-similarity criteria (Nesvorny and Vokrouhlicky 2006, Jopek and Williams 2013) to look for periodic comets of possible common origin, using their nominal JPL ephemerides, which typically extend some 400 years into the past. For interesting cases, we will investigate how the comets' minimum approach distances vary within the uncertainties of their ephemerides and assumptions of the strength of nongravitational forces. Finally, we will investigate the putative splitting event of 42P and 53P, using the linkage code employed by Hui et al. (2017) and Hui and Ye (2020).
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