@gutenberg_org I recently learned about a brighter comet that came some months before, the so-called Great Comet of 1910, which many people apparently mistook for Haley's. This comet has an eccentricity ridiculously close to one, and so is probably the closest thing you'll find to a parabolic orbit in the known history of the solar system. I had a lot of fun discovering this and working out the explicit time dependence of the parabolic orbit, which is just do-able by solving a cubic equation.
@gutenberg_org https://en.m.wikipedia.org/wiki/Great_January_Comet_of_1910
There's a book with more detail:
Burnham, R. & Levy, D. (2000), Great Comets, New York: Cambridge University Press, p. 184, ISBN 0-521-64600-6.