As found in this answer to What makes scientists already so certain that Comet C/2019 Q4 (Borisov) is a comet and not an asteroid? the orbital parameters of this eccentricity > 3 visitor to our solar system can be found in Minor Planet Electronic Circular (MPEC) K19RA6. The amateur telescope that discovered this object (and the amateur comet-discoverer themselves) can be seen in Why is this telescope so short? How hard is it to make such a fast primary?

Suppose in this post-ʻOumuamua age we had had a cometary analysis spacecraft already built and ready to go, so that we could check isotopic abundances from its coma and/or tail to sniff out what another solar system's abundances might be, and a rocket had been procured and dedicated to a short-notice deep-space launch.

Question: Would any of the likely rocket candidates and upper stage boosters be able to catch up to Comet C/2019 Q4 (Borisov) assuming it were lauched today, based on it's orbital parameters linked above?

A ballpark answer is fine, it's not necessary to calculate the exact trajectory. I have a hunch that the answer is no, or at least not for a hundred years when the spacecraft will be so far away that we can't receive any data from it, but I don't know.

While ε>3 means that unless something unusually happens it's going to exit the solar system, it doesn't necessarily mean beyond any doubt that it's from outside the solar system.

Screen shot of Scott Manley's video Water Found On Distant 'Super Earth' (or Mini Neptune) AND A New Interstellar Comet! showing an orbitsimulator.com simulation of the comet 13-Sep-2019 using some paramgeters, presumably pretty good ones considering the source. Click for full size or watch the video after about 07:10.

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Not a chance. As detailed in Bill Gray's FAQ for C/2019 Q4, the velocity at "infinity" when it leaves the Solar System will be ~32.6 km/s, one of the strongest signs that this was an interstellar object. This is considerably larger than the fastest moving spacecraft, the Voyagers, at 16 km/s. So with current conventional rockets or ion propulsion there is no way to catch up. If the recently selected ESA Comet Interceptor had already been launched and was out at the Earth-Sun L2 point, then it might have been possible for it to do a flyby investigation.

  • $\begingroup$ It's a 3D timing problem so I'm not sure that it can be answered solely and conclusively with $v_{\infty}$ alone, However "As it went past us, its path was "bent" by about 34 degrees" suggests that it's not moving towards the Earth but away from it (and/or the Sun). In other words, the comet was discovered too late. That additional piece of information would then make an intercept "comet-sniffing" trajectory impossible. Thanks for the ESA Comet Interceptor link, what a great idea! $\endgroup$ – uhoh Sep 13 '19 at 4:06
  • $\begingroup$ I found this short pdf presentation: Comet Interceptor A proposed ESA mission to an ancient world though I don't exactly understand the timing of the "Short cruise and fast flyby near 1 AU" on slide 6 because of the 2D projection, and this poster in Emily Lakdawalla's blogpost. $\endgroup$ – uhoh Sep 13 '19 at 4:21
  • $\begingroup$ What would the remaining delta-v be on the fly-by of the object if it had been at L2? How much faster would the object have been going than the probe-- would it even have been observable (for data that is of scientific importance) if it flew by at 10km/s + velocity difference? $\endgroup$ – Magic Octopus Urn Sep 17 '19 at 16:04

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