Nightmarish! It is not possible, as the Mars surface team's deadline to launch approaches to know for sure that the diversion of the warship is even necessary--that the comet will come close enough to Earth for significant damage to result, let alone hit it full on, is not a certainty. As I understand it comets are more unpredictable than most cosmic objects in that they are outgassing sporadically, in effect the gases form half-assed thruster pulses changing the orbit at random. So, even if we had uncanny perfect data on its current trajectory and the ability to compute a Newtonian, heck even to factor in relativistic effects, with great precision, all that gives us is a probability fan, and a significant part of that will intersect Earth. Also, comets "calve." They don't come in one solid chunk; they split into a cluster of loosely affiliated separate gravel filled snowballs. That's why I mention a penumbra of partial encounter surrounding the prospect of the center of mass hitting square in the middle. Below a certain size fragments will burn up in the atmosphere, but this thing is coming in at the maximum plausible speed--there is little time for the material to disperse even if it all gets vaporized to plasma--the relatively dense mass of plasma can punch through almost like it were solid and deposit the majority of its energy on the surface. (And of course energy released in the atmosphere, and even chemical consequences of enough material vaporizing, even if high up, can do a lot of ruining of days. But this will be a footnote versus the impact damage to the surface unless the mass were quite dispersed indeed! It isn't that loose!) So--there can be no knowing whether the thing will fortunately veer and pass far enough away that the loose material that does encounter the atmosphere will all be small stuff. Maybe it won't veer quite that far and only a fraction of its material hits, and that will be dozens to hundreds of impacts scattered around the globe that do a lot of damage on the scale of say WWII-to WWIII, somewhere in there. The stuff is presumably not being aimed so up to a certain point, diverting massive effort to making shelters, to ride out the period of shockwaves and terrible weather and stockpile enough food plus warehousing tools and hardware and raw materials for reconstruction, evacuating coastlines to withdraw from inevitable tsunamis (not really technically tsunamis, having a different cause and detailed behavior, but anyway big waves, OK?) Stuff like that. Obviously if food is going to be stockpiled the question comes up just how hand to mouth the human species is right now and whether we are talking about leaving the majority of humanity to inevitable starvation, versus the prospect there might be enough and new crops coming in fast enough despite wonky weather. Or the comet could veer to come in straight on--a certain percentage of its mass will be scattered stuff hitting all around the globe; equally loose but densely packed masses will in effect strike as one thing, hundreds of technically separate impact craters being pretty much continuous and indeed overlapping in the center. So--perhaps the fact that the combined astronomical resources of humanity will only be able to plot the Newtonian path of an idealized single object with only limited precision is of no consequence because the expected uncertainty of its path due to randomly maneuvering itself with outgassing in spurts overwhelms observation uncertainty. In that case the calculation, not of its sure course but determining the probability fan, is indeed as refined as humans not gifted with the gift of mystic prophecy can get it, not because of our low tech but because the object is inherently unpredictable. In that case, it could be known within weeks of initial observation just how closely aimed the core of the effective shotgun blast is at Earth. The ability to gently nudge the thing, as far out from the Sun as possible, might be enough to move it so that the core of the probability fan is far enough from Earth that we can anticipate limited damage from peripheral stuff. The terrible thing is, if observation and calculation showed Earth is currently dead center on its most probable core path, moving it might be futile, and yet worth trying to do in the slim chance that it gets pushed enough and then by good fortune gets pushed further out of the way by its own behavior in sunlight. Vice versa if calculation showed that it would most likely bypass Earth with only a one in ten let us say chance of civilization wrecking damage, still that one chance in ten might come up and then it would have made a difference if the ship had tried to do what it could to move it--or the difference it manages to make could be that between a mass extinction event assuring extinction of our species versus a somewhat tangential and partial hammering that kills 90 percent of humanity but leaves survivors, or again between that and a lower intensity grazing that merely hurts us like ten world wars all at once. So it could be that if the Mars mission simply sticks to flight plan and comes home, everything would be fine. Then plans to send it comet chasing are a pointless death sentence. Or it could be humanity is doomed and everything is futile. But there simply can be no knowing, and the chance that they might accomplish something really significant in terms of human survival is high enough that they have to be asked to doom themselves trying. In this context the decision of the lander crew to refrain from burdening the ship crew and stretch their options is quite noble, and there really is no alternative--they are doomed never to reach Earth either way, as are the crew they abstain from rejoining--arguably they do them no favors adding weeks of extra endurance with the same end still inevitably claiming them, but if those weeks are weeks enabling them to come up with a comet-kicking plan and implement it, versus everyone starving or choking in excess CO2 or whatever gets them first before they can reach the comet, or anyway set up automated sequences designed to optimize their comet-pushing punch with the dead mass of their starved bodies adding to the inertia, then staying down might be crucial to saving the species.