Comet C/2013 A1 (Siding Spring)'s trajectory past Mars
C/2013 A1 (Siding Spring) will pass extremely close to Mars on October 19, 2014. This orbital diagram was based on slightly older observational data that showed the closest approach happening on October 20. The comet will be coming up from south of the ecliptic in a direction opposite to that of Mars'. (The orbits are drawn in dark colors where they dip below the ecliptic, and bright colors when they rise above the ecliptic. Since Earth's orbit is, by definition, in the ecliptic, its orbit is bright everywhere.)
When astronomers report the distances between two objects in space, they are almost always referring to the distances of the centers of the two objects. Distances are usually so great in space that this is a perfectly fine approximation that greatly simplifies calculations. But in cases like this one, you can't make that approximation anymore; you have to account for the size of Mars, which is roughly 7000 kilometers in diameter. So the comet will be passing within 38,000 kilometers of Mars' surface. That is very, very close. Note though that the uncertainty in the orbit is such that the possibility of a Mars impact can't yet be ruled out, though it's very unlikely.
How close is 38,000 kilometers? One way we talk about that for close passes by Earth is to compare the distance to that of Earth-orbiting satellites. If it were Earth, 38,000 kilometers would be within the orbit of geosynchronous satellites. At Mars there are no geosynchronous satellites, and if there were, they'd be in a closer orbit, at 20,000 kilometers. So it's outside that distance. Probably more relevant is the question of whether there are any satellites at Mars that do get out to 38,000 kilometers; the answer to that is no. Mars Express has the largest orbit, and it gets to an altitude of about 10,000 kilometers. All the other active orbiters are down closer to 300 or 400 kilometers. So there's not likely to be a direct hazard to spacecraft in the form of a potential impact.
But wait a minute. This is not a close-approaching asteroid we're talking about here. It is a comet. And the thing that makes comets comets is that as they approach the Sun they start evaporating, spouting jets of formerly frozen gases that entrain dust and ice particles into a gigantic coma easily spanning tens of thousands of kilometers. The coma can be observed telescopically at distances up to 100,000 kilometers from the nucleus, and I imagine that there is more material beyond that, though it's too sparse to be observed. So when Siding Spring visits Mars it will be bringing with it a lot of dust particles to which Mars and every spacecraft orbiting or on it will be exposed.
So, are spacecraft at risk from comet C/2013 A1 (Siding Spring)? I am sure that there are "tiger teams" being convened by space agencies to investigate this question. I don't know enough to know the answer, though I can get some clues by querying the scientific literature. Of major importance is the size of the particles in the comet's coma. According to this review article in the Comets II tome, "the dust emitted from comets spans a broad size range, from submicrometer to millimeter or centimeter and larger." In fact, "most of the particulate mass shed from the nucleus is concentrated in large particles." Of course, these large particles are few and far between, much sparser than tiny (sub-micrometer) dust particles, which pose no risk to spacecraft. Still, I am nervous about what the larger-than-dust particles could do if they were in the wrong place at the wrong time.
One thing that adds to the risk is that the particles will be moving at a very high relative speed. The comet has a hyperbolic, retrograde orbit, so its velocity with respect to Mars will be 56 kilometers per second. Wow.
Still, space is very empty; the density of material in a sphere of radius 100,000 kilometers centered on a cometary nucleus only a couple of kilometers in diameter is near zero. So I suspect that the risk to orbiters is either "small" or "vanishingly small". I'm looking forward to reading what experts have to say.
As for the rovers, my initial instinct is that spacecraft on the surface should be safe from dust; most particles would burn up in the atmosphere, briefly flaring into meteors. Still, the smallest impact craters yet seen on Mars are only 10 centimeters wide. According to one study, the smallest object that could survive to the surface would be about 5 millimeters in diameter. Which is pretty small. Something that small would be greatly slowed by its passage through the atmosphere. How many of these particles are there, and how dense a "rain" would they present? Is it only one particle per square kilometer? Then we're probably fine. Is it one per square meter? Then I'm more scared.
Leaving aside the question of safety, what will the rovers be able to see from the surface? Again, I'm not sure. Comets can be bright but this one will be spread out over so much of the sky that I'm not sure what we'll see. It's way too soon to plan rover observations though. As we learn more about the comet and can better predict how bright it will be, the imaging teams will do their calculations to figure out whether the rovers will see anything if they gaze skyward. If they will -- and if the rovers are both still functioning then -- I'm sure they'll shoot photos!
More observations of the comet are needed to pin down its orbit. It's getting close to the Sun now in our sky now, so it's getting harder to see it, but will be in a better position for observation by late summer. I'll sure be keeping my eye on this one!