The Mars Encounter of Comet C/2013 A1 (Siding Spring)

4 March 2013 by Michael Khan, posted in Uncategorized

You'll have heard that on October 19, 2014 Martians will be treated to a rare spectacle. A recently discovered comet named C/2013 A1 (Siding Spring) will pass the red planet at a very close distance (at most some hundreds of thousands of kilometers; though the latest orbit determination leads to a distance of around 70,000 km). The comet might also hit Mars, and if it does, it will create quite a bang. The diameter of the comet's nucleus can be up to 50 km, and it will encounter Mars at a relative velocity of 56 km/s.

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The orbit determination results are still somewhat inaccurate. With optical observations of a comet that is still far beyond the orbit of planet Jupiter, the plane-of-sky measurements do not discriminate well even for significant differences in the orbital elements. When propagating ahead numerically over 20 months from an inaccurately known starting point, one will inevitably end up with a large uncertainty ellipsoid that encompasses planet Mars and much of the surrounding space. With time, observations will cover a growing arc of the comet's trajectory and become much more accurate. At some point in time, at the latest by the end of 2013, taking into account that from spring to summer the Sun will block our view of the comet, we will have much more reliable predictions of the relative geometry at flyby, and we will also know whether there will be an impact or (more likely) not.

If you make a cut through the dispersion ellipsoid at the time of closest approach to Mars, you get an ellipse, or rather, you get a series of concentric ellipses of different sizes, depending on the number of standard deviations (i.e., the level of uncertainty) you are regarding. Let's assume we are talking about a 3 sigma confidence level, which means that the ellipse will include 99.7% of all expected flyby trajectories. In close approximation, at an encounter velocity of over 55 km/s, we can assume that the impact radius is equal to the planet radius. This means that if planet Mars is completely encompassed by the uncertainty ellipse, the impact probability can, in good approximation, be computed as the ratio between the area of a circle with the Mars body radius (~3400 km) and the area of the uncertainty ellipse.

This in turn means that as the orbit determination accuracy improves, the error ellipse at Mars will shrink. As long as it still covers Mars, the impact probability might then actually appear to increase, though this need not be so. Then, either of two things can happen: Either Mars will cease to lie within the uncertainty ellipse. Then the impact probability - after seeing a continuous increase - will suddenly collapse to near-zero. In fact, the latest information by astronomers tracking the comet indicates that the impact probability is not increasing. Or Mars will continue to lie within the uncertainty ellipse, which will then mean that an impact might be in the realm of the likely. If comet C/2013 A1 however does not hit, it will pass its perihelion - still considerably beyond the Earth orbital radius - after the Mars encounter and then disappear into the depths of space. In all probability, this is what will happen.

C/2013 A1 is on a parabolic orbit. Its perihelion radius, the point where it is closest to the Sun, is at a solar distance of just over 200 million km. The orbital inclination is almost 130 degrees, making the orbit retrograde. If you view the comet's orbit from the North pole direction of the ecliptic, it will appear to be moving clockwise, in contrast to the planets, which are moving counter-clockwise. For comets that came from the Oort cloud (i.e., from very far out) this is not rare - such objects can approach the Sun at any inclination.

Celestial mechanics is rife with apparent paradoxes. Case in point: Currently nobody can say for sure whether this comet will hit Mars or miss by a considerable margin. But we can predict quite accurately from where it will approach Mars and at what local time it will hit, if it does hit. And of course one can plot and analyze the trajectories through the solar system, which is what I did. I obtained the orbital data from JPL Horizons and created two diagrams, one showing the inner solar system seen from the ecliptic North, the other seen from along the ecliptic plane. (please click on the pictures to see them at full resolution) The indicated locations of planets Mercury through Mars correspond to where they will be on October 19, 2014, 12:00 UTC.

The orbit of comet C/2013 A1 (Siding Spring) seen from the ecliptic North, source: Michael Khan/ESA

The orbit of comet C/2013 A1 (Siding Spring) seen from the ecliptic North, source: Michael Khan/ESA

The orbit of comet C/2013 A1 (Siding Spring) seen from along the ecliptic plane, source: Michael Khan/ESA

The orbit of comet C/2013 A1 (Siding Spring) seen from along the ecliptic plane, source: Michael Khan/ESA

These diagrams clearly show one thing: Comet C/2013 A1 will not get close to the Earth, no matter what happens. There is no way Mars can appreciably deflect the comet from its pre-computed path. The relative velocity is much too high for that.The comet will approach Mars from the South and speed off towards the North.  

Now let's look at where on Mars an impact could happen, if it happens. This applies not just to the nucleus proper, but also to large and small debris that might have separated from the nucleus and will then be flying on parallel but distant trajectories. Even if the nucleus does give Mars tens or hundreds of thousands of kilometers of berth, debris might still hit. The probability for this rises with the activity the comet will have delivered by then. That is another thing nobody can tell for sure. Experience with previous large comets, e.g., Hale-Bopp in the late 1990s, does indicate that a significant coma and tail might have developed even at a sun distance of 1.4 AU. Every piece of approaching debris will however be approaching from virtually the same direction and therefore all analysis made hereafter applies to the debris as well.

Possible entry locations on Mars for entry FPA up to -15 deg for comet C/2013 A1 on Oct. 19, 2014, source: Michael Khan/ESA

Possible entry velocities for comet C/2013 A1 on Mars on Oct 19, 2014, source Michael Khan/ESA

 The following statements can be made already now with a high level of confidence.

  • If anything from C/2013 A1 hits Mars at a shallow angle of attack (here, I looked at entry angles of up to -15 degrees), it can hit anywhere on the Surface except for the North polar cap. If objects enter steeply, they will impact near the equator.
  • The chances for impact at local day or night are 50/50.
  • There is a fair chance that a major impact will be observable from the Earth. If entry is steep, visibility from the Earth is certain. If it is shallow, the probability of visibility from the Earth is around 75%.
  • Die entry velocity at 100 km of altitude is around 56 km/s

So much for the analysis. However, there is more to this event than just math and physics.

The part of me that is a scientist, actively engaged in space exploration, is of course jubilant. No matter how much of this comet, if anything at all, will reach the Mars surface, this close encounter constitutes a unique opportunity to learn about comets and their interaction with a tellurian planet. In October 2014 there will be up to four active spacecraft in orbit around Mars, each of them equipped with cameras, spectrometers and other science instruments with which the impact of the nucleus or debris can be observed and studied, and also the aftermath. All of this in real time. This is the first time such a golden opportunity came along.

Even if nothing at all reaches the surface, there still will be the chance to observe a vigorous, young comet at close quarters. The nucleus must still be in possession of almost all of its primordial, volatile material. We're talking about very ancient and fragile material here, material that will have remained largely unchanged from when the solar system accreted, because everything out in the Oort cloud will have remained largely unaffected by the violent changes wrought much closer to the Sun. This should allow some fantastic science.

But every scientist is also an earthling. As an earth dweller, this encounter gives me the creeps. Eons ago, a very insignificant orbital perturbation dislodged this 50 kilometer chunk of ice and assorted dirt from its orbit through the Oort cloud, around one light year distant, and sent it hurtling towards the inner solar system, imperceptibly at first, but slowly gaining speed and turning into an unstoppable juggernaut. had this perturbation been different by just a minute amount, the comet might now be on a course that would intersect the Earth orbit exactly at the time when the Earth happens to be at the same spot. There is no reason why this should not have happened, other than sheer chance. For all we know, someone might discover another comet tomorrow that actually is on a collision course with Earth. The resulting impact would de disastrous. It would put an end to civilization and perhaps trigger mass extinction, eradicating most plant and animal species and making room for others. It can happen at any time. One day, it will happen. I perceive C/2013 A1 as a chilling reminder that our existence in the vastness of space is precarious and perilous.

Comet C/2013 A1 was discovered around 2 years before it reaches its perihelion. That is typical for long-period comets. Two years are not enough to mount any meaningful defenses, which in view of the size and speed of a comet nucleus are at any rate extremely challenging, even with sufficient warning time.  There is no reason for panic. The fact that a comet was discovered that might hit a neighboring planet does not suddenly expose the Earth to a higher risk than before. The only thing this discovery does is to drive home the point that we have a problem here. A big problem, but one whose probability of occurring can be significantly reduced if we pull our collective socks up, extend the realm of human activity to as far as our technological capabilities allow and implement an effective system for early warning and countermeasures. We can do it, so if we don't and as a consequence get clobbered, then we didn't deserve better.

Further Information

List of posts related to C/2013 A1 on spaceobs.org


7 Responses to “The Mars Encounter of Comet C/2013 A1 (Siding Spring)”

  1. Ed Davies Reply | Permalink

    “This means that if planet Mars is completely encompassed by the uncertainty ellipse, the impact probability can, in good approximation, be computed as the ratio between the area of a circle with the Mars body radius (~3400 km) and the area of the uncertainty ellipse.”

    Really? That doesn't sound like a good approximation to me as surely the probability falls really quite significantly towards the edge of the ellipse. Hence the paradox of the probability appearing to increase then suddenly drop to zero.

    • Michael Khan Reply | Permalink

      I agree that my statement was anything but clear. Actually, with "in good approximation" I was referring only to the simplification inherent to taking the area of a circle with the radius of Mars and relating that to the area of the uncertainty ellipse. For "normal" approach velocities this would have been quite wrong because one should always apply the impact radius rather than the body radius. The impact radius is always larger than the body radius (for approach velocities that you have with spacecraft, quite considerably larger).

      The concept of the impact radius takes into account the fact that a flyby orbit will always be bent towards the encountered planet because of the gravitational attraction. However, this deflection of the flyby trajectory is negligible at very high hyperbolic approach velocities. Therefore, one can, in good approximation, neglect this effect in the given case.

      As for the other inherent assumption, that of a uniformly distributed probability distribution within the uncertainty ellipse, that certainly is not applicable towards the boundaries of the ellipse. However, just comparing the areas, as I described, does give a feel for the impact probabilities. For anything more accurate, one would have to do what Leonid Elenin is describing in his contributions on spaceobs.org, i.e., a Monte Carlo analysis, or at least a covariance analysis, from the reference epoch for which the orbit determination has been performed 20 months into the future, up to the Mars encounter.

      That however is a complex and time-consuming calculation which requires a good knowledge of the covariance of the obtained orbit determination solution.

      • Ed Davies Reply | Permalink

        Fair points, thanks. However, I can't help feeling that just assuming a normal distribution within the ellipse is going to be much better than a uniform distribution and, given the uncertainties in the uncertainties, going for the full Monte Carlo or otherwise evaluating the skew in the probability distribution is rather overdoing things.

  2. Jan van Oort Reply | Permalink

    You are quite right about this event "giving the creeps" to earthlings. It should. Which raises the question: any incoming juggernaut of this type being not observable for several months, due to earth-sun-comet alignment, would a hypothetical first-line-of-warning system not necessarily include a component deployed somewhere else in the solar system ? E.g. an early-warning system in an orbit around Jupiter ?

    • Michael Khan Reply | Permalink

      Yes, an early warning system appears a good idea to me. I don't think it should be in orbit around Jupiter. It would needlessly cost propellant and expose the spacecraft to radiation. It should be sufficient to send some orbital telescopes to Jupiter and to use swingbys at the gas giant to deploy them to wide orbits that roam somewhere between Jupiter and Saturn. What is important is that each spacecraft should be at a different orbital location and that each should be designed to allow a long lifetime.

  3. Jan van Oort Reply | Permalink

    I can not help but wonder what happens if and when the comet approaches Mars to within the Roche limit ? Although there will be tidal forces being exerted upon the comet, these would not immediately yield effects... ? How long does it take for, say, a comet of average composition to decompose under the effect of tidal forces ?

    • Michael Khan Reply | Permalink

      The Roche limit is perhaps a somewhat misleading concept in this context. It is more of relevance of you have a small body in orbit around a large body. Also, strictly speaking, the equations to compute the Roche limit all implicitly assume that the small object is gravitationally bound. If there is more cohesive force than just mutual gravitational of the constituents of the smaller body, then the Roche limit will move much closer to the surface of the major body or it may not apply at all.

      For the case of Shoemaker-Levy 9, which is often mentioned in this context and is something that springs to mind when the Roche limit is mentioned, let's keep in mind that the comet that impacted Jupiter was in fact in orbit around Jupiter. It had undergone an earlier gravitational capture, which is possible if the approach velocity to Jupiter is low and the geometry between Jupiter, Sun and approaching small body is just right. What happened with SL-9 is that it went through a very low perijove already in July 1992, where it was disrupted by tidal forces. The components continued on their highly elliptical orbit and drifted slowly apart along the trace of their orbit due to small differences in orbital period induced by the acceleration during disruption. Two years later, in July 1994, they again approached perijove. However, orbital perturbations had by then lowered the perijove altitude such that the trajectory intersected denser layers of Jupiter's atmosphere. The debris of SL-9 then came in one after the next, bang-bang-bang ....

      The point is that tidal disruption when going below the Roche limit does not make a body explode. Typically, you get a cloud of debris that drifts apart slowly. For C/2013 A1 and Jupiter, what you'd have even if the comet nucleus got close enough to get disrupted, i.e., below several thousand kms, is a debris cloud that is still approaching Mars at 56 km/s. This means that if there were an impact, then you would still have all lumps coming down approximately at the same place. Perhaps a little bit fanned out, but I am not sure that would make any difference in terms of destruction wrought.

      Conversely, if the nucleus got really close to Mars and got disrupted by tidal forces, but then missed the red planet, all the debris would still fly on, basically following orbits that are very similar to that which the comet would have flown without the disruption. We would likely see that such a disruption has occurred because much of the volatile material from the nucleus' interior would suddenly be exposed to sunlight and the brightness would increase instantaneously, perhaps by orders of magnitude.

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