J. Brit. Astron. Assoc., 109, 1, 1999, p.39

1997 XF11 – the true story

by Brian G. Marsden

The text of a talk given by Dr Brian Marsden to the meeting of the British Astronomical Association on 1998 October 28.

Much of the public, as well as many astronomers, rather missed the point about the 1997 XF11 announcement, which was that an intriguing situation had been virtually ignored. There was a need for further observations, and it was because the Minor Planet Center specifically provided an ephemeris for 1990 on its web page that the 1990 images that solved the problem of the 2028 approach to the Earth were quickly found. Surely, that is science working at its best. Furthermore, even with a miss distance of almost 1 million km in October 2028, the approach will be the closest known for any asteroid or comet estimated to be as large as 2km across.

The two principal criticisms concerned the initial statements that it was 'virtually certain' that the object would come closer than the Moon, and that a collision with the Earth 'a little more than 30 years from now' was 'not entirely out of the question'.

An extensive and sophisticated analysis recently published by the Finnish astronomer Karri Muinonen concludes that, given the three-month arc of observations available at the time, the chance that 1997 XF11 would have come closer than the Moon was 72%, while there was something like a 99% chance that it would come closer than the distance we now know from the 1990 data to be correct. The term 'virtually certain' was perhaps a little strong, but Muinonen's work clearly shows an unusual tendency towards very small distances. There is a strong departure from Gaussian statistics, with the true distance rather amazingly right in the tail of the distribution.

As for the possibility of a collision, it was quickly understood that one would be possible in 2028 only under highly unusual circumstances, such as a prior encounter with an asteroid not allowed for in the computation, or the presence of unmodelled nongravitational forces that could arise if the object were really an almost-defunct comet. Under 'normal' circumstances, it would be impossible for 1997 XF11 to have approached in 2028 to within 30,000km of the centre of the Earth. In 1998, on the other hand, the minimum distance between the orbits is as much as 150,000 km. The distance is in fact decreasing rather steadily at some 4000km per year. This means that the orbits will actually intersect around 2036, although this date could change by a few years, depending on how close the asteroid were actually to come in 2028. If 1997 XF11 were destined to impact the Earth, this would therefore have had to occur within a few years of 2036.

So was an impact possible? The short answer is 'yes'! A longer answer is that the asteroid's revolution period, some 1.73 years prior to the 2028 encounter, could subsequently be anything between about 1.53 and 1.99 years, the value depending on how close the asteroid comes in 2028. If the period in years were to end up close to a simple fraction, like 5/3, 7/4, or even 17/10 (i.e., approximately 1.67, 1.75 and 1.70, all within the acceptable range), another close approach to the Earth would be expected in the October following 2028 by the number of years given in the numerator of the fraction. For these three examples, there would therefore be further encounters with the Earth in October 2033, 2035 and 2045. None of these cases seems actually to result in a collision, but the miss distances could be as small as 15,000km.

My investigation, still incomplete, did in fact yield possible impacts corresponding to the fractional periods 9/5 and 12/7, i.e., in 2037 and 2040. The first of these apparently gives the possibility of the asteroid's grazing the surface of the Earth, while the second allows a 'deep impact' that, unimpeded, would take the object only 3000km from the Earth's centre. Fortunately, of course, we do have the 1990 observations that show no possibility that 1997 XF11 could pass within some 30 million km of the Earth during this time. Since the orbits of the asteroid and the Earth then separate, we can say we are in fact completely safe from impact by this asteroid for some considerable time, perhaps tens of millennia.

What was the probability that 1997 XF11 would impact the Earth during one of the 'dangerous' Octobers? It is difficult to give a precise answer to this question because to do so would require the examination of millions of possible trajectories. In general terms, however, we can say that the 4000km annual change means that it would take three years for the intersection point to cross the diameter of the Earth. During the middle year the point would therefore come quite close to the Earth's centre. The probability of having the Earth in the right place is therefore essentially the ratio of the diameter of the Earth to the circumference of the Earth's orbit, or 1.4×10^–5. This has to be multiplied by the probability that the asteroid would be at that point during the year, i.e., by the reciprocal of the asteroid's period in years. Since that reciprocal can be as small as 1.53, the resulting impact probability could be almost as high as 1 in 100 000. This is perhaps two orders of magnitude larger than the probability of a hit by an unknown 2km object during the year.

The moral of the story is that it is probably a good idea to search, at some level, for asteroids that come to the Earth's general vicinity. But merely counting the asteroids found is not sufficient. It is desirable to follow up each discovery to examine whether it can or can not be a threat during the next century or so. Objects for which the threat cannot be eliminated should be singled out for special study, notably to the extent of searching for old images in photographic archives. 1997 XF11 was noteworthy for the apathy shown to it prior to the very widespead announcement in March. If proper attention had been given to it earlier, the circumstances that led to the announcement would never have occurred. Sometimes statistics will conspire to draw attention to a problem. Maybe they are trying to tell us something...

Brian G. Marsden
Minor Planet Center, 60 Garden Street, Cambridge, MA 02138, USA.

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