Abstract.The 140 m sized asteroid 2011 AG5 has recently received much attention by the media, due to its non negligible probability of impacting Earth in February 2040. The chance of this event is bound to a close approach to Earth on February 3, 2023, at a distance of 1.86 +/- 0.24 million km, which will produce a slight “shrinking” of the asteroid’s orbit. If the actual distance of the approach was to fall within a well defined and narrow window, 370 km wide and centred at 1,838,260 km from the Earth, then the orbit of the body would get the exact “correction” needed to aim at our planet 17 years (10 orbits) later, on February 5, 2040. Since the uncertainty about the asteroid’s actual position propagates itself in an essentially one-dimensional “along-track” way, not only it is possible to estimate the probability of an impact (about 1/500), but also it is possible to predict the relatively narrow geographic “corridor” on the Earth’s surface where such impact could possibly take place.
Sometimes a ship ends up crashing upon a rock. This article, instead, is about a rock which might fall upon Earth and crash upon – us.
Due to its possible impact with Earth in 2040, this rock (a small asteroid named 2011 AG5) has gained wide popularity on the web (with over 400,000 pages) as well as on TV and the press. Discovered on January 8, 2011 by the 1.5 m telescope of Mt. Lemmon, AZ, 2011 AG5 was observed until September 21, when – at a distance of nearly 1 AU from Earth – it became too faint even for the large telescopes of Mauna Kea. Astronomers have recently unearthed some images of the asteroid prior to its official discovery (November-December 2010), thus extending the record of observations to 317 days – about one-half of the orbital period.
This chunk of rock became famous when the two major centers dealing with NEOs (Near Earth Objects), i.e. the Jet Propulsion Laboratory (http://neo.jpl.nasa.gov/risk/) and the NEODyS consortium of the University of Pisa (http://newton.dm.unipi.it/neodys), estimated at 1/500 the probability of an impact with the Earth on February 5, 2040. Judging from the predicted size (~140 m) and collision speed (15 km/s), the asteroid would not trigger a global catastrophe, but its impact would be devastating on a regional scale (i.e., several tens of kilometres) anyway . Although the chance is remote, it surely deserves some further study. Data from JPL show the “nominal” distance expected for the close encounter in 2040 to be about one million kilometres – two times and half the distance of the moon. Why, then, is a collision possible and how to estimate the odds? I will try to clarify this rather complicated issue. The starting point is the determination of the orbit of a Solar System object, based upon the recording of its path in the sky. I treated this topic in the March issue of Astronomia Nova, where I described the development of the SOLEX and EXORB codes, which make extensive use of numerical integration. The same software I used to study the orbit of 2011 AG5.
One single real asteroid, a cloud of possible ones
Since experimental observations are never ‘totally accurate’ – in the sense that they are always affected by small random errors – an ‘exact’ calculation of an orbit can be never attained. Leaving details aside, the usual approach is Gauss-Newton’s, or least-squares method. Starting from the data record, and taking into account all perturbative effects, this method computes the set of orbital parameters which minimize the sum of squared differences between observed and calculated positions. The parameters thus calculated provide the so-called ‘nominal’ orbit which – apart from systematic errors – should be the best approximation of the ‘true’ one (which remains unknown). However, we have a host of other possible orbits, having slightly different parameters. Although the nominal orbit is in better agreement with the observed positions, the other ones cannot be ruled out, because of the uncertainties in the data.
Consequently, we are left with a bundle of possible orbits clustered around the nominal one. More accurate observations give, as a result, a tighter clustering. It’s just as if we had a cloud of thousands (virtual) asteroids instead of a single (real) body. Due to the small errors in orbit calculation, this evolving cloud tends to disperse over time – the bigger the errors, the faster the process.
To estimate the chance of a collision with a planet, we need to know the shape, size, and density of the cloud at the time of the alleged collision. This can be done in various ways; the most reliable and simplest approach (although it takes a lot of computing) is the “Monte Carlo” method, which generates the virtual cloud of asteroids via the same code previously used to calculate the orbits. At this stage, however, it is not necessary to use real data, but rather a corresponding set of virtual observations, all carried out at the same instants and randomly scattered around the theoretical positions of the asteroid, with the same nominal average gap of the real observations. In other words, a different random set of fictitious – but, nevertheless, realistic – observations is created each time; from such a set the orbital parameters of a virtual asteroid (a ‘clone’ of the nominal one) are calculated. Repeating the procedure many times – each time selecting at random a different set of virtual observations – a cloud of ‘clones’ appears, which represents the best statistical distribution of uncertainties available on the orbital parameters of the real asteroid. This cloud of clones, evolved over time via a numerical integration code like SOLEX, will tell us how far and to what extent the course of the asteroid is predictable.
More “trail” than “cloud”
As the asteroid and its ‘clones’ (Fig. 1) proceed along their path, the orbits of the clones remain nearly unchanged with regard to their geometry in space. The laws of dynamics (at least, in the two-body approximation) require that small differences in the geometric elements (semi-major axis, eccentricity, inclination of the ecliptic, longitude of perihelion and ascending node), remain constant over time, unless they are changed by a sudden event – like an approaching planet. What does change over time is their position along the orbit. Small differences in the semi-major axis result in slightly different orbital periods, and as the set of clones moves along its path, some of them come first while others delay, so that the initial cloud begins to disperse and becomes a thin trail, stretched along the orbit like a string of pearls (Fig. 2).
Course correction and stretching of the trail
But why did we mention a “course correction” in our title? It’s the result of a computed trajectory which will take asteroid 2011 AG5 on Feb. 3, 2023, to a minimum distance of 1.87 million kilometres from our planet. On that occasion, the asteroid will pass ‘in front of’ Earth, and because of the gravitational pull of our planet it will slow down a little bit in its journey around the Sun. This will result in a small contraction of the orbit, with a shortening of its orbital period – from 625.1 days to 620.9 days (~ 1.7 years). Without this change, the asteroid would not bother us until – at least – next century, but the ‘course correction’ above mentioned will take it closer to us after 17 years, i.e. in early February 2040 (corresponding to 10 revolutions of 2011 AG5 – and 17 of the Earth – around the Sun).
At present, we cannot tell whether the asteroid will hit, nor are we able to reduce the distance – and time-uncertainties below the values of one million kilometres and one day, respectively. This is primarily because the ‘course correction’ of February 2023 will considerably expand the cloud – or, rather, stretch the ‘string of pearls’ – of the virtual asteroids. This will increase our uncertainty, since each virtual asteroid will pass over at different distances from the Earth (Fig. 2), in turn receiving a slightly different course correction. After 10 orbits, in 2040, this ‘trail’ or virtual string of beads will be stretched to a length of about 25 million km (Fig. 3) – 25 times the length it would have without the ‘course correction’ of 2023.
Probability of collision
Although unable to say where the real asteroid will be in 2040, we can estimate the chance that the course correction may trigger a collision with Earth at that time. That’s what I did with the code EXORB, by generating through the Monte Carlo method 140,000 ‘clones’ of the asteroid 2011AG5, and verifying through SOLEX how many of these end up crashing on the Earth. This was a long work for my PC – taking a total computing time of 48 hours – but, eventually, 259 ‘virtual impactors’ came out. This gives a probability of 259/100.000 = 1/540, in agreement with the results obtained by JPL and the consortium NEODyS via much faster methods. A close-in examination of the specific trajectory of these ‘virtual impactors’ (Fig. 4 shows their last orbit, prior to the impact) shows that all of them will pass on February 3, 2023 at a minimum (geocentric) distance from the Earth ranging between 1,838,074 km and 1,838,445 km – a ‘window’ 371 km wide, about 32,000 km closer to Earth than the point calculated for the ‘nominal’ asteroid, and within a maximum range of about 400,000 km.
Results expected from the next observing campaign for AG2011 AG5 – in September 2013, and afterwards from spring to autumn of 2015 – are likely to reduce the range of uncertainties around the ’nominal’ position, perhaps even placing it a little farther, up to the point of ruling out any possibility of dangerous impacts. If, however, the new nominal position expected for 2023 should get closer to the dangerous window, we will have two more chances to re-assess our models – in 2018 and 2020, respectively. In case of lingering doubts even after that (which is unlikely), we will only have to wait until 2023 to get a definite answer.
In case it should really hit us…
What if we can’t get a clear answer until 2023? Although we cannot tell whether the asteroid will hit, we can predict where it might hit – or, better, where it surely won’t. Paradoxical as it may seem, this is just a necessary consequence of the distribution of uncertainties along a very narrow corridor. The points corresponding to the ‘virtual impactors’ are not distributed on the surface of the Earth like a circle of hunting pellets, but rather they are aligned along a curve, corresponding to the intersection with Earth of the trail of possible impactors. So we can already say that, in the (unfortunate) case that the asteroid 2011 AG5 hits our planet in 2040, that would happen on February 5, between 3:42 and 4:07 UT, within a strip a hundred km across, passing through the Pacific Ocean – south of the equator – and crossing South America (southern Peru, Bolivia and southern Brazil between Rio de Janeiro and São Paulo), then going through southern Atlantic Ocean up to the southern tip of Africa, and eventually ending in the Indian Ocean (Fig. 5). Actually the prediction of such a narrow strip is a bit flawed by not taking into account a non-gravitational force that can be effective on small bodies: the Yarkovsky effect (http://en.wikipedia.org/wiki/Yarkovsky_effect). Due to the rotation of the body, infrared radiation is emitted in a direction different from that of the incoming solar photons, and the result is a tiny tangential thrust, having an order of magnitude 50 million times smaller than the solar attractive force. This tends to gradually expand or contract the orbit of the body, depending on whether its rotation takes place in the same direction of the orbital motion (prograde) or in the opposite direction (retrograde). In the short time range of thirty years, a simulation showed that the result could only be a moderate widening of the “corridor” of possible impacts, from a few dozens to a few hundreds km, and the stretching by a few minutes of the time interval in which the impact could possibly take place, leaving substantially unchanged its track on the Earth’s surface.
In any case, with or without the Yarkovsky effect, about one-fifth of the ‘virtual impactors’ are expected to fall upon South America (Fig. 5) – some of these in the most densely populated areas of Brazil – and therefore our hope is to be able in a few years to rule out even the slightest chance of impact.
(Traduzione di Manlio Bellesi)
è nato a Napoli nel 1948. Laureato in Chimica nel 1971, è ordinario di Chimica Generale ed Inorganica presso l’Università di Napoli Federico II, dove svolge le sue ricerche nel campo della chimica dei composti organometallici. Da quasi due decenni si interessa anche di meccanica celeste, con particolare riguardo alle applicazioni della integrazione numerica nel calcolo di effemeridi e nella determinazione e studio di orbite, per le quali ha sviluppato il software SOLEX (http://chemistry.unina.it/~alvitagl/solex/). A riconoscimento di questo lavoro gli è dedicato l’asteroide 5168 Vitagliano.
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