Asteroid  2000SG344  is a small piece of rock, estimated to be 30-70 m in diameter, which rides an orbit very similar to that of Earth, with a semimajor axis of  0.975 AU, an eccentricity of 0.0737 and a period close to 350 days.   It approaches Earth a few times per century, and therefore it does have a finite chance of impacting us sooner or later. Due to the small size of the body, a possible impact will only have local consequences, comparable to those of a big nuclear bomb (but without radioactive fallout) or to the Tunguska event of june 30, 1908. Maybe much less than that, because the "asteroid" could even be the empty rest of a Saturn rocket and therefore less massive and more fragmentable than expected from a solid rock of the same size.
    Below is a table of the approaches closer than 10 Gm (10 million km) which are predicted by Solex up to year 2070. The five close encounters taking place in the years 2028-2030 not only induce large perturbations in the orbit of SG344, but also result in a progressive amplification of the present positional uncertainty, so that the close encounter of 2069 is very undetermined.  The timing and distance given in the last row of the table are just nominal values with  little meaning.

   Date      TDT     Dmin (Gm)    T error (d)  D Error (Gm)
2028/05/07 03:32:05   2.93643       0.0007       0.012
2029/02/16 08:13:30   7.88746       0.31         0.020
2029/07/28 11:43:48   5.11718       0.55         0.017
2029/11/21 16:11:07   6.76341       0.65         0.033
2030/09/22 21:36:24   5.15947       0.11         0.10
2069/05/01 15:51:54   0.13535      20            6

If the orbit of SG344 becomes so much uncertain after 2030, how can possibly an Earth impact be predicted ?
Indeed, it cannot be predicted: the chaotic nature of the asteroid's orbit forbids that. Nevertheless it is possible to estimate the probability of such event. How ?
The orbital elements of SG344, as any other experimentally determined entity, are not known exactly. They are just what appears to be (on the ground of the available experimental measurements) the most likely approximation to the "true" values. Suppose that we generate a large number of "virtual" asteroids, having orbital elements slightly different from the nominal ones, but not so much different to represent unlikely orbits. Each of them will represent a possible asteroid, i.e. an approximation to the true one not much less likely than the nominal SG344. Suppose that we integrate the orbits of all these virtual bodies, checking for their close approaches to Earth, and we find out that a fraction of them will impact Earth within a given time interval. We can then say that this fraction represents our best estimate of the probability that the true asteroid will actually impact Earth within the given time range.

The most reliable method of generating representative "virtual bodies" or "clones" is to start from the very beginning, i.e. from the observations. We can (re)determine the orbital elements of our body by a least-square fit to the observation (this can be done by ExOrb (formerly named Findorb), the companion program to Solex). From the fitting procedure, we also get the root-mean-square deviation (or average residual). We can then generate a set of "virtual" observations (one for each of the actual observations), randomly distributed around the calculated positions with the same root-mean-square deviation determined by the original fitting. This set of observations will represent a possible set, which might have been the actual one, but just happened not to be. If we now redetermine the orbital elements from this "virtual" set of observations, we get possible new elements, about equally likely than the original ones, which will represent an acceptable "clone" of the original body. By repeating the procedure N times, we can generate N acceptable "clones". The larger N is, the bigger the statistical significance of the "cloud" of virtual bodies that we obtain.
The whole procedure described above can be automatically performed by ExOrb, the companion program to Solex. It is very time-consuming, but it is computer time, not your time. You can comfortably sleep or go fishing or attend your business, while your computer does the job for you. Once you get your "cloud" of virtual bodies, you can feed it to Solex and investigate the future (or past) evolution of the original body from a statistical point of view.
By applying this method to SG344 one obtains that 10 out of a cloud of 4000 "clones" end up with an Earth impact on September 16, 2071, from which an impact probability of 0.25% can be inferred.
All the 10 "virtual impactors" belong to a family of "clones" having the same semimajor axis (0.97738964 AU at epoch March, 2, 2003), which is well within the 1-sigma deviation (7e-7 AU) from the nominal value of the parent body (0.97738943 AU). When further observations will lead to the determination of the semimajor axis with a higher precision (by 1 or 2 orders of magnitude), then the chance of impact in 2071 will probably be excluded. Unfortunately further observations are not likely to be available until the next close approach of 2028, because the small body will never come closer than 0.6 AU before year 2026.
Here you can download the orbital elements of the "original" SG344 and those of a bunch of "virtual impactors" and a few "virtual grazers", in a form readable by Solex.  Back to Solex page