4. In the long run

Asteroid 1999 AN₁₀ was observed until the angular distance from the sun became $<70^\circ$. It will be again at $>60^\circ$ from the Sun after the beginning of June; by that time the uncertainty of its position on the sky will grow to 1.5 arc minutes (corresponding to $\sigma=3$), that is any new observation will significantly contribute to an improvement of the orbit. It is very likely that the observations made in the second half of this year will constrain the orbit well enough to predict accurately the 2027 encounter. This implies that some of the returns of the Table will be discarded as incompatible with the observations; in fact, most of them if the 2027 encounter is not very deep.

The problem, however, will not go away, because all along the LOV there are possible encounters occurring later, almost every six months. We have analysed with our global method the same $1\,001$multiple solutions over a time span of 50 years after 2027, and found 165 possible returns, out of which 117 in the moderate to low stretching region. This situation is qualitatively stable: whatever the actual orbit is, it will not be possible to predict with certainty the returns after the next close approach for a time span longer than a few decades.

Since at least one node of 1999 AN₁₀ will remain close to the orbit of the Earth for centuries, this asteroid shall have to be monitored, by observations and computations, for a very long time. It is conceivable that at some time in the future a decision could be made to deflect it; but, a deflection decreasing the depth of some specific close approach could increase the impact risk at a later date. Thus before such a decision can be contemplated we need to better understand the theory of resonant and non-resonant returns, which has only been outlined in this paper.