Long Term Impact Monitoring: Difficult but Necessary
Valsecchi, G. B.¹; Milani, A.²; Chesley, S. R.³; Sansaturio, M. E.⁴; Bernardi, F.²; Arratia, O.^4
1IASF-Roma, INAF; ²University of Pisa; ³Jet Propulsion Laboratory; ⁴University of Valladolid

How long should we extend the predictability horizon of impact monitoring? How long should be the advance time before an impact to allow for realistic deflection? The current impact monitoring systems cover up to 80-100 years in the future. There are two main difficulties in extending this time span: the chaotic effects of repeated close approaches and the non gravitational perturbations.

We have selected as case study the asteroid (101955) 1999 RQ36, which has a very well determined orbit, thanks to 290 optical and 13 radar astrometric observations. However, the orbital uncertainty is grossly underestimated by a purely gravitational solution. The non-gravitational Yarkovsky perturbation on the semimajor axis of this asteroid (560 m diameter) is much larger than the formal uncertainty.

The secular evolution of the Minimum Orbital Intersection Distance for (101955) is such that collisions with the Earth are in principle possible between 2100 and 2230. The prediction uncertainty for this orbit is dominated by the Yarkovsky effect until 2080, later the chaotic divergence of solutions driven by the close approaches to the Earth becomes dominant.

We have run impact monitoring for (101955) up to the year 2200 by using both methods currently in use: Monte Carlo and Line Of Variations sampling. The orbit uncertainty region which was sampled included not only the six orbital elements but also an empirical parameter describing the secular perturbation to the semimajor axis due to Yarkovsky. We have found a large number of Virtual Impactors (VI), that is subsets of the uncertainty space leading to an Earth impact, for dates in the 22nd century. The total Impact Probability (IP) can be estimated at 0.00092. The unexpected result is that 0.00054, more than half of the total IP, is for impacts in the year 2182 and corresponds to just 2 VIs.

To understand the origin of the particularly large size of the 2182 VIs, and also why there are two of them, we have to refer to the theory of interrupted returns, which we have developed in the last years. The divergence of impacting orbits is moderate until 2060, grows by 4 orders of magnitude as a result of close approaches between 2060 and 2080, then again grows moderately until the 2162 encounter with the Earth and decreases afterwards. This decrease is due to an interrupted return from the 2162 encounter. The keyholes leading to a 2182 impact on the 2162 target plane are extremely large.

The consequence of this complex dynamics is not just the comparatively large IP, but also that a realistic deflection procedure could be performed only before the 2080 encounter, more easily before 2060. If this object had been discovered after 2080, deflection would require a technology which is not currently available.

This example suggests that impact monitoring extended to a time span exceeding one century might be necessary to allow for a deflection initiative with moderate technological and economical requirements.