1. Near Earth Asteroids Long Term Impact Monitoring: Difficult but Necessary F. Bernardi 1,2, A. Milani², G. B. Valsecchi¹, S. R. Chesley³, M. E. Sansaturio 4, O. Arratia 4 ¹IASF-Roma, INAF, Italy ²University of Pisa, Italy ³Jet Propulsion Laboratory, U.S.A. 4 University of Valladolid, Spain

2. Current impact monitoring It is about 15 years since NASA and the astronomical community are involved into the search and monitoring of Near Earth Asteroids (NEA) and comets that can potentially hit the Earth In all world there are two independent impact monitoring systems:  CLOMON2 of NEODyS in Pisa and a duplicate in Spain  Sentry of JPL in Pasadena, CA, USA The two systems monitor the impact hazard for our planet for the next 80-90 years, determining the Impact Probability (IP) for each NEA http://newton.dm.unipi.it/neodys http://neo.jpl.nasa.gov/risk/

3. Current impact monitoring: direct hits Direct hits, i.e. collisions taking place without intervening planetary approaches, are easier to spot than resonant and non-resonant returns Probabilities are comparatively higher Deflections are more expensive in terms of Δv Deflection decisions are comparatively easier to take (if time allows)‏

4. Current impact monitoring: resonant returns Resonant and non-resonant returns are less easy to spot than direct hits Probabilities are comparatively lower Deflections are (generally) less expensive in terms of Δv Deflection decisions are less easy to take, as much better orbital information is needed (see Apophis), but more time may be available

5. Current impact monitoring: resonant returns Collision regions (keyholes) are found at peculiar locations on the b-plane (the plane normal to the unperturbed geocentric velocity of the impactor) of a pre-impact encounter They tend to be small, whence the gain in Δv in case of deflection, and the greater difficulty in deciding a deflection

6. Future impact monitoring For large impactors, current impact monitoring may not give sufficient advance time for deflection If Δt is the number of years between deflection and collision, Ahrens and Harris (1992, 1994) estimate that, to avoid a direct hit, the needed Δv in m/s is 0.07/Δt So, the longer our predictability horizon, the easier the deflections How far could/should we push the predictability horizon?

7. The problems We have basically two problems: chaos and dynamical model Chaos: encounter sequences lead to multiplicative accumulation of the along-track separation from each encounter (i.e., to exponential divergence and chaos) with maximum Lyapounov exponent proportional to encounter frequency So, no matter how precisely determined is a NEA orbit, after sufficient time we are led to a situation resembling that of a newly discovered NEA, with all the uncertainty concentrated along-track

8. The problems Dynamical model: given the sensitivity of encounter outcomes to small changes in the initial conditions, the possibility to extend the predictability horizon for a NEA, beyond a certain date, depends from the accurate modelling of so-far neglected non-gravitational perturbations like the Yarkovsky effect We have selected (101955) 1999 RQ 36, a NEA with a very well determined orbit, to test the possibility of extending the predictability horizon (see Milani et al. 2009 for details)‏

9. The problems Note: The non-gravitational effect called Yarkovsky effect is due to the solar radiation that is re-emitted through thermal radiation in a different direction, because the object is rotating and because the material has thermal inertia

10. (101955) 1999 RQ 36 (101955) 1999 RQ 36 has the lowest formal uncertainty in semimajor axis at epoch of any asteroid: 5 m The Yarkovsky effect causes a change of the semimajor axis of the order of 200 m/y for this asteroid Orbits determined accounting for the Yarkovsky effect differ from the purely gravitational solution by about 40 times more than the formal uncertainty Very long propagations could be within the predictability horizon in a purely gravitational model, but non- gravitational effects make this horizon closer

11. (101955) 1999 RQ 36 Time evolution of the Minimum Orbit Intersection Distance (MOID) for (101955) 1999 RQ 36 The MOID is less than the effective radius of the Earth (horizontal lines) many times, between about 2100 and 2230

12. Monte Carlo runs We have run Monte Carlo (MC) simulations with the method of Chodas & Yeomans (1999): 500000 MC samples drawn from a 7-dimensional space of initial conditions (6 elements and the Yarkovsky-induced da/dt), and followed until 2200 All MC samples remain close together up to a pair of Earth encounters in 2060 and 2080, after which they become widely scattered 461 MC samples collide with the Earth, giving an Impact Probability (IP) of about 0.00092 272 MC samples collide in 2182; of these, 268 have similar dynamical histories: thus, there is a dynamical route leading to impact in 2182 with an IP of about 0.00054

13. The 2182 impact In 2182, the IP is high because the LoV portion close to the Earth is folding, crossing our planet twice close to the fold tip This means that the along-track separation is very small: something in the previous evolution has refocused the impactors

14. The 2162 b-plane The double keyhole for impact in 2182 seen on the b-plane of the 2162 encounter The fold tip is marked in red The green circle shows the size of the lunar orbit The along-track size of the two keyholes are 187 and 118 Earth radii: the keyhole is larger than the door!

15. The 2182 impact Time evolution of the stretching (essentially, the along-track separation) for a typical 2182 impactor In 2182 the stretching has come back near the value it had almost a century before Consequence: an along- track deflection would have to be attempted no later than 2080

16. Conclusions Long-term impact monitoring is doable, provided we determine the Yarkovsky drift in individual cases NEAs whose MOIDs are small and decreasing in the next few centuries have to be carefully monitored Question: how typical is 1999 RQ 36 ?....2001WN5.... see “Long term impact risk for (101955) 1999 RQ 36 ” Milani et al. 2009, submitted to Icarus

17. Extra slides

18. Yarkovsky parameters The χ 2 of the least squares fit to the value of da/dt The quadratic approximation for the χ 2 is obtained by a parabola fit to 5 data points (the asterisks) The horizontal line corresponds to a 90% confidence level for the fit

19. Monte Carlo runs Above: a subset of our MC samples plotted in the plane da/dt in AU/Myr vs a-1.1 AU at epoch 2081-Jan-01.0 Below: the orbits leading to an impact The star represents the purely gravitational solution

20. The folds of the 2162 encounter The relevant LoV portion 5 months after the September 2162 encounter with Earth (blue sphere)‏ The yellow sphere marks the LoV segment where the 2182 impactors are located The nearby fold reaches the yellow sphere exactly in time for the 2182 impact