1. Limits of Stability in Earth Co-orbital Motion of Asteroids Martin Connors, Athabasca University Christian Veillet, CFHT R. Greg Stacey, Athabasca University & UofA Ramon Brasser, Queen’s University Paul Wiegert, UWO Seppo Mikkola, Tuorla Observatory Kimmo A. Innanen, York University CASCA 2006, Calgary

2. There are presently 25 asteroids known with semimajor axis a between 0.99 and 1.01 AU and thus potentially affected by 1:1 resonant interaction with Earth. On average they follow Earth’s orbit so are called co-orbital. Of these, four are in horseshoe orbits, three are currently quasi-satellites, and at least one has a complex high-e high-i interaction (Cruithne).

3. 2002 AA29 and 2003 YN107 move on low- eccentricity orbits very similar to that of the Earth, with moderate inclination i of 11 and 4 degrees. These objects both have horseshoe orbits with respect to Earth and are capable of being captured as quasisatellites (which 2003 YN107 currently is).

4. 2002 AA29 has a horseshoe orbit, approaching Earth and being perturbed to move away. This is a classic example of Kepler’s third law with change in a. The full orbit is not shown, it passes the other side of the Sun. Libration period ca. 190 yr.

5. This results in a characteristic alternation of the semimajor axis around 1.0 AU

6. 2003 YN107 has a similar horseshoe behavior at times but lower inclination. It is currently trapped as a quasi-satellite near Earth.

7. During QS the semimajor axis stays near 1.0 and eccentricity changes notably. 2003 YN107 brief QS

8. 2001 GO2 (a short arc object) and 2000 PH5 have similar horseshoe orbits, e~0.2, move in-out more. 2001 GO2 will do QS motion in the gap of its horseshoe (insert).

9. 2004 GU9 is a very regular quasi-satellite (QS) resembling a high- inclination orbit of Earth. The heliocentric inclination is 13.6º and eccentricity 0.136. This state lasts 1000 years. Top View – note closeness to Earth Side View – note high apparent i

10. 2006 FV35 is a recently discovered quasi-satellite, already well-observed with a good orbit. Its inclination is 7.1º and eccentricity 0.377. The high e guarantees a short lifetime as it is both Mars and Venus crossing. 600 years of motion – colour change at present to show libration Google “Paul Wiegert UWO” for QS info & animations.

11. 2006 FV 35 shows typical QS behaviour of a libration and change in e. The large e (0.377) makes it planet crossing. It encounters Venus in about 750 years and is scattered out of QS.

12. 2004 FU 162 was our closest nonimpacting visitor. It is a short arc (1-night) object so the discussion is hypothetical based on the best orbit. The a behaviour shows horseshoe libration as does the complicated distance. Fear Factor – these can’t hit us, or can they…

13. Some of the co-orbital asteroids could be suitable targets for space missions. The to-date known objects on very Earth-like orbits are not energetically the most favorable, largely due to their inclinations. We follow Shoemaker & Helin 1978 for delta-Vs.

14. Among 2561 NEAs the delta-V needed for rendezvous is minimal at a=1.0. e dependence is not strong except in discovery statistics.

15. Low-eccentricity target orbits are energetically favored, but the dependence is not strong. For example, Hayabusa target Itokawa has e=0.28 but is only 29 th on the list.

16. i affects the energy needed more. If … 2002 AA29 had very low i, it could be one of the most energetically favored. Stable QS should be low i.

17. QS are stable at low i if in the right orientation. Recall this i is 13.6º but if lower than 7º our clones and also theory give long-term stability. Where are the QS? Do present searches detect them?

18. 2002 AA 29 1980-2020 Finding Co-orbitals, Earth Trojans, QS Co-orbitals are currently usually found when near Earth (by LINEAR). Scanning high latitudes could be a good place to look and currently undersurveyed. QS could be anywhere in a big sky! For Trojans, the search region is smaller. CFHT searches for 1º/day objects in this region could find both types of object.

19. Athabasca University Robotic Telescope (AURT) project will patrol high latitudes from a dark site (0.4m aperture). Petit pipeline for faster-moving objects and use with CFHT and AURT. We will apply for more time on CFHT for searches for Trojans in morning or evening searches, bad luck with weather or queue priority to date.

20. When … low-i HS or QS targets are found… Relatively long periods spent near Earth when at one end of a horseshoe orbit or as QS favor mission operations. Earth-like orbits can favor short missions. The small size of objects known to date would present a targeting challenge but may mean lack of regolith. Some of these objects could have primordial Earth-zone material.

21. Acknowledgements and Reference Rob Whiteley kindly supplied rendezvous results used for comparison purposes. Initial parameters were taken from the MPC and NeoDys =================================== Shoemaker, E. M. & E. F. Helin, Earth- Approaching Asteroids as Targets for Exploration, in Asteroids: An Exploration Assessment, NASA, Washington, 1978.