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

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).

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).

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.

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

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

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

Two other objects are known to have horseshoe orbits deviating further from Earth's orbit (2000 PH5) and short-arc object 2001 GO2 have eccentricities of about 0.2 and low inclinations. They move ‘in and out’ more and ‘up and down’ less than the preceding objects.

2001 GO2 (a short arc object) and 2000 PH5 have similar horseshoe orbits GO2 will do QS motion in the gap of its horseshoe (insert).

Motion of Quasi-Satellite – Inertial to Corotating Frames In the inertial frame the QS remains on one side of the planet. Relative to the planet the QS appears to ‘orbit’ once a year

Quasi-Satellite in the corotating frame appears to follow a bean-shaped orbit. In most known cases the apparent inclination is high (unlike in this clip). Google “Paul Wiegert UWO” for more info & animations.

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

2006 FV35 is a recently discovered quasi-satellite, already well-observed with a good orbit. Its inclination is 7.1º and eccentricity 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

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.

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…

The remaining objects have eccentricity higher than 0.2 and may have high inclinations. At least one such object, 3753 Cruithne, has a complex horseshoe-like orbit with respect to Earth, but most do not show resonant interaction.

We find that some of the co-orbital asteroids are suitable targets for space missions. The 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.

Among 2561 NEAs the delta-V needed for rendezvous is minimal at a=1.0. The sample is biased by e needed to discover if a<1.0.

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.

These considerations suggest low-e objects with semimajor axis close to 1.0 will be energetically favorable as targets. Earth horseshoe objects have these characteristics. Shoemaker already in 1978 suggested Earth Trojans would be favorable but none are known. We are looking….bad luck so far….

Unfortunately, known horseshoe objects have high e or i. If … 2002 AA29 had very low i, it could be one of the most energetically favored.

Intuitively it seems low-e low-i HS orbits should be less stable. A clone study of 2002 AA29 shows a stable band around i=5º and not lower.

We find that despite the interesting dynamics and naïve considerations that HS objects should make good targets, we are unlikely to find low-i HS objects as needed. We have not yet discussed Earth Trojans (ETs) since using only known objects or their clones. ETs could be good for long-duration missions. They potentially could have primordial material.

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

Advertisement: See poster by Shelton et al. for our Athabasca University Robotic Telescope (AURT) project to patrol high latitudes from a dark site. See Lerner et al. poster about our adaptation of Petit pipeline for faster-moving objects and use with CFHT and AURT.

If … somewhat better HS targets are found… Relatively long periods spent near Earth when at one end of a horseshoe orbit favor mission operations. Earth-like orbits can favor short missions (manned?). The small size of objects known to date would present a targeting challenge but may mean lack of regolith.

The co-orbital objects investigated to date have shown relatively short periods of stability in their current orbits and are thus not likely primordial. They likely are recent arrivals from the asteroid belt, which is also the case for most other NEAs. Earth Trojans could be the place to find primordial material from the Earth formation zone. Either one would be a great spacecraft target.

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.