2002 AA29

A further characteristic is that its mean orbital period about the Sun is exactly one sidereal year. This means that it is locked into a relationship with the Earth, since such an orbit is only stable under particular conditions. As yet only a few asteroids of this sort are known, locked into a 1:1 resonance with the Earth. The first was 3753 Cruithne, discovered in 1986.

Asteroids that have a 1:1 orbital resonance with a planet are also called co-orbital objects, because they follow the orbit of the planet. The most numerous known co-orbital asteroids are the so-called trojans, which occupy the L4 and L5 Lagrangian points of the relevant planet. However, 2002 AA₂₉ does not belong to these. Instead, it follows a so-called horseshoe orbit along the path of the Earth.

Orbit

Orbital data

Shortly after the discovery by LINEAR, Scientists at the Jet Propulsion Laboratory (JPL), the Athabasca University (Canada), the Queen's University in Kingston (Ontario, Canada), the York University in Toronto and the Tuorla Observatory of the University of Turku in Finland determined the unusual orbit of 2002 AA₂₉, and through further observations at the Canada–France–Hawaii Telescope in Hawaii it was confirmed that:

• Its orbit lies for the most part inside Earth's orbit. The orbits of most asteroids lie in the asteroid belt between Mars and Jupiter. Through orbital disturbances by the gas giant planets, mainly Jupiter and the Kirkwood gaps, and through the Yarkovsky effect (force due to asymmetrical absorption and emission of infrared radiation) asteroids are diverted into the inner Solar System, where their orbits are further influenced by close approaches with the inner planets. 2002 AA₂₉ has probably been brought in the same way from the outer Solar System into Earth's influence. However, it is also suggested that the asteroid has always been on a near-Earth orbit and thus that it or a precursor body was formed near Earth's orbit. In this case one possibility is that it could be a fragment from a collision of a middle-sized asteroid with Earth or the Moon.
• Its mean orbital period is one sidereal year. After it was diverted into the inner Solar System – or formed on a path near Earth's orbit – the asteroid must have been moved into an orbit corresponding with Earth. In this orbit it was repeatedly pulled by Earth in such a way that its own orbital period became the same as that of Earth. In the current orbit, Earth thus holds the asteroid in synchronicity with its own orbit.

• The orbit of the asteroid is almost circular, with an eccentricity of 0.012 which is even lower than that of the Earth at 0.0167. The other near-Earth asteroids have on average a significantly higher eccentricity of 0.29. Also, all other asteroids in 1:1 resonance with Earth known before 2002 have very strongly elliptical orbits – e.g. the eccentricity of (3753) Cruithne is 0.515. At the time of its discovery the orbit of 2002 AA₂₉ was unique, because of which the asteroid is often called the first true co-orbital companion of Earth, since the paths of previously discovered asteroids are not very similar to Earth's orbit. The very low orbital eccentricity of 2002 AA₂₉ is also an indication that it must always have been on a near-Earth orbit, or the Yarkovsky effect must have comparatively strongly caused it to spiral into the inner Solar System over billions of years, since as a rule asteroids which have been steered by planets have orbits with higher eccentricity.
• The orbital inclination with respect to the ecliptic (orbital plane of Earth) of 2002 AA₂₉ is a moderate 10.739°. Hence its orbit is slightly tilted compared with that of Earth.

Shape of the orbit

If one looks at the orbit of 2002 AA₂₉ from a point moving with the Earth around the Sun (the reference frame of the Earth–Sun system), it describes over the course of 95 years an arc of almost 360°, which during the next 95 years it retraces in reverse. The shape of this arc is reminiscent of a horseshoe, from which comes the name "horseshoe orbit". As it moves along the Earth's orbit, it winds in a spiral about it, in which each loop of the spiral takes one year. This spiral motion (in the Earth–Sun reference frame) arises from the slightly lower eccentricity and the tilt of the orbit: the inclination relative to the Earth's orbit is responsible for the vertical component of the spiral loop, and the difference in eccentricity for the horizontal component.

When 2002 AA₂₉ is approaching the Earth from in front (i.e. it is moving slightly slower, and the Earth is catching it up), the gravitational attraction of the Earth shifts it onto a slightly faster orbit, a little nearer the Sun. It now hurries ahead of the Earth along its new orbit, until after 95 years it has almost lapped the Earth and is coming up from behind. Again it comes under the Earth's gravitational influence; this time it is lifted onto a slower orbit, further from the Sun. On this orbit it can no longer keep pace with the Earth, and it falls behind until in 95 years it is once again approaching the Earth from in front. The Earth and 2002 AA₂₉ chase each other in turn around the Sun, but do not get close enough to break the pattern.

On 8 January 2003, the asteroid approached the Earth from in front to a distance of 0.0391 AU (5,850,000 km; 3,630,000 mi), its closest approach for nearly a century. Since that date, it has been hurrying ahead (with a semi-major axis less than 1 AU), and will continue to do so until it has reached its closest approach from behind on 11 July 2097 at a distance of 0.037712 AU (5,641,600 km; 3,505,500 mi). As a result of this subtle exchange with the Earth, unlike other Earth orbit crossing asteroids, it is not expected to ever collide with the Earth. Calculations indicate that in the next few thousand years it will never come closer than 4.5 million kilometres, or about twelve times the distance from the Earth to the Moon.

Because of its orbital inclination of 10.739° to the ecliptic, 2002 AA₂₉ is not always forced by the Earth on its horseshoe orbit however but can sometimes slip out of this pattern. It is then caught for a while in the neighbourhood of the Earth. This will next happen in about 600 years i.e. in the 26th century. It will then stay within the small gap in the Earth's orbit which it does not reach in its previous horseshoe orbit, and will be no further than 0.2 astronomical units (30 million km) away from the Earth. There it will slowly circle the Earth almost like a second moon, although it takes one year for a circuit. After 45 years it finally switches back into the horseshoe orbit, until it again stays near the Earth for 45 years around the year 3750 and again in 6400. In these phases in which it stays outside its horseshoe orbit it oscillates in the narrow region along the Earth's orbit where it is caught, moving back and forth in 15 years. Because it is not bound to the Earth like the Moon but is mainly under the gravitational influence of the Sun, it belongs to the bodies called quasi-satellites. This is somewhat analogous to two cars travelling side by side at the same speed and repeatedly overtaking one another but which are however not attached to each other. Orbital calculations show that 2002 AA₂₉ was in this quasi-satellite orbit for 45 years from about 520 AD but because of its tiny size was too dim to have been seen. It switches approximately cyclically between the two orbital forms, but always stays for 45 years in the quasi-satellite orbit. Outside the time frame from about 520–6500 AD, the calculated orbits become chaotic i.e. not predictable, and thus for periods outside this time frame no exact statements can be made. 2002 AA₂₉ was the first known heavenly body that switches between horseshoe and quasi-satellite orbits.