page_title: 2002 AA29
section_title: Shape of the orbit
hierarchical_section_title: 2002 AA29 / Orbit / Shape of the orbit
caption_attribution_description: English: Horseshoe-orbit of 2002 AA29. The graphic shows a full revolution of 95 years. The position of 2002 AA29 along the orbit is that of year 2003 (last nearest approach to earth). Deutsch: Hufeisenumlaufbahn von 2002 AA29 entlang der Erdbahn im Verlauf von 95 Jahren vom mit der Bahnbewegung der Erde mitbewegten Bezugssystem betrachtet. Deutsch: Hufeisenumlaufbahn von 2002 AA29 entlang der Erdbahn im Verlauf von 95 Jahren vom mit der Bahnbewegung der Erde mitbewegten Bezugssystem betrachtet; Bild: JPL English: The horseshoe orbit of AA29 with respect to the Earth every 95 years. Image: JPL
context_page_description: 2002 AA₂₉ is a small near-Earth asteroid that was discovered on January 9, 2002 by the LINEAR automatic sky survey. The diameter of the asteroid is only about 20–100 metres. It revolves about the Sun on an almost circular orbit very similar to that of the Earth. This lies for the most part inside the Earth's orbit, which it crosses near the asteroid's furthest point from the Sun, the aphelion. Because of this orbit, the asteroid is classified as Aten type, named after the asteroid 2062 Aten.
  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.
context_section_description: 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, we need have no fear that it could 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 betw
caption: Horseshoe orbit of 2002 AA29. The graphic shows a full revolution of 95 years. The position of 2002 AA29 along the orbit is that of year 2003 (last nearest approach to Earth). Image: JPL
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