Nature © Macmillan Publishers Ltd 1997 NATURE | VOL 387 | 12 JUNE 1997 685 letters to nature An asteroidal companion to the Earth Paul A. Wiegert*, Kimmo A. Innanen* & Seppo Mikkola† * Department of Physics and Astronomy, York University, 4700Keele Street, North York, Ontario M3J 1P3, Canada † Tuorla Observatory, University of Turku, 21500 Piikkio ¨, Finland ......................................................................................................................... Near-Earth asteroids range in size from a few metres to more than 30 km: in addition to playing an important role in past and present impact rates on the Earth, they might one day be exploited as bases for space exploration or as mineral resources. Many near- Earth asteroids move on orbits crossing that of the Earth, but none has hitherto been identified as a dynamical companion to the Earth. Here we show that the orbit of asteroid 3753 (1986 TO), when viewed in the reference frame centred on the Sun but orbiting with the Earth, has a distinctive shape characteristic of ‘horseshoe’ orbits. Although horseshoe orbits are a well-known feature of the gravitational three-body problem 1 , the only other examples of objects moving on such orbits are the saturnian satellites Janus and Epimetheus 2 —and their behaviour is much less intricate than that of 3753. Moreover, the fact that 3753 exhibits such a dynamical relationship with the Earth shows that, although it is not a satellite of our planet per se, it is, apart from the Moon, the only known natural companion of the Earth. Figure 1 shows a view of the inner Solar System projected onto the ecliptic plane in a frame which co-rotates with the Earth; in this frame, the Earth appears stationary. The path of asteroid 3753 over a little more than one year is indicated by the line with arrowheads. The path has roughly the shape of a kidney bean, owing simply to the eccentricity of the asteroid’s orbit. As the asteroid’s orbital period is currently slightly shorter than that of the Earth, its orbit does not close on itself but rather advances slightly each year: the asteroid thus spirals forward along the orbit of the Earth. This behaviour is not unusual in itself. What distinguishes 3753 from other near-Earth asteroids (NEAs) is its behaviour as it approaches the Earth: our planet’s gravitational pull acts to increase the asteroid’s period from slightly below to slightly above one year. As a result, the asteroid begins to fall behind, and hence to move away from the Earth. A possible collision with our planet is avoided: the closest approach during this leg is indicated by the heavy line A in Fig. 1. Having reversed its direction, the asteroid eventually approaches the Earth from the other side. In this case, however, the Earth acts to decrease the asteroid’s period to its previous value slightly below one year, and 3753 begins moving away from the Earth again. At closest approach on this leg, the edge b of the ‘kidney bean’ trajectory coincides with the heavy line labelled B in Fig. 1. The cycle of reversals then goes on to repeat itself, the Earth effectively repelling the asteroid at each close approach. The previous two reversals occurred in approximately AD 1515 and 1900; the next two will occur in AD 2285 and 2680. The variation in semimajor axis of 3753 over the next 2,000 years is shown in Fig. 2, the reversals corresponding to transitions across the semimajor axis of the Earth (1 astronomical unit, AU, the average Earth–Sun distance). It should be noted that reversals occur when edge a (not b; see Fig. 1) approaches the Earth. Owing to the inclination and orienta- tion of the asteroid’s orbit, edge b never approaches the Earth closely, despite its appearance when projected onto the ecliptic plane. Figure 3 presents a view of the inner Solar System from an ecliptic edge-on perspective, and the asteroid’s high inclination (20°) is evident. The orientation of the asteroid’s orbit allows edge b to overlap the position of the Earth in Fig. 1 with no danger of collision. The complete orbit of 3753 is thus an ‘overlapping horseshoe’ (the outer envelope of which is indicated by the heavy line in Fig. 1), a kind which has never been observed before, even in theoretical studies. The asteroid’s significant inclination and eccen- tricity (e  0:5) have evidently caused it to escape more intensive scrutiny since its discovery, as they serve effectively to obscure the nature of its trajectory. The asteroid’s orbit is chaotic, on a timescale of 150 years, but it remains a near-Earth object in our simulations for timescales of a million years. However, not all of this time is spent in a horseshoe orbit: the asteroid can switch between its current orbit and a non- horseshoe orbit with semimajor axis around 1.1 AU on timescales of a few hundred thousand years. Asteroid 3753 passes from inside to outside the Earth’s orbit, but its minimum yearly approach distance is usually quite large. During the closest approaches, which happen only every 385 years, the asteroid passes within 0.1 AU (roughly 40 times the Earth–Moon distance) of our planet, the last such approach having occurred about 100 years ago. Over the next year, the closest approach will be only to within 0.31 AU. The relative proximity of 3753 to the Earth during recent times presumably aided in its discovery by Waldron in October 1986 3,4 . Asteroid 3753 has an absolute visual magnitude of 15.1 (ref. 5), brighter than typical of NEAs, and from which one can estimate a diameter of 5 km (refs 6, 7). Asteroid 3753 crosses the orbits of Venus and Mars as well as that of the Earth. Though its orbit does not currently intersect that of any planet, the asteroid’s argument of perihelion precesses at a rate of roughly ˙ q  þ0:6° per century. As a result, its orbit will intersect that of the Earth in 2,750 years, and (if it survives this crossing) that of Venus in about 8,000 years. Similarly, the asteroid’s orbit inter- sected Mars’s roughly 2,500 years ago. These results suggest that the asteroid’s current horseshoe orbit may not be stable for arbitrarily long times, unless there is some dynamical ‘safety mechanism’ which preserves it against close planetary encounters. At this point, the existence of such a safety mechanism seems unlikely, and yet the very low a priori probability of an object being injected Figure 1 A view of the inner Solar System projected onto the ecliptic plane in a frame which co-rotates with the Earth; in this frame, the Earth appears stationary and is located at the symbol . The average distances of the planets Mercury, Venus, Earth and Mars from the Sun are indicated by dotted circles. The path of asteroid 3753 over slightly more than a year, beginning approximately in AD 2000, is shown by the line with arrowheads, with the outer envelope of the horseshoe indicated by the heavy lines. Reversals occur when a coincides with A, and when b coincides with B (see text).