Elsevier

Icarus

Volume 171, Issue 1, September 2004, Pages 102-109
Icarus

Transient co-orbital asteroids

https://doi.org/10.1016/j.icarus.2004.04.019Get rights and content

Abstract

We analyze the orbital behavior of four new co-orbital NEOs and the Earth horseshoe object 2002 AA29. The new objects are 2001 CK32, a 3753 Cruithne-like co-orbital of Venus, 2001 GO2 and 2003 YN107, two objects with motion similar to 2002 AA29. 2001 CK32 is on a compound orbit. The asteroid reverses its path when the mean longitude difference is −50°. Its motion is chaotic. 2001 GO2 is an Earth HS orbiter with repeated transitions to the QS phase, the next occurring 200 years from now. The HS libration period is 190 years and the QS phases last 45 years. For 2002 AA29, our simulations permit us to find useful theoretical insights into the HS–QS transitions. Its orbit can be simulated with adequate accuracy for 4400 years into the future and 1483 years into the past. The new co-orbital 2003 YN107 is at present an Earth QS. It has entered this phase in 1997 and will leave it again in 2006, completing one QS cycle. Like 2002 AA29, it has frequent transitions between HS and QS. One HS cycle takes 133 years.

Introduction

Co-orbital motion, which is a common phenomenon in the Solar System, manifests itself in three types of motion: the classical tadpole, the horseshoe (HS) and the quasi-satellite (QS) Jackson, 1913, Mikkola and Innanen, 1997. The latter orbits are retrograde satellite orbits with large heliocentric eccentricity and are well known in the context of the three-body problem. Such orbits are stable with increasing relative orbital energy (Hénon, 1969). The three orbit-types can be distinguished through the librational properties of the mean longitude difference between the asteroid and the planet. The latter is defined as φ=λλp, where the subscript is used to denote planetary quantities.

Tadpole orbits librate about φ=±60° depending on whether they are leading (+60°) or trailing the planet (−60°). Horseshoe orbits librate around φ=180° and quasi-satellite orbits librate around φ=0°. For orbits with large enough eccentricity and/or high enough inclination, transitions between these orbit types are possible (Namouni, 1999) as well as the formation of so-called ‘compound orbits’ (Namouni et al., 1999). Co-orbital asteroids in tadpole motion are termed Trojans. Today, more than a thousand jovian Trojans are known, several martian, and one neptunian. The saturnian system contains tadpole orbiters as well as the horseshoe companions Janus and Epimethius (see, e.g., Dermott and Murray, 1981). It is conjectured that the majority of these are primordial objects (see, e.g., Brasser et al., 2004, Mikkola et al., 1994, Tabachnik and Evans, 2000). The Earth has four co-orbital companions: 3753 Cruithne Wiegert et al., 1997, Wiegert et al., 2002 AA29 (Connors et al., 2002), 2000 PH5 Wiegert et al., 2002, Margot and Nicholson, 2003, 2001 GO2 (Wiegert et al., 2002) and one QS object that will soon revert back to HS (Connors et al., 2004). Venus has one co-orbital object, 2002 VE68, which is also the first known QS in action at present (Mikkola et al., 2004). Christou (2000) has studied the behavior of probable Earth and Venus co-orbitals and found that 10563 Izdhubar, 3362 Khufu and 1994 WF2 may become Earth co-orbitals in the future while 1989 VA may become a Venus co-orbital.

Morais and Morbidelli (2002) have obtained the size and orbital distributions of Near-Earth Asteroids (NEAs) that are expected to be co-orbitals of the Earth in a steady-state scenario. They predict 0.65 objects with H<18 and 16 with H<22 and conclude that these objects are not easily observed as they are distributed over a large area in the sky and spend most of the time away from opposition where they may be too faint.

The presentation of this paper is divided as follows: in Section 2, the method used for our numerical orbit computations is outlined. Section 3 is devoted to a summary of the motion of 3753 Cruithne, 2002 VE68 and the temporary Earth HS object 2000 PH5. In Section 4, the motion of 2001 CK32, a new Venus co-orbital with motion similar to that of 3753 Cruithne is described. Section 5 deals with the orbit of 2002 AA29, Section 6 with 2001 GO2, and Section 7 with the Earth QS 2003 YN107. In Section 8 the summary and conclusions are provided.

Section snippets

Numerical experiments

The orbital elements for all objects were taken from the NeoDys1 pages. From the covariance matrix, a further 49 clone orbits were generated to take uncertainties in the elements into account. The variations in the element vector q were computed using δq=∑k=16ξkλkXk, where λk and Xk are, correspondingly, the eigenvalues and eigenvectors of the covariance matrix C, while ξk are random numbers with a nearly Gaussian distribution and ξ̄k2=1 (see Brasser et al.,

Overview

We performed a search of those asteroids whose semimajor axis is in an annulus |aap|<ε where ε=(1/3μ)1/3, with μ the planetary mass in solar masses. We simulated these objects and their clone orbits and determined which ones showed co-orbital behavior. The resulting objects have their elements listed in Table 1. These objects are transient co-orbitals: they are injected, through some mechanism, into the co-orbital zone of one of the inner planets, remain there for awhile and then leave. This

2001 CK32: 3753 Cruithne's twin

2001 CK32 is a Venus compound HS–QS orbiter on a very chaotic orbit. Its orbit is relatively well known with an observed arc length of 511 days and its motion is similar to that of 3753 Cruithne. Figure 1 shows the mean longitude difference of a sample orbit for the next 7000 years. At present the offset is at −50°. From the figure one observes that there is also some temporary QS motion and pure HS motion or compound motion with the offset at +50°. The mean period of the current compound

The orbit of 2002 AA29

Asteroid 2002 AA29, except for its inclination of 10.7°, has a low-eccentricity orbit that is similar to that of the Earth (Connors et al., 2002). The HS libration period is 190 years and the extrema of φ are φ0≈2.5° and φ1≈357.5°, in agreement with Connors et al. (2002). It was further confirmed that the transitions between HS and QS motion occur near t=2600 and t=3750, each QS phase lasting 45 years. The period of libration while in the QS phase is 15 years. While Connors et al. (2002) list a

2001 GO2: Earth HS 2

The trajectory of 2001 GO2 enables it to have frequent transitions between the HS and QS states. The extrema of φ are φ1≈18° and φ2≈342°. The period is 190 years: the same as 2002 AA29. The orbit of 2001 GO2 is chaotic and has an observed arc of only five days, so that the following results need to be interpreted with some caution. The Lyapunov time for this object is about 180 years.

The divergence between neighboring orbits is accelerated during the first HS–QS transition at t=2201. These QS

2003 YN107: an Earth QS in action

The Earth co-orbital 2003 YN107 is at present a QS of the Earth (see Connors et al., 2004).

Summary and conclusions

We have analyzed the orbits of several new co-orbital asteroids in the inner Solar System as well one already known. These are 2001 CK32, a Venus co-orbital whose orbit is similar to 3753 Cruithne, 2001 GO2, a second Earth HS companion, and 2002 AA29 and 2003 YN107. The orbit of 2001 CK32 is a compound one, with a libration period of 330 years and is highly chaotic. The orbits of 2002 AA29, as well as 2001 GO2, both have a libration period of 190 years (see Connors et al. (2002) about 2002

Acknowledgements

R.B., K.I., M.C., and P.W. thank the Natural Sciences and Engineering Research Council of Canada for its partial support in funding this research. We are greatly indebted to Robert McNaught for quick follow-up observations of 2003 YN107 after its discovery.

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