A population of Main Belt Asteroids co-orbiting with Ceres and Vesta
Highlights
► We search for Main Belt Asteroids in the coorbital resonance with Ceres and Vesta. ► 95 MBAs are found presently in the resonance. ► Transient Quasi-Satellite (QS) orbiters can exist around both Ceres and Vesta ► We argue for the present existence of decametre-size QS orbitersaround Vesta.
Introduction
The coorbital resonance, where the gravitational interaction between two bodies with nearly the same orbital energy leads to stable and predictable motion, is ubiquitous in the Solar System. Objects attended by known co-orbital companions include Jupiter, Mars as well as the saturnian satellites Tethys, Dione, Janus and Epimetheus (see Christou (2000a) for a review). More recently, the planet Neptune was added to this list (Sheppard and Trujillo, 2006) while an additional coorbital of Dione was discovered by the Cassini mission (Murray et al., 2005). In all these cases, the motion has been shown to be stable against all but the most slow-acting perturbations (Lissauer et al., 1985, Levison et al., 1997, Brasser et al., 2004, Scholl et al., 2005).
The discovery of a coorbital attendant of the Earth on a highly inclined and eccentric orbit (Wiegert et al., 1997, Wiegert et al., 1998) motivated new theoretical work in the field. Namouni (1999), using Hill’s approximation to the Restricted Three Body Problem (R3BP) showed analytically that the introduction of large eccentricity and inclination modifies considerably the topology of coorbital dynamics near the secondary mass. It results in the appearance of bounded eccentric orbits (Quasi-Satellites; Mikkola and Innanen, 1997) and, in three dimensions, “compound” orbits and stable transitions between the different modes of libration. Further, he demonstrated numerically that these results hold when the full R3BP is considered. In this case, the appearance of new types of compound orbits, such as asymmetric modes or compounds of tadpoles and retrograde satellites, was shown in Namouni et al. (1999) to be due to the secular evolution of the coorbital potential. Such types of coorbital libration were identified in the motion of the object highlighted by Wiegert et al. (1997) as well as other near-Earth asteroids but the secular forcing of the potential in that case is provided by planetary secular perturbations (Namouni et al., 1999, Christou, 2000a). The expected characteristics of the population of co-orbitals of Earth and Venus were investigated by Morais and Morbidelli, 2002, Morais and Morbidelli, 2006 respectively.
Christou (2000b), motivated by Pluto’s ability, as demonstrated by Yu and Tremaine, 1999, Nesvorný et al., 2000, to trap other Edgeworth–Kuiper Belt objects in co-orbital motion with itself, demonstrated in turn that Main Belt Asteroids can co-orbit with the dwarf planet 1 Ceres and the large Main Belt Asteroid (MBA) 4 Vesta. Four such asteroids were identified, two co-orbiting with Ceres and two with Vesta.
Here we report the results of a search for additional coorbitals of these two massive asteroids. This was motivated partly by the large growth in the number of sufficiently well-known MBA orbits during the intervening decade, but also a refinement of the search criterion used in the work by Christou. As a result, we find over 200 new transient co-orbital MBAs of Ceres and Vesta. In this work we examine their ensemble properties, use existing dynamical models to understand how they arise and identify similarities with co-orbital populations elsewhere in the Solar System, in particular the transient coorbital NEAs of Earth and Venus.
The paper is organised as follows: In the next Section we expose our Search methodology, in particular those aspects which differ from the search carried out by Christou (2000b). In Section 3 we describe the statistics of coorbital lifetime and orbital element distribution found in our integrations. In addition, we examine the robustness of the dynamical structures we observe. In Section 4 we investigate the degree to which the model of Namouni et al. (1999) can reproduce the observed dynamics. Section 5 deals with the effects of additional massive asteroids in the three-body dynamics while Section 6 focuses on the stability of so-called Quasi-Satellite orbits. Finally, Section 7 summarises our conclusions and identifies further avenues of investigation.
Section snippets
Search methodology
Christou (2000b) searched for candidate Ceres coorbitals by employing the osculating semimajor axis ar of the asteroid relative to that of Ceres (equal to (a − aCeres)/aCeres) to highlight objects that merited further investigation. This method, although it led to the successful identification of two coorbitals, 1372 Haremari and 8877 Rentaro, ignores the existence of high frequency variations in a due to perturbations by the planets, especially Jupiter. This is illustrated in the upper panel of
Population statistics
In our runs, we observed a total of 129 and 94 asteroids enter in one of the known libration modes of the 1:1 resonance with Ceres or Vesta respectively at some point during the integrations. A full list of these asteroids is available from the corresponding author upon request. Table 2 shows a statistical breakdown of the observed population according to different types of behaviour. The first row identifies the secondary (Ceres or Vesta). The top part of the Table shows the number of
Analysis of the dynamics
The dynamical context presents some similarities with coorbitals of the Earth and Venus such as non-negligible eccentricities and inclinations. Here we attempt to model the evolution using the framework of the Restricted Three Body Problem where a particle’s state evolves under the gravity of the Sun and the secondary mass (Namouni et al., 1999). This is done through the expression where Here, a, e, I, ω and λ denote the semimajor axis, eccentricity,
The role of other massive asteroids
Christou (2000a) showed that Venus and Mars play a key role in the evolution of Earth co-orbitals. These can force transitions between different libration modes or escape from the resonance altogether. Here the only candidates available to play a similar role are other massive asteroids. In this paper we have focused on the effects of Ceres and Vesta – as well as Pallas – on Vesta or Ceres co-orbitals respectively. In a first experiment to determine their role (if any), we have integrated the
Quasi-Satellites
This section is devoted to the existence, as well as stability, of so-called “Quasi-Satellite” (QS) or “bound” orbits. These appeared first in the literature as Retrograde Satellite (RS) orbits (as it turned out, a special case of the QS state; Jackson, 1913) and later studied in the context of dynamical systems analysis (Hénon, 1969, Hénon and Guyot, 1970). More recently, the survival of this libration mode in the real Solar System was examined by Mikkola and Innanen, 1997, Wiegert et al., 2000
Conclusions and discussion
In this work we have demonstrated the existence of a population of Main Belt Asteroids (MBAs) in the coorbital resonance with the large asteroid (4) Vesta and the dwarf planet (1) Ceres. Libration within the resonance is transient in nature; our integrations show that these episodes can last for >2 × 106 yr. Partly due to the significant eccentricities and inclinations of these asteroids, we find that their dynamics are similar to those that govern the evolution of near-Earth asteroids in the 1:1
Acknowledgments
The authors thank Dr. Fathi Namouni for kindly answering our numerous questions regarding eccentric and inclined coorbital motion. Part of this work was carried out during a visit of A.A.C. at UWO, funded by NASA’s Meteoroid Environment Office (MEO). Astronomical research at the Armagh Observatory is funded by the Northern Ireland Department of Culture, Arts and Leisure (DCAL).
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