Elsevier

Icarus

Volume 217, Issue 1, January 2012, Pages 27-42
Icarus

A population of Main Belt Asteroids co-orbiting with Ceres and Vesta

https://doi.org/10.1016/j.icarus.2011.10.016 Get rights and content

Abstract

We have carried out a search for Main Belt Asteroids (MBAs) co-orbiting with the large MBA Vesta and the dwarf planet Ceres. Through improving the search criteria used in Christou (Christou, A.A. [2000b]. Astron. Astrophys. 356, L71–L74) and numerical integrations of candidate coorbitals, we have identified approximately 51 (44) objects currently in co-orbital libration with Ceres (Vesta). We show that these form part of a larger population of transient coorbitals; 129 (94) MBAs undergo episodes of co-orbital libration with Ceres (Vesta) within a 2 Myr interval centred on the present. The lifetime in the resonance is typically a few times ∼105 yr but can exceed 2 × 106 yr. The variational properties of the orbits of several co-orbitals were examined. It was found that their present states with respect to the secondary are well determined but knowledge of it is lost typically after ∼2 × 105 yr. Objects initially deeper into the coorbital region maintain their coorbital state for longer. Using the model of Namouni et al. (Namouni, F., Christou, A.A., Murray, C.D. [1999]. Phys. Rev. Lett. 83, 2506–2509) we show that their dynamics are similar to those of temporary coorbital NEAs of the Earth and Venus. As in that case, the lifetime of resonant libration is dictated by planetary secular perturbations, the inherent chaoticity of the orbits and close encounters with massive objects other than the secondary. In particular we present evidence that, while in the coorbital state, close encounters with the secondary are generally avoided and that Ceres affects the stability of tadpole librators of Vesta. Finally we demonstrate the existence of Quasi-Satellite orbiters of both Ceres and Vesta and conclude that decametre-sized objects detected in the vicinity of Vesta by the DAWN mission may, in fact, belong to this dynamical class rather than be bona-fide (i.e. Keplerian) satellites of 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 a r 2 = C - 8 μ 3 S ( λ r , e , I , ω ) where S = 1 2 π - π π a S | r - r S | - r · r S aa S d λ 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).

References (40)

  • P. Wajer

    Dynamical evolution of Earth’s Quasi-Satellites: 2004 GU9 and 2006 FV35

    Icarus

    (2010)
  • R. Brasser et al.

    Long-term evolution of the Neptune Trojan 2001 QR322

    Mon. Not. R. Astron. Soc.

    (2004)
  • D. Brouwer et al.

    The secular variations of the orbital elements of the principal planets

    Amer. Ephem. Naut. Alm.

    (1950)
  • A. Cellino

    Understanding the origin of the asteroids through the study of Vesta and Ceres: The role of DAWN

    Adv. Geophys.

    (2006)
  • J.E. Chambers

    A hybrid symplectic integrator that permits close encounters between massive bodies

    Mon. Not. R. Astron. Soc.

    (1999)
  • A.A. Christou

    Co-orbital objects in the main asteroid belt

    Astron. Astrophys.

    (2000)
  • E. Everhart

    An efficient integrator that uses Gauss–Radau spacings

  • J.D. Giorgini

    JPL’s on-line Solar System data service

    Bull. Am. Astron. Soc.

    (1996)
  • M. Hénon

    Numerical exploration of the restricted problem. V. Hill’s case: Periodic orbits and their stability

    Astron. Astrophys.

    (1969)
  • M. Hénon et al.

    Stability of periodic orbits in the Restricted Three-Body Problem

  • Cited by (19)

    • Resonances in the asteroid and trans–Neptunian belts: A brief review

      2018, Planetary and Space Science
      Citation Excerpt :

      While Jupiter's resonant population was very well documented in the past, more recently considerable progress has been done in the study of Neptune's resonant population (Gladman et al., 2012; Volk et al., 2016). Although along the years there were found individual asteroids in resonance with some terrestrial planets, only recently a large population of asteroids was identified in resonance with Mars (Gallardo, 2007b; Gallardo et al., 2011), as well as some in resonance with Venus, Earth, Saturn and Uranus (Gallardo, 2006; Connors et al., 2008; de la Fuente Marcos and de la Fuente Marcos, 2013) and tens of asteroids in coorbital motion with Ceres and Vesta (Christou and Wiegert, 2012). Ceres and Vesta also imprint a secular dynamics on some asteroids as showed by Tsirvoulis and Novaković (2016).

    • Secular resonances with Ceres and Vesta

      2016, Icarus
      Citation Excerpt :

      Recently in Novaković et al. (2015) we have reported on the role of the linear secular resonance with (1) Ceres on the post-impact orbital evolution of asteroids belonging to the (1726) Hoffmeister family. Contrary to previous belief, in which massive asteroids were only considered to be able to influence the orbits of smaller bodies by their mutual close encounters (Nesvorný et al., 2002) and maybe low order mean-motion resonances (Christou and Wiegert, 2012), we have a concrete example that they can strongly affect the secular evolution of the orbits of the latter through secular resonances. Also, Li and Christou (2016) have found that a secular resonance between two members of the Himalia jovian satellite group can affect their orbital evolution, and Carruba et al. (2016) showed that secular resonances with Ceres tend to drive away asteroids in the orbital neighborhood of Ceres, giving more evidence that secular resonances in general can be important even if the perturbing body is relatively small.

    • Dynamical sequestration of the Moon-forming impactor in co-orbital resonance with Earth

      2016, Icarus
      Citation Excerpt :

      An additional class of co-orbital resonance is composed of the quasi-satellites. Examples of these include several asteroids associated with Earth's quasi-satellite resonance (Connors et al., 2002, 2004; Wiegert et al., 2005; Wajer, 2010) and other quasi-satellites hosted by Venus (Mikkola et al., 2004), Jupiter (Kinoshita and Nakai, 2007), Saturn (Gallardo, 2006), and Neptune (de la Fuente Marcos and de la Fuente Marcos, 2012a) as well as the minor planets (1) Ceres, (4) Vesta (Christou and Wiegert, 2012), and (134,340) Pluto (de la Fuente Marcos and de la Fuente Marcos, 2012b). Among all these examples only the jovian and neptunian Trojans are stable on time scales extending to the age of the solar system (Levison et al., 1997; Lykawka et al., 2011).

    • Trapping and dynamical evolution of interplanetary dust particles in Earth's quasi-satellite resonance

      2013, Icarus
      Citation Excerpt :

      These are near-Earth asteroids trapped in Earth’s quasi-satellite resonance (Connors et al., 2002, 2004; Wiegert et al., 2005; Wajer, 2010). In the decade since the first objects were recognized, dynamicists have identified additional quasi-satellites hosted by the planets Venus (Mikkola et al., 2004), Jupiter (Kinoshita and Nakai, 2007), Saturn (Gallardo, 2006), and Neptune (de la Fuente Marcos and de la Fuente Marcos, 2012a) as well as the minor planets (1) Ceres, (4) Vesta (Christou and Wiegert, 2012), and (134340) Pluto (de la Fuente Marcos and de la Fuente Marcos, 2012b). There is one orbital characteristic that is unique to the quasi-satellite resonance compared to all other mean–motion resonances, including other classes of the 1:1 co-orbital resonance.

    • Asteroids

      2013, Treatise on Geochemistry: Second Edition
    View all citing articles on Scopus
    View full text