Orbit and size distributions for asteroids temporarily captured by the Earth-Moon system
Introduction
The phenomenon of planets temporarily capturing asteroids and comets has been known for a long time, and has been studied especially for gas giants in the solar system. Temporarily captured objects have been extensively studied particularly in the case of Jupiter, not least due to the fact that comet Shoemaker-Levy 9 (Noll et al., 1996) was a temporarily-captured object from the 1970s up until its impact into Jupiter in July 1994. Bailey (1972) showed that temporary capture of satellites is possible for all known planets in the solar system in the framework of the elliptic restricted three-body problem. However, it was not realized until recently that there is a constant population of temporarily captured objects around the Earth (Granvik et al., 2012, hereafter GVJ).
Natural Earth satellites (NES) is a population of objects in the vicinity of the Earth on elliptic geocentric orbits for a limited amount of time that are temporarily captured from the near-Earth-object (NEO) population. So far, the first and only confirmed NES has been asteroid 2006 RH120 (Kwiatkowski et al., 2009) which made four revolutions around the Earth from July 2006 to July 2007. GVJ divided Earth’s temporary satellites into two subcategories: temporarily-captured orbiters (TCOs) and temporarily-captured flybys (TCFs). TCOs make at least one complete revolution around the Earth while TCFs make less than one revolution around the Earth.
The main source replenishing the temporarily-captured population is the NEO population, as asteroids enter the Earth’s Hill sphere through the Earth’s L1 and L2 regions. An alternative source for Earth’s natural satellites is lunar ejecta. The presence of lunar impact ejecta on geocentric orbits is supported by the presence of lunar meteorites. The lifetime of lunar ejecta on geocentric orbits is comparable to the lifetime of captured objects, i.e., on the order of months (Gladman et al., 1995) after which they either impact the Earth or the Moon or evolve into the NEO population. However, the number of NESs is likely to experience only sporadic increases caused by lunar impacts, because impacts capable of producing meter-scale ejecta are stochastic events when compared to the timescale it takes to replenish the NES population with NEOs.
Moorhead and Cooke (2014) investigated aerobraking, i.e., the change in the kinetic energy of a test particle due to friction caused by the Earth’s atmosphere, with the resulting trajectory outside the atmosphere. Only 0.2% of meter-sized objects (geocentric hyperbolic NEO flybys) experience the aerobraking phenomenon. A steady-state population for aerobrake captures of meter-sized objects is of the population captured from the NEO population. We will not consider this mechanism as a source for NESs, because it is deemed negligible for cm-sized and larger objects. In what follows we therefore only consider the dynamical capture of NEOs.
NES can provide unique constraints at the lower end of the asteroid size-frequency distribution. Apart from serendipitous observations of NEO flybys, they are the only population which allow for follow-up observations and provide detailed information on sub-meter-sized asteroids in general. Recently, there has been increased interest in asteroid boulders, i.e., separate objects observed by in-situ missions on the surfaces of asteroids such as (25143) Itokawa by Hayabusa (Fujiwara, Kawaguchi, Yeomans, Abe, Mukai, Okada, Saito, Yano, Yoshikawa, Scheeres, Barnouin-Jha, Cheng, Demura, Gaskell, Hirata, Ikeda, Kominato, Miyamoto, Nakamura, Nakamura, Sasaki, Uesugi, 2006, Saito, Miyamoto, Nakamura, Ishiguro, Michikami, Nakamura, Demura, Sasaki, Hirata, Honda, Yamamoto, Yokota, Fuse, Yoshida, Tholen, Gaskell, Hashimoto, Kubota, Higuchi, Nakamura, Smith, Hiraoka, Honda, Kobayashi, Furuya, Matsumoto, Nemoto, Yukishita, Kitazato, Dermawan, Sogame, Terazono, Shinohara, Akiyama, 2006) or (4179) Toutatis by Chang’e 2 (Huang et al., 2013). As boulders are of comparable size to the asteroids present in the steady-state population of NES, studying the physical properties of NES allows constraining the physical properties of boulders. Vice versa, the retrieval of a boulder from the surface of a larger asteroid, the goal for NASA’s Asteroid Redirect Mission (Abell et al., 2016), would expand our knowledge about meter-sized asteroids.
Publications focusing on NESs were scarce until 2011 as shown by the review in GVJ. Since the realization that there is a population of macroscopic objects orbiting the Earth and thus requiring the lowest possible Δv for space missions to asteroids, there has been an increased interest in the subject, particularly in assessments of potential asteroid rendez-vous and recovery missions to these objects. The assessment of rendez-vous possibilities was pioneered by Chyba et al. (2014), who calculated spacecraft transfer orbits for 96% of synthetic TCOs provided by GVJ. The work was expanded by Brelsford et al. (2016) to include realistic spacecraft behaviour. The most plausible mechanism for missions to NESs is a horde of hibernating satellites (e.g., CubeSat class) parked on a waiting orbit, and triggered upon a suitable NES discovery. Also, García Yárnoz et al. (2013) assessed temporarily-captured objects in terms of being easily-retrievable potential asteroid mission targets, and Verrier and McInnes (2015) investigated the artificial temporary capture of asteroids into Earth orbit by altering their velocities, after passing near or through KAM tori regions.
The difficulty of detecting NESs is a major bottleneck, holding back the enthusiasm of the community. Bolin et al. (2014) investigated the detectability of TCOs by optical, radar and spaceborne infrared observatories and concluded that TCOs can occasionally be found by current state-of-the-art optical and radar telescopes. The Large Synoptic Survey Telescope (LSST, Jones et al., 2009) is anticipated to find TCOs on a regular basis when it starts operations in 2020s. Also, Ruprecht et al. (2014) investigated the possibility of detecting Earth’s natural satellites with the Space Surveillance Telescope, and aim to find a handful of meter-sized objects on geocentric orbits annually. Out of these, 10% will be TCOs and the rest TCFs. As of early 2016, there has been one dedicated survey of NESs using the wide-field Hyper Suprime-Cam on the Subaru Telescope in Hawai’i, but results from that survey are still pending.
The sole known TCO 2006 RH120 attracted the attention of Urrutxua et al. (2014) who studied the external impulse needed to capture that particular asteroid on a more stable geocentric orbit. Recently, the meteor EN130114, which occured on January 13, 2014, most probably originated from a TCO orbit (Clark et al., 2016) and may thus be the first known terrestrial impact of a natural object from a geocentric orbit. It is possible that other NES have also been observed but have not been recognized as natural objects.
Distinguishing natural objects from man-made space debris has caused problems to observers, as some observations attributed to artificial space debris have afterwards been deemed to have belonged to natural objects. For example, 2006 RH120 was initially classified as an artificial object. On the contrary, the object WT1190F, which impacted Earth on November 13, 2015, has not yet been explicitly attributed to any known artificial object although it is widely accepted of being an artificial object due to its high area-to-mass ratio. WT1190F was initially speculated to be a natural TCO, because its orbit was highly untypical compared to the vast majority of orbits of artificial satellites and space debris.
GVJ concentrated on the properties of TCOs. TCFs did not receive much attention, although they do play a significant role in the overall steady-state population of Earth’s natural satellites (NES). In the present work we revisit the definition of TCFs, and treat them as an integral part of the NES population. For example, the presence of TCFs captured for a long time has not previously been investigated. For possible rapid-response missions to recently discovered asteroids the total number of complete revolutions is of a lesser significance compared to the capture duration of these objects.
Section snippets
Permanent captures
An external perturbation during the temporary capture is required for an asteroid to become captured on a permanent orbit. Taking aside artificial scenarios (Baoyin, Chen, Li, 2010, Verrier, McInnes, 2015, Urrutxua, Scheeres, Bombardelli, Gonzalo, Peláez, 2014), the realistic natural mechanisms for such a perturbation would be the previously mentioned aerobraking (Moorhead and Cooke, 2014), the effect of which is small for objects which are possible to observe with optical telescopes, or a
Initial conditions
To conduct various statistical studies on the NES population, we generated a distribution of initial orbital elements similar to GVJ. The basic principles upon which the generation was based, as well as differences from the previous analysis and their justifications are discussed below; for details, we refer the reader to GVJ.
The phase space of heliocentric Keplerian elements (semimajor axis a⊙, eccentricity e⊙ and inclination i⊙) from where the captures on heliocentric orbits is possible is
Conclusions
We have updated and extended the analysis carried out by GVJ. Our estimate for the TCO and TCF steady-state populations, which require the combination of the NEO model by Granvik et al. (2016) and either one of the models by Rabinowitz et al. (2000) or Brown et al. (2002), confirm most of the findings by GVJ and, in addition, show that TCFs form an important part of the NES population. Although TCF are systematically captured for shorter times than TCOs, there is also a non-negligible fraction
Acknowledgements
We are greatful to Giovanni Valsecchi for pointing out an important reference explaining the residence-time distribution. We also would like to thank Alan W. Harris and an anonymous reviewer for their helpful review comments. GF was supported by the Magnus Ehrnrooth foundation. MG was supported by the Academy of Finland grant #137853 and the University of Hawai’i. Computation resources were provided by CSC - The Finnish Centre for Scientific Computing, Ltd. A portion of the work was supported
References (43)
- et al.
Detecting Earth’s temporarily-captured natural satellites – Minimoons
Icarus
(2014) - et al.
Debiased orbital and absolute magnitude istribution of the near-Earth objects
Icarus
(2002) - et al.
Rendezvous missions to temporarily captured near Earth asteroids
Planet. Space Sci.
(2016) - et al.
The dynamical evolution of lunar impact ejecta
Icarus
(1995) - et al.
The population of natural Earth satellites
Icarus
(2012) - et al.
The population of near-Earth asteroids
Icarus
(2015) Secular perturbations of asteroids with high inclination and eccentricity
Astron. J. (N. Y.)
(1962)- et al.
Two alternative scenarios to expain the strange extraterrestrial spinel grain record of the late eocene
47th Lunar and Planetary Science Conference
(2016) - et al.
Detailed images of asteroid 25143 itokawa from hayabusa
Science
(2006) - et al.
What does it take to capture an asteroid? A case study on capturing asteroid 2006 RH120
24th AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, New Mexico
(2014)
Overview and updated status of the asteroid redirect mission (ARM)
AAS/Division for Planetary Sciences Meeting Abstracts
Chaos-assisted capture of irregular moons
Nature
Studies on planetary satellites. Satellite capture in the three-body elliptical problem
Astron. J. (N. Y.)
Capturing near-Earth asteroids
Res. Astron. Astrophys.
The flux of small near-Earth objects colliding with the Earth.
Nature
A 500-kiloton airburst over Chelyabinsk and an enhanced hazard from small impactors
Nature
Designing rendezvous missions with mini-moons using geometric optimal control
J. Ind. Manage. Optim.
Impact detection of temporarily captured natural satellites
Astron. J.
Features of encounters of small bodies with planets
Sol. Syst. Res.
Horseshoe and Trojan orbits associated with Jupiter and Saturn
Astron. J. (N. Y.)
The Rubble-Pile asteroid Itokawa as observed by Hayabusa
Science
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