Families of periodic orbits in Hill’s problem with solar radiation pressure: application to Hayabusa 2

This work studies periodic solutions applicable, as an extended phase, to the JAXA asteroid rendezvous mission Hayabusa 2 when it is close to target asteroid 1999 JU3. The motion of a spacecraft close to a small asteroid can be approximated with the equations of Hill’s problem modified to account for the strong solar radiation pressure. The identification of families of periodic solutions in such systems is just starting and the field is largely unexplored. We find several periodic orbits using a grid search, then apply numerical continuation and bifurcation theory to a subset of these to explore the changes in the orbit families when the orbital energy is varied. This analysis gives information on their stability and bifurcations. We then compare the various families on the basis of the restrictions and requirements of the specific mission considered, such as the pointing of the solar panels and instruments. We also use information about their resilience against parameter errors and their ground tracks to identify one particularly promising type of solution.     

Identifying near-Earth object families

The study of asteroid families has provided tremendous insight into the forces that sculpted the main belt and continue to drive the collisional and dynamical evolution of asteroids. The identification of asteroid families within the NEO population could provide a similar boon to studies of their formation and interiors. In this study we examine the purported identification of NEO families by Drummond [Drummond, J.D., 2000. Icarus 146, 453-475] and conclude that it is unlikely that they are anything more than random fluctuations in the distribution of NEO osculating orbital elements. We arrive at this conclusion after examining the expected formation rate of NEO families, the identification of NEO groups in synthetic populations that contain no genetically related NEOs, the orbital evolution of the largest association identified by Drummond [Drummond, J.D., 2000. Icarus 146, 453-475], and the decoherence of synthetic NEO families intended to reproduce the observed members of the same association. These studies allowed us to identify a new criterion that can be used to select real NEO families for further study in future analyses, based on the ratio of the number of pairs and the size of strings to the number of objects in an identified association.     

Massive identification of asteroids in three-body resonances

An essential role in the asteroidal dynamics is played by the mean motion resonances. Two-body planet–asteroid resonances are widely known, due to the Kirkwood gaps. Besides, so-called three-body mean motion resonances exist, in which an asteroid and two planets participate. Identification of asteroids in three-body (namely, Jupiter–Saturn–asteroid) resonances was initially accomplished by Nesvorný and Morbidelli (Nesvorný D., Morbidelli, A. [1998]. Astron. J. 116, 3029–3037), who, by means of visual analysis of the time behaviour of resonant arguments, found 255 asteroids to reside in such resonances. We develop specialized algorithms and software for massive automatic identification of asteroids in the three-body, as well as two-body, resonances of arbitrary order, by means of automatic analysis of the time behaviour of resonant arguments. In the computation of orbits, all essential perturbations are taken into account. We integrate the asteroidal orbits on the time interval of 100,000 yr and identify main-belt asteroids in the three-body Jupiter–Saturn–asteroid resonances up to the 6th order inclusive, and in the two-body Jupiter–asteroid resonances up to the 9th order inclusive, in the set of ～250,000 objects from the “Asteroids – Dynamic Site” (AstDyS) database. The percentages of resonant objects, including extrapolations for higher-order resonances, are determined. In particular, the observed fraction of pure-resonant asteroids (those exhibiting resonant libration on the whole interval of integration) in the three-body resonances up to the 6th order inclusive is ≈0.9% of the whole set; and, using a higher-order extrapolation, the actual total fraction of pure-resonant asteroids in the three-body resonances of all orders is estimated as ≈1.1% of the whole set.     

Motion of a Meteoroid Released from an Asteroid

Evidence of asteroid surface features as regolith grains and larger boulders implies resurfacing possibility due to external forces such as gravitational tidal force during close planet encounters. Motion of a meteoroid released from an asteroid in the gravitational fields of the asteroid and the Earth is modeled. We are interested mainly in a distance between the meteoroid and the asteroid as a function of the time. Applications to Itokawa and some close approaching NEAs are presented.     

Asteroid taxonomic signatures from photometric phase curves

We explore the correlation between an asteroid’s taxonomy and photometric phase curve using the H, G₁₂ photometric phase function, with the shape of the phase function described by the single parameter G₁₂. We explore the usability of G₁₂ in taxonomic classification for individual objects, asteroid families, and dynamical groups. We conclude that the mean values of G₁₂ for the considered taxonomic complexes are statistically different, and also discuss the overall shape of the G₁₂ distribution for each taxonomic complex. Based on the values of G₁₂ for about half a million asteroids, we compute the probabilities of C, S, and X complex membership for each asteroid. For an individual asteroid, these probabilities are rather evenly distributed over all of the complexes, thus preventing meaningful classification. We then present and discuss the G₁₂ distributions for asteroid families, and predict the taxonomic complex preponderance for asteroid families given the distribution of G₁₂ in each family. For certain asteroid families, the probabilistic prediction of taxonomic complex preponderance can clearly be made. In particular, the C complex preponderant families are the easiest to detect, the Dora and Themis families being prime examples of such families. We continue by presenting the G₁₂-based distribution of taxonomic complexes throughout the main asteroid belt in the proper element phase space. The Nysa–Polana family shows two distinct regions in the proper element space with different G₁₂ values dominating in each region. We conclude that the G₁₂-based probabilistic distribution of taxonomic complexes through the main belt agrees with the general view of C complex asteroid proportion increasing towards the outer belt. We conclude that the G₁₂ photometric parameter cannot be used in determining taxonomic complex for individual asteroids, but it can be utilized in the statistical treatment of asteroid families and different regions of the main asteroid belt.     

Asteroid Confusions with Extremely Large Telescopes

Asteroids can be considered as sources of contamination of point sources and also sources of confusion noise, depending whether their presence is detected in the image or their flux is under the detection limit. We estimate that at low ecliptic latitudes, ≈10,000–20,000 asteroids/sq. degree will be detected with an E-ELT like telescope, while by the end of Spitzer and Herschel missions, infrared space observatories will provide ≈100,000 serendipitous asteroid detections. The detection and identification of asteroids is therefore an important step in survey astronomy.     

Stability of Binary Asteroids

The stability and final outcome of a strongly interacting binary asteroid system is considered. We discuss the implications of the system transferring energy and angular momentum between rotational and translational motion while conserving the total system energy and angular momentum. Using these results we can develop a set of sufficient conditions for stability against escape and impact. These allow us to delineate several classes of final outcomes for a binary asteroid system, each of which may have implications for asteroid observations. The effects of energy dissipation on an asteroid binary system are also considered and are shown to be able to change the stability of the system against escape and impact. An example computation for the near-Earth asteroid binary 1996 FG3 is given along with a series of numerical explorations of an evolving binary system consisting of an ellipsoid and a sphere of equal mass.     

Physical properties of near‐Earth asteroids from thermal infrared observations and thermal modeling

Abstract— We review the physical principles on which asteroid thermal models are based and their application in the derivation of asteroid sizes and albedos. In particular, the use of simple thermal models to derive reliable diameters and albedos of near‐Earth asteroids is discussed.     

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.     

The asteroid belt and its evolution

We have reinvestegated the suggestion that collisional fragmentation in the asteroid belt can account for its present luminosity function. We suggest, based on the usual Boltzmann-type equation for this process, that for the brightest asteroids the time scale for a catastropic collision is 1.2 × 10⁹yr. However, the assumption of molecular chaos is not valid in the asteroid belt and we demonstrate a new method to determine the necessary corrections. We then obtain, using the new procedure, a lower limit for a collision time. For the above sample it is 2 × 10¹¹yr. This, we believe, rules out collisional evolution of the asteroid belt since its formation. Finally, we also show histograms of eccentricity, inclination, absolute magnitude, height above the ecliptic plane, and argument of perihelion for the 2829 asteroids with well-determined orbits. This represents a synthesis of the numbered asteroid and PLS data.     

Physical characteristics of Hayabusa target Asteroid 25143 Itokawa

In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.     

Determination of asteroid masses from their close encounters with Mars

An obstacle to the asteroid mass determination lies in the difficulty in isolating the gravitational perturbation exerted by a single asteroid on the planets, being strongly correlated and mixed up with those of many other asteroids. This hindrance may be avoided by the method of analysis presented here: an asteroid mass is estimated in correspondence with its close encounters with Mars where the acceleration it induces on the planet can be sufficiently disentangled from those generated by the remaining asteroid masses to calculate. We test this technique in the analysis of range observations to Mars Global Surveyor and Mars Express performed from 1999 to 2007. For this purpose, we adopt the dynamical model of the planetary ephemeris INPOP06 (Fienga et al., 2008), which includes the gravitational influences of the 300 most perturbing asteroids of the Martian orbit. We obtain the solutions of 10 asteroid masses that have the largest effects on this orbit over the period examined: they are generally in good agreement with determinations recently published.     

小行星网络数据库发展评述

评述了近年来国际上与小行星相关的网络数据库的发展概况和意义。概要介绍了小行星轨道数据库、小行星测光数据库、小行星红外数据库、近地小行星数据库和小行星综合数据库的开发成果和应用价值，以及基于小行星数据库的历表服务；展望了小行星网络数据库的发展趋势。     

Asteroid lightcurve phase shift from rough‐surface shadowing

We have simulated asteroid lightcurves for simple shape models using a realistic surface scattering law. The scattering law includes a shadowing function computed with numerical ray‐tracing. We computed lightcurves in a variety of illumination geometries for both the traditional Lommel–Seeliger law and our seminumerical law. We observe a shift in the rotational phase of the lightcurves, which depends on the parameters of the scattering law as well as the illumination geometry and the direction of the spin axis of the asteroid. This phase shift is always zero at opposition, and can be as large as 10° for illumination geometries typical for Main Belt asteroids. The phase shift has implications on the accuracy of other results which are based on asteroid lightcurve analysis, such as spin‐state or shape determination.     

Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions.     

An Analytic Model of Three-Body Mean Motion Resonances

It has been recently shown that the resonances among the mean motions of an asteroid, Jupiter and Saturn are very important for the origin of chaos in the asteroid belt. We develop an analytic model for these three-body resonances which allows quantitative predictions on their amplitude and libration timescale. We also discuss why these resonances are chaotic. This revised version was published online in July 2006 with corrections to the Cover Date.     

The orbital evolution of NEAs and the resonances with Jupiter

two near-earth-asteroids associated with resonances with Jupiter are studied over a time span of 10⁵ yrs. We found that asteroid (887) is temporary trapped in the 3:1 resonance; thus indicating that this resonance could be a source of short-lived NEAs. We also found that asteroid (3552) with a large eccentricity and a high inclination is wandering about the 1:1 resonant region.     

Dynamical parameters of spacecraft motion near small celestial body

The paper considers how a spacecraft can be put into orbit around a small asteroid to function as its artificial moon. We study the general behavior of perturbations that affect the current coordinates of an orbiting spacecraft and estimate the perturbations caused by the main perturbing factors, i.e., (1) the irregular shape of an asteroid and (2) celestial bodies of the Solar System. With specific orbital parameters, a long-term targeted operation of a spacecraft can be actualized in a mission to the asteroid Apophis where the spacecraft will carry a radio beacon transponder.     

Discovery of asteroid 1976 AA

Asteroid 1976 AA was discovered as a result of a continuing systematic search for planet-crossing asteroids. It is the first asteroid to be thoroughly investigated by means of photometry and radiometry on its discovery apparition. It is also the first asteroid found with a semimajor axis and period less than that of the Earth and the first Earth-crossing asteroid which does not cross the orbit of either Mars or Venus. We estimate that there might be several tens of objects to absolute magnitude 18, which are exclusively Earth crossing. Some of these objects might be exceptionally easy to reach by spacecraft.