The Uppsala‐DLR Trojan Survey of L4, the preceding Lagrangian cloud of Jupiter

We have used the ESO Schmidt telescope during the apparitions 1996, 1997 and 1998 to study the preceding Lagrangian cloud of Jupiter, L₄. In our observed field of view, about 700 square degrees, during 1996 we found 399 moving objects that we classified as Trojans. From this we conclude that down to absolute magnitude H ≤ 13.0 there are ≈ 1100 Trojans in the L₄ cloud. Proper elements of 696 numbered and multiopposition Trojans were calculated and one of these in the L₅ cloud were found to be a non Trojan. A discussion of the Trojan proper elements is also presented.     

On the definition of asteroid magnitudes

The problem of a sharp definition of two photometric parameters for asteroids in the presence of empirical phase functions is discussed. In a rational magnitude system advantage should be taken of the nearly linear phase curve.     

The 2/1 and 3/2 Resonant Asteroid Motion: A Symplectic Mapping Approach

A comparative study is made between the 2/1 and the 3/2 resonant asteroid motion, with the aim to understand their different behaviour (gap in the 2/1 resonance, group in the 3/2 resonance). A symplectic mapping model is used, for each of these two resonances, assuming the asteroid is moving in the three-dimensional space under the gravitational perturbation of Jupiter. It is found that these resonances differ in several points, and although there is, in general, more chaos in the phase space close to the 3/2 resonance, even in the model of circular orbit of Jupiter, there are regions, close to the secondary resonances, which are less chaotic in the 3/2 resonance compared to the 2/1 resonance, and consequently trapping can take place.     

Transformation of Trojans into quasi-satellites during planetary migration and their subsequent close-encounters with the host planet

We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus test particle Trojans and quasi-satellites. We find that the libration frequencies of Trojans are similar to those of quasi-satellites. This similarity enables a dynamical exchange of objects back and forth between the Trojan and quasi-satellite resonances during planetary migration. This exchange is facilitated by secondary resonances that arise whenever there is more than one migrating planet. For example, secondary resonances may occur when the circulation frequencies, f, of critical arguments for the Uranus-Neptune 2:1 mean-motion near-resonance are commensurate with harmonics of the libration frequency of the critical argument for the Trojan and quasi-satellite 1:1 mean-motion resonance . Furthermore, under the influence of these secondary resonances quasi-satellites can have their libration amplitudes enlarged until they undergo a close-encounter with their host planet and escape from the resonance. High-resolution simulations of this escape process reveal that ≈80% of jovian quasi-satellites experience one or more close-encounters within Jupiter’s Hill radius (R_H) as they are forced out of the quasi-satellite resonance. As many as ≈20% come within R_H/4 and ≈2.5% come within R_H/10. Close-encounters of escaping quasi-satellites occur near or even below the 2-body escape velocity from the host planet. Finally, the exchange and escape of Trojans and quasi-satellites continues to as late as 6-9τ in some simulations. By this time the dynamical evolution of the planets is strongly dominated by distant gravitational perturbations between the planets rather than the migration force. This suggests that exchange and escape of Trojans and quasi-satellites may be a contemporary process associated with the present-day near-resonant configuration of some of the giant planets in our Solar System.     

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.     

行星内部地震波及其对卫星轨道的影响

本文指出地震学在天文和行星学科里的重要作用.我们主要介绍最近提出的“潮汐—地震波共振”(tidal-seismic resonance)效应,并且讨论它对卫星轨道演化的作用.当在同步轨道以下周期运动的卫星引起的引潮力的频率和行星内部自由震荡频率吻合时,就会发生潮汐—地震波共振.此时,行星内部的地震波将被激发并引起行星表面的显著位移.升高和下降的地面会对卫星产生一个力矩从而使得卫星轨道下降.因为潮汐共振引起的动态地面位移可以比单纯引潮力引起的位移大两个数量级,所以潮汐共振会显著加速卫星下降速率.我们用我们开发的三维地震波场模拟程序AstroSeis数值计算了潮汐—地震波共振对轨道的影响,进而推测这一共振效应可能对行星早期吸积速度有显著影响.另外,因为行星内部的Q值和S波的波速对潮汐共振影响很大,未来研究微重力环境下的小行星或陨石内部地震波的速度和Q值对研究行星演化和太阳系的形成至关重要.     

(47171) 1999 TC36, A transneptunian triple

We present new analysis of HST images of (47171) 1999 TC₃₆ that confirm it as a triple system. Fits to the point-spread function (PSF) consistently show that the apparent primary is itself composed of two similar-sized components. The two central components, A1 and A2, can be consistently identified in each of nine epochs spread over 7 years of time. In each instance, the component separation, ranging from 0.023 ± 0.002 to 0.031 ± 0.003 arcsec, is roughly one half of the Hubble Space Telescope’s diffraction limit at 606 nm. The orbit of the central pair has a semi-major axis of a ∼ 867 km with a period of P ∼ 1.9 days. These orbital parameters yield a system mass that is consistent with M_sys = 12.75 ± 0.06 × 10¹⁸ kg derived from the orbit of the more distant secondary, component B. The diameters of the three components are . The relative sizes of these components are more similar than in any other known multiple in the Solar System. Taken together, the diameters and system mass yield a bulk density of . HST photometry shows that component B is variable with an amplitude of ?0.17 ± 0.05 magnitudes. Components A1 and A2 do not show variability larger than 0.08 ± 0.03 magnitudes approximately consistent with the orientation of the mutual orbit plane and tidally distorted equilibrium shapes. The system has high specific angular momentum of J/J′ = 0.93, comparable to most of the known transneptunian binaries.     

Detailed prediction for the BYORP effect on binary near-Earth Asteroid (66391) 1999 KW4 and implications for the binary population

A previous theory by the authors for detailed modeling of the binary YORP effect is reviewed and expanded to accommodate doubly-synchronous binary systems, as well as a method for non-dimensionalizing the coefficients for application to binary systems where a shape model to compute its own coefficients is not available. The theory is also expanded to account for the effects of primary J₂ and the Sun’s 3rd body perturbation on the secular orbit evolution. The newly expanded theory is applied to the binary near-Earth Asteroid 1999 KW4, for which a detailed shape model is available. The result of simulation of the secular evolutionary equations shows that the KW4 orbit will be double in size in approximately 22,000 years, and will reach the Hill radius in approximately 54,000 years. The simulation also shows that the eccentricity will alternate growing and shrinking in magnitude, depending on the location of the solar node in the body-fixed frame. Therefore the eccentricity is not fixed to evolve in the opposite sign as the semi-major axis unless the circulation of the node (with a period of 500 years) is averaged out as well. The current orbit expansion rate for KW4 of 7 cm per year is shown to be detectable with observations of the mean anomaly which grows quadratically in time with an expanding orbit. Finally, the KW4 results are scaled for application to a number of other binary systems for which detailed shape models are not available. This application shows that the orbits considered can expand to their Hill radius in the range of 10⁴-10⁶ years. This implies rapid formation of binary systems is necessary to support the large percentage of binaries observed in the NEA population.     

Asteroid detection at millimetric wavelengths with the PLANCK survey

The PLANCK mission, originally devised for cosmological studies, offers the opportunity to observe Solar System objects at millimetric and submillimetric wavelengths. In this paper we concentrate on the asteroids of the Main Belt, a large class of minor bodies in the Solar System. At present, more that 40 000 of these asteroids have been discovered and their detection rate is rapidly increasing. We intend to estimate the number of asteroids that can be detected during the mission and to evaluate the strength of their signal. We have rescaled the instrument sensitivities, calculated by the LFI and HFI teams for sources fixed in the sky, introducing some degradation factors to properly account for moving objects. In this way a detection threshold is derived for asteroidal detection that is related to the diameter of the asteroid and its geocentric distance. We have developed a numerical code that models the detection of asteroids in the LFI and HFI channels during the mission. This code performs a detailed integration of the orbits of the asteroids in the timespan of the mission and identifies those bodies that fall in the beams of PLANCK and their signal strength. According to our simulations, a total of 397 objects will be observed by PLANCK and an asteroidal body will be detected in some beam in 30% of the total sky scan-circles. A significant fraction (in the range from 50 to 100 objects) of the 397 asteroids will be observed with a high S/N ratio. Flux measurements of a large sample of asteroids in the submillimeter and millimeter range are relevant since they allow to analyze the thermal emission and its relation to the surface and regolith properties. Furthermore, it will be possible to check on a wider base, the two standard thermal models, based on a nonrotating or rapidly rotating sphere. Our method can also be used to separate Solar System sources from cosmological sources in the survey. This work is based on PLANCK LFI activities.     

A closer look at main belt asteroids 1: WF/PC images

We present new reconstructions of images of main belt Asteroids 9 Metis, 18 Melpomene, 19 Fortuna, 216 Kleopatra, and 624 Hektor, made with the uncorrected Wide-Field/Planetary Camera (WF/PC) on the Hubble Space Telescope (HST). Deconvolution with the MISTRAL algorithm demonstrates that these asteroids are clearly resolved. We determine diameters, albedos, and lower limits to axial ratios for these bodies. We also review the process used to restore the aberrated images. No surface features or companions are found, but the rotation of 216 Kleopatra is clearly seen. The asteroidal albedos are similar to those determined by other procedures.