On the transfer of radiation at asteroidal surfaces in relation to their orbit deflection — II

The efficiency of absorption of X-rays generated by a nuclear explosion at the surface of an asteroid, estimated earlier, is used to calculate the explosion yield needed to deflect the orbit of an asteroid. Following the work of Ahrens &38; Harris, it is shown that a recoil velocity of 1 cm s⁻¹ is required to deflect an asteroid from a collision course with the Earth, and the necessary yield of explosion energy is estimated. If it is assumed that the scaling law between the energy and the diameter of the resulting crater, obtained from experiments carried out on the Earth, remains valid on the asteroid surface, where gravity is much weaker, an explosion energy of 8 and 800 megaton (Mton) equivalent of TNT would be required for asteroids of diameter 1 and 10 km respectively. If, on the other hand, the crater diameter is proportional to a certain power of the gravity g , the power being determined from a dimension analysis, 130 kton and 12 Mton would be required to endow asteroids of diameters 1 and 10 km with the required velocity, respectively. The result indicates that in order to estimate the required explosion energy, a better understanding of cratering under gravity much weaker than on the Earth would be required.     

Averaging on Earth‐Crossing Orbits

The orbits of planetcrossing asteroids (and comets) can undergo close approaches and collisions with some major planet. This introduces a singularity in the Nbody Hamiltonian, and the averaging of the equations of motion, traditionally used to compute secular perturbations, is undefined. We show that it is possible to define in a rigorous way some generalised averaged equations of motion, in such a way that the generalised solutions are unique and piecewise smooth. This is obtained, both in the planar and in the threedimensional case, by means of the method of extraction of the singularities by Kantorovich. The modified distance used to approximate the singularity is the one used by Wetherill in his method to compute probability of collision. Some examples of averaged dynamics have been computed; a systematic exploration of the averaged phase space to locate the secular resonances should be the next step.'Alice sighed wearily. I think you might do something better with the time she said, than waste it asking riddles with no answers(Alice in Wonderland, L. Carroll)     

Asteroid Mean Elements: Higher Order and Iterative Theories

Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation; they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step, used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory, resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete, fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements, incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain. This revised version was published online in July 2006 with corrections to the Cover Date.     

Clast sizes of ejecta from explosive eruptions on asteroids: implications for the fate of the basaltic products of differentiation

We use a simple model of the formation, growth, coalescence and migration of veins of basaltic melt generated by partial melting in chondritic asteroids to deduce the sizes of, and pressures within, the fluid-filled dikes reaching the surfaces of such bodies. The gas contents ( 1000 ppm of mainly CO and N₂) of the asteroids were high enough that bubbles of free gas trapped in the melt veins gave the basaltic melts significant buoyancy; expansion of these gases as a dike opened to the vacuum at the surface led to fragmentation of the melts into liquid droplets which were transported upwards by the accelerating gases to the surface. The sizes of these droplets and, hence, of the pyroclastic glass beads into which they cooled, are calculated to lie in the range 30 μm to 4 mm; this range is essentially independent of the size or gas content of the asteroid parent and only weakly dependent on the internal pressure of the erupting fluid. The fate of the pyroclasts, however, does depend on all of these factors. At very low internal pressures, significant separation of the gas and liquid in a rising dike may take place and not all of the liquid will be expelled from the dike when it opens to the surface. For relatively large ( 100 km radius) asteroids with relatively low ( 300 ppm) gas contents, the larger clasts are too heavy to be lifted from the level at which magma fragmentation takes place by the gas flow and so would also remain behind to form basaltic veins. The apparent absence of basaltic veins in meteorites then implies both that internal pressures in near-surface dikes were generally greater than 0.3 MPa and that low gas contents were not common. Finally, as long as pyroclasts are lofted from the magma fragmentation level, they will be accelerated to at least 90% of the final gas speed. If this speed exceeds the escape speed from the asteroid (as happens readily for high gas contents and small asteroids), the pyroclasts will be expelled into space and lost from the meteorite record. Otherwise (low gas contents or large asteroids), they will eventually fall back to be incorporated into the surface regolith, modifying the chemical and physical properties of meteorites subsequently derived from it.     

亚暴膨胀相近磁尾位形不稳定性模型Ⅱ.中磁尾等离子体流与近磁尾亚暴活动的关系

在单流体MHD近似下，研究了有背景等离子体流存在时的近磁尾位形不稳定性．分析表明，等离子体地向流使两支漂移气球模DBM1和DBM2的不稳定增长更快．与卫星观测资料对比显示，诸多的观测观象与本模型的预言一致．这个结果对中磁尾磁场重联及高速等离子体流与亚暴膨胀相在近地触发之间的关系给出了新的解释．     

Meteorites from the asteroid 6 Hebe

We have numerically integrated the orbits of 18 fictitious fragments ejected from the asteroid 6 Hebe, an S-type object about 200km across which is located very close to theg=g ₆ (orv ₆) secular resonance at a semimajor axis of 2.425AU and a (proper) inclination of 15° .0. A realistic ejection velocity distribution, with most fragments escaping at relative speeds of a few hundredsm/s, has been assumed. In four cases we have found that the resonance pumps up the orbital eccentricity of the fragments to values >0.6, which result into Earth-crossing, within a time span of 1Myr; subsequent close encounters with the Earth cause strongly chaotic orbital evolution. The closest Earth and Mars encounters recorded in our integration occur at miss distances of a few thousandths ofAU, implying collision lifetimes <10⁹ yr. Some other fragments affected by the secular resonance become Mars-crossers but not Earth-crossers over the integration time span. Two bodies are injected into the 3 : 1 mean motion resonance with Jupiter, and also display macroscopically chaotic behaviour leading to Earth-crossing. 6 Hebe is the first asteroid for which a realistic collisional/dynamical evolutionroute to generate meteorites has been fully demonstrated. It may be the parent body of one of the ordinary chondrite classes.     

小天体离散元仿真软件的搭建与测试

小天体探测是当今太阳系探测的一大热点, 对小行星演化的研究有助于人们了解太阳系的起源. 演化研究的一项重要内容是小天体结构的演化, 即小天体在多种力学机制作用下自身形状与结构的演化. 在小天体碎石堆结构的假设之下, 一种比较常见的模拟小天体结构演化的方法是离散元仿真算法(Discrete Element Method, DEM), 目前国内外有数个团队开发了相关算法软件. 本文介绍了团队开发的《基于DEM仿真算法的多粒子系统模拟软件》的基础理论、实现方法以及加速算法, 并使用二体接触模型、声速传播仿真、小行星内部压强、小行星旋转稳定性仿真算例验证了算法的可靠性.     

An equal-area map projection for irregular objects

An increasing number of objects discovered in the Solar System have irregular shapes which require unconventional mapping techniques. Here we present a technique that produces equivalent maps of such objects. As such maps preserve surface area they are especially useful for mapping the distribution of geological features on irregular objects. Maps of blocks and craters on the Asteroid 433 Eros are used to illustrate the potential use of the technique. Two equal-area maps are adequate to cover the entire asteroid and convincingly demonstrate variations in surface density of mapped features. Similar coverage by orthographic views requires 4 to 6 plots. The distortion of the maps are comparable to the distortions of maps created by other techniques.     

Earth impact probability of the Asteroid (25143) Itokawa to be sampled by the spacecraft Hayabusa

The Japanese spacecraft Hayabusa is planed to reach the Asteroid Itokawa in September 2005, and to bring back some samples of its surface to Earth in 2007. We have studied the future possible evolution of this asteroid by integrating numerically over 100 Myr a set of 39 initially indistinguishable orbits (clones), obtained either by small variations of the nominal initial conditions, or by using different computers (introducing different round-off errors). The results indicate that an Earth impact of this 500-m-size asteroid is likely within a million years, which is only a factor of four larger than the average impact frequency of asteroids of this size. The mission Hayabusa may thus sample a good candidate for being among the next 500-m-size Earth impactors.     

Physical properties of Asteroid (25143) Itokawa—Target of the Hayabusa sample return mission

We present results of a ground-based observational study of the Hayabusa mission target near-Earth Asteroid (25143) Itokawa. Our data consist of BVRI-filter CCD photometry and low resolution CCD spectroscopy, from which the asteroid's rotation period, axial ratio, broadband colors, and taxonomic classification are derived. Analysis of the R-filter lightcurve data shows a synodic rotation period of 12.12±0.02 h, consistent with results from other observers. We observed a maximum peak-to-peak amplitude of 1.05 magnitudes, which—depending on the taxonomic class assumed when correcting for phase angle effects—implies a minimum axial ratio of 2.14. The shape of the rotation lightcurves varies considerably between data sets due to the changing viewing geometry. The lightcurve data from this study has been included in the shape model analysis of Kaasalainen et al. (2003 Astron. Astrophys, 405, L29-L32) and the Hapke analysis of Lederer et al. (2005 Icarus 173,153-165). Color variations were also observed, with the interpolated color indices at lightcurve midpoint being: (B-V)=0.94±0.05, (V-R)=0.40±0.06, and (V-I)=0.74±0.07. Our low resolution Palomar spectra from March 2001 covered a wavelength range of 0.3-1.0 μm. We measured a spectral slope of 9.3±0.3%/100 nm between 0.55-0.70 μm and a deep 1 μm absorption (equivalent ECAS color: w-x=−0.111±0.003, v-x=0.031±0.003). Comparison of our spectra with published ECAS data from Zellner et al. (1985 Icarus 61, 355-416) indicates that this object is most likely of Q- or S-type, similar to ordinary chondrite meteorites. Our data are more consistent with a Q-type body when both the spectroscopic data and the available BVRI photometry are taken into account.