Computing the critical points of the distance function between two Keplerian orbits via rigorous global optimization

A novel method to compute all critical points of the distance function between two Keplerian orbits (either bounded or unbounded) with a common focus is presented. The problem is attacked as a global optimization problem, solved by a rigorous global optimizer based on Taylor models. Thus, thigh enclosures of the stationary points are obtained. The embedded capability of the method of delivering high-order Taylor expansions is then used to analyze how uncertain orbital parameters affect the position of the stationary points and the associated distance values. Sample orbital sets and Apophis asteroid are used as test cases.     

Secular evolution of the orbits of hypothetical satellites of Uranus

The problem of the secular perturbations of the orbit of a test satellite with a negligible mass caused by the joint influence of the oblateness of the central planet and the attraction by its most massive (or main) satellites and the Sun is considered. In contrast to the previous studies of this problem, an analytical expression for the full averaged perturbing function has been derived for an arbitrary orbital inclination of the test satellite. A numerical method has been used to solve the evolution system at arbitrary values of the constant parameters and initial elements. The behavior of some set of orbits in the region of an approximately equal influence of the perturbing factors under consideration has been studied for the satellite system of Uranus on time scales of the order of tens of thousands of years. The key role of the Lidov–Kozai effect for a qualitative explanation of the absence of small bodies in nearly circular equatorial orbits with semimajor axes exceeding ~1.8 million km has been revealed.     

Generalization of Levi-Civita regularization in the restricted three-body problem

A family of polynomial coupled function of n degree is proposed, in order to generalize the Levi-Civita regularization method, in the restricted three-body problem. Analytical relationship between polar radii in the physical plane and in the regularized plane are established; similar for polar angles. As a numerical application, trajectories of the test particle using polynomial functions of 2,3,…,8 degree are obtained. For the polynomial of second degree, the Levi-Civita regularization method is found.     

一种高精度时间同步器的研制与性能测试

针对移动通信网络基站间需要建立高精度时间同步的需求,研制了一种具有高精度时间同步功能和高精度频率输出的时间同步器,并设计了相应的性能测试方法。测试结果表明,在同等条件下,不同时间同步器输出的1PPS平均同步精度优于5ns／d,24h内输出的频率准确度优于10^-12／s,其他各项指标基本合格,符合设计要求。     

Mapping the substructure in the Galactic halo with the next generation of astrometric satellites

We run numerical simulations of the disruption of satellite galaxies in a Galactic potential to build up the entire stellar halo, in order to investigate what the next generation of astrometric satellites will reveal by observing the halo of the Milky Way. We generate artificial DIVA , FAME and GAIA halo catalogues, in which we look for the signatures left by the accreted satellites. We develop a method based on the standard Friends-of-Friends algorithm applied to the space of integrals of motion. We find this simple method can recover about 50 per cent of the different accretion events, when the observational uncertainties expected for GAIA are taken into account, even when the exact form of the Galactic potential is unknown. The recovery rate for DIVA and FAME is much smaller, but these missions, like GAIA , should be able to test the hierarchical formation paradigm on our Galaxy by measuring the amount of halo substructure in the form of nearby kinematically cold streams with, for example, a two-point correlation function in velocity space.     

A test for assessing the goodness-of-fit of luminosity function models to magnitude–redshift data

We propose a test which allows us to check whether a luminosity function model can account for the intrinsic luminosity distribution of a magnitude–redshift sample complete in apparent magnitude. No a priori assumptions are required concerning the redshift-space distribution of the sources, so neither the clustering nor an eventual evolution of the mean number density of the galaxies affects the conclusions of the goodness-of-fit test. The statistical efficiency of the test, if used as a fitting technique for estimating the best-fitting solution of a parametric luminosity function model, is comparable to the efficiency of standard maximum likelihood fitting techniques. The goodness-of-fit test presents however a major improvement compared with fitting techniques in general: the capacity to assess the adequacy of the proposed parametric model to the data. The computational implementation of this new test is straightforward. Its potential is illustrated on the Southern Sky Redshift Survey of da Costa et al.     

A Research on the Collision Probability Calculation of Space Debris for Nonlinear Relative Motions†

The calculation of collision probability is the foundation of collision detection and avoidance maneuver for space objects. Now an assumption of linear relative motion is usually applied in the calculation of collision probability and then the complex 3-dimensional problem can be reduced to a 2-dimensional integral of probability density function over the area of circle. However, if the relative velocity value is very small, the term of linear relative motion is not valid. So it is necessary to consider the calculation of collision probability for nonlinear relative motions. The method used to calculate collision probability for nonlinear relative motion is studied, and test cases are designed to justify the validity of this method. It is applicable to collision probability problems involving relative velocity and error covariance varying with time. The results indicate that it is necessary to calculate collision probability with this nonlinear method under certain circumstances. For example, for elliptical relative motions in Satellite Formation Flying, when the relative velocity is below 100 m/s, the relative error between the linear method and the nonlinear method exceeds 5%; for the problem of conjunction analysis of two satellites with circular orbits, when the relative velocity is below 10 m/s, the relative error is also larger than 1%. Some significant conclusions are obtained for the collision detection system of our country.     

硬X射线成像仪量能器测试系统的设计与实现

硬X射线成像仪(Hard X-ray Imager, HXI)是先进天基太阳天文台(Advanced Space-based Solar Observatory, ASO-S)的3大载荷之一, 其中量能器作为其重要组成部分, 承担着观测30--200keV能段的太阳硬X射线的任务. 在卫星发射之前, 需要开展大量的测试工作, 以确保HXI量能器的各项功能和性能满足设计需求. HXI量能器通道数众多, 内含99个溴化镧探测器, 分别由8块相同的前端电子学板控制. 除了对各个通道的性能进行测试外, 地检系统还需模拟量能器在轨面对不同太阳活动时的运行情况, 对量能器进行全面完备的测试. 此外, 地检系统还需足够稳定, 能满足量能器在单机测试、环境试验、热真空与振动等多个不同测试项目的长时间测试需求. 为此, 设计了地检板与上位机软件, 结合放射源、直流电源、高压模块等组成一套HXI量能器的地检系统, 对8块前端电子学板实现同步配置与管理, 能高效完成指令发送与数据接收, 满足量能器最大数据输出带宽400Mbps的需求. 利用该系统, 在地面完成了HXI量能器的功能、性能验证, 获得了量能器的线性、死时间、能量分辨率等各项性能指标, 为HXI量能器的在轨高性能运行提供了保障.     

Observations of photometric profiles of two planetary nebulae

It is noted that the Abel integral of a Gaussian function is a Gaussian function. This special property is used in order to develop an analytic method for studying photometric profile in Planetary Nebulae. Monochromatic observations have been made at the Haute-Provence Observatory using the RCA-CCD (320×512 pixels) mounted at theF/6 Newtonian focus of the 1.2 m telescope. Among the observed nebulae, two of them (NGC 6778 and NGC 7354) are regular enough to test the photometric profile method. The nebular emissivity per volume unit is then obtained for H⁺ and O⁺⁺ ions.     

Determination of the azimuth error of the transit instrument by means of prime vertical observations

We present the principle and some test results of determining the instrumental azimuth by measuring the times of passage of the same stars through the meridian and the prime vertical. The test measurements were made on a reconstructed Zeiss transit instrument, equipped with four supporting pillars. The results of the test (TABLE 1) show that the method is successful. Applied to the meridian circle, this method replaces the traditional method of determining the absolute azimuth by observing circumpolar stars and thereby by-passes the difficulties inherant therein and the errors involved in the method of transfer via the azimuth mark.     

Bars and the symmetry of star formation patterns in the discs of spiral galaxies

We present a test for the degree of symmetry in the distribution of the Hα brightness along the arms of a sample of spiral galaxies. The test consists of deriving the cross-correlation function of the Hα brightness as a function of curvilinear distance along pairs of opposed arms, after unfolding the arms geometrically. Our results reveal a significantly greater degree of symmetry in the non-barred population than in the barred. We derive parameters for both bar strength and bar ellipticity, and compare these with the derived cross-correlations to strengthen this conclusion. We suggest that density waves are a probable cause for the appearance of global, i.e. disc-wide, two-fold symmetry in spiral discs. Comparison with published work on abundance gradients in the discs of barred and non-barred galaxies indicates that, as for the abundances, mixing in the spiral disc as a result of the bar potential may well be responsible for our observation that stronger bars are related to reduced two-fold symmetry in the distribution of star-forming regions along the spiral arms.     

R-N场中雷达回波延迟实验的后后牛顿修正

从球对称引力场中光子在赤道面上的运动微分方程出发,采用后牛顿近似方法,讨论了Reissner-Nordstr(o|¨)m度规场中雷达回波延迟实验的后后牛顿修正.通过计算给出了后牛顿以及后后牛顿的修正结果,当荷电量Q为零时,该结果适用于电中性天体,其后牛顿部分的修正与经典文献一致.文中采用的近似展开方法同样适用于讨论更高阶的修正.雷达回波的高阶修正对目前展开的高精度空间引力试验有着重要的参考价值.     

Scattered light - a comparison between theory and experiments during the 1973 transit of Mercury

We check the formalism used to derive stray light corrections from measured aureole intensities and correct an error in the pertinent literature. We solve the alledged problem of appropriately normalizing the spread function by treating blurring and scattering separately. We test the method by comparing stray light corrections derived from both the aureole and from intensity profiles across Mercury's disc obtained during the transit of November 10, 1973.     

Frequency analysis of the stability of asteroids in the framework of the restricted three-body problem

The stability of some asteroids, in the framework of the restricted three-body problem, has been recently proved in (Celletti and Chierchia, 2003), by developing an isoenergetic KAM theorem. More precisely, having fixed a level of energy related to the motion of the asteroid, the stability can be obtained by showing the existence of nearby trapping invariant tori existing at the same energy level. The analytical results are compatible with the astronomical observations, since the theorem is valid for the realistic mass-ratio of the primaries. The model adopted in (Celletti and Chierchia, 2003), is the planar, circular, restricted three-body model, in which only the most significant contributions of the Fourier development of the perturbation are retained. In this paper we investigate numerically the stability of the same asteroids considered in (Celletti and Chierchia, 2003), (namely, Iris, Victoria and Renzia). In particular, we implement the nowadays standard method of frequency-map analysis and we compare our investigation with the analytical results on the planar, circular model with the truncated perturbing function. By means of frequency analysis, we study the behaviour of the bounding tori and henceforth we infer stability properties on the dynamics of the asteroids. In order to test the validity of the truncated Hamiltonian, we consider also the complete expression of the perturbing function on which we perform again frequency analysis. We investigate also more realistic models, taking into account the eccentricity of the trajectory of Jupiter (planar-elliptic problem) or the relative inclination of the orbits (circular-inclined model). We did not find a relevant discrepancy among the different models.     

Full-sky correlations of peaks in the microwave background

We compute precise predictions for the two-point correlation function of local maxima (or minima) in the temperature of the microwave background, under the assumption that it is a random Gaussian field. For a given power spectrum and peak threshold there are no adjustable parameters, and since this analysis does not make the small-angle approximation of Heavens & Sheth, it is essentially complete. We find oscillatory features which are absent in the temperature autocorrelation function, and we also find that the small-angle approximation to the peak–peak correlation function is accurate to better than 0.01 on all scales. These high-precision predictions can form the basis of a sensitive test of the Gaussian hypothesis with upcoming all-sky microwave background experiments MAP and Planck , affording a thorough test of the inflationary theory of the early Universe. To illustrate the effectiveness of the technique, we apply it to simulated maps of the microwave sky arising from the cosmic string model of structure formation, and compare the two-point correlation function of peaks with the bispectrum as a non-Gaussian discriminant. We also show how peak statistics can be a valuable tool in assessing and statistically removing contamination of the map by foreground point sources.     

Estimates for the luminosity function of galaxies and its evolution

A new method is presented to obtain a non-parametric maximum likelihood estimate of the luminosity function and the selection function of a flux-limited redshift survey. The method parametrizes the selection function as a series of stepwise power laws and allows possible evolution of the luminosity function. We also propose a new technique to estimate the rate of evolution of the luminosity function. This is based on a minimization of the observed large-scale power with respect to the evolutionary model. We use an ensemble of mock surveys extracted from an N -body simulation to verify the power of this method. We apply our estimators to the 1.2-Jy survey of IRAS galaxies. We find a far-infrared luminosity function in good agreement with previously published results and evidence for rather strong evolution. If the comoving number density of IRAS galaxies is assumed to scale ∝ (1 +  z ) ^P , we estimate P  = 4.3 ± 1.4.     

中性大气折射映射函数和大气折射母函数方法

回顾了作为实用天文学和大地测量学中基本研究课题之一的大气折射函数研究的最新进展;介绍了近几年发展的大气折射母函数方法。对如今广泛地应用在空间测量技术中的几种映射函数,如ＣｆＡ２．２、ＭＴＴ等模型作出评述;特别分析了ＮＭＦ模型的优点和不足之处。还介绍了由大气折射母函数方法引出的大气延迟新连分式映射函数和天文大气折射的映射函数方法,利用ＶＬＢＩ实验中高度截止角与基线长变化的关系和探空气球（ｒａｄｉｏｓ     

Galaxy shear estimation from stacked images

Statistics of the weak lensing of galaxies can be used to constrain cosmology if the galaxy shear can be estimated accurately. In general, this requires accurate modelling of unlensed galaxy shapes and the point spread function (PSF). I discuss suboptimal but potentially robust methods for estimating galaxy shear by stacking images such that the stacked-image distribution is closely Gaussian by the central limit theorem. The shear can then be determined by radial fitting, requiring only an accurate model of the PSF rather than also needing to model each galaxy accurately. When noise is significant, asymmetric errors in the centroid must be corrected, but the method may ultimately be able to give accurate unbiased results when there is a high galaxy density with constant shear. It provides a useful baseline for more optimal methods, and a test case for estimating biases, though the method is not directly applicable to realistic data. I test stacking methods on the simple toy simulations with constant PSF and shear provided by the GREAT08 project, on which most other existing methods perform significantly more poorly, and briefly discuss generalizations to more realistic cases. In the Appendix , I discuss a simple analytic galaxy population model where stacking gives optimal errors in a perfect ideal case.     

Optimizing point-source parameters for scanning satellite surveys

We describe a method for deriving the position and flux of point and compact sources observed by a scanning survey mission. Results from data simulated to test our method are presented, which demonstrate that at least a 10-fold improvement is achievable over that of extracting the image parameters, position and flux, from the equivalent data in the form of pixel maps. Our method achieves this improvement by analysing the original scan data and performing a combined, iterative solution for the image parameters. This approach allows for a full and detailed account of the point-spread function (PSF), or beam profile, of the instrument. Additionally, the positional information from different frequency channels may be combined to provide the flux-detection accuracy at each frequency for the same sky position. Ultimately, a final check and correction of the geometric calibration of the instrument may also be included. The Planck mission was used as the basis for our simulations, but our method will be beneficial for most scanning satellite missions, especially those with non-circularly symmetric PSFs.