中国探月：嫦娥2号成功进入绕月轨道

2010年10月1日18：59：57,中国嫦娥2号月球探测卫星（以下简称嫦娥－2）在西昌卫星发射中心发射由长征-3C运载火箭直接送入近地点200千米、远地点380000千米的地月转移轨道。在奔月飞行期间。嫦娥－2只进行了1次轨道修正,并开展了X频段测控、紫外敏感器自主导航试验,还打开了3台科学探测仪器进行工作。     

经过月球旁近的低能地月转移轨道

基于日、地、月构成的双圆问题(BCP,Bicircular Problem)研究了经过月球旁近的低能地月转移轨道,总结了这些轨道在相空间的分布特点.首先基于BCP模型,利用BCP系统的不变流形,搜索出经过月球旁近的低能地月转移轨道.然后把时间作为非自治系统相空间的增广维度,给出了能够反映出转移轨道在增广相空间分布情况的状态空间图,研究表明转移轨道以族的形式分布于相空间中,并且任意时刻都可以作为此类轨道的出发时刻.最后分析了不同转移轨道族各自速度增量、飞行时间以及系统能量的变化规律,分别得到了速度增量最优轨道族和飞行时间最优轨道族.     

从地面发射月球探测器的窗口选择

典型的月球探测器飞行轨道包括地球停泊轨道段、地月转移轨道段、月球卫星轨道段和着月轨道段。首先介绍了设计从地面发射月球探测器轨道典型的约束条件;然后,借助于二体假设,建立解析表达式,分析各种约束对窗口选择的影响,给出了各轨道段概略的飞行时间和粗窗口;最后,利用精确的探测器轨道动力学模型,计算精窗口,并给出了一则算例,所得结论可为月球探测器轨道发射、轨道设计提供依据。     

主带小行星深空探测可接近性与多目标探测轨道的实现

小行星探测是当前深空探测的热点之一,探测目标的可接近性又是探测任务首先要解决的问题.根据直接转移轨道方式下太阳系中可以探测到的区域和小行星的空间分布,确认发射能量C_3=50 km~2/s~2的直接转移轨道,可以探测大部分主带小行星;使用少量的速度修正还能够实现多目标飞越任务.同时指出,这种多目标的飞越可以达到△V-EGA轨道方案中的深空机动同样的效果,经地球引力助推,以较小能量实现小行星伴飞或更遥远小行星的探测;据此提出了一个探测器先飞越多颗主带小行星,然后借助地球引力助推探测更遥远小行星的轨道设计方案,并给出了设计实例.     

木星探测轨道分析与设计

研究了与木星探测相关的轨道设计问题.重点关注木星探测轨道与火星、金星等类地行星探测轨道的不同及由此带来的轨道设计难点.首先分析了绕木星探测任务轨道的选择.建立近似模型讨论了向木星飞行需要借助多颗行星的多次引力辅助,对地木转移的多种行星引力辅助序列,使用粒子群算法搜索了2020年至2025年之间的燃料最省飞行方案并对比得到了向木星飞行较好的引力辅助方式为金星-地球-地球引力辅助.结合多任务探测,研究了航天器在飞向木星途中穿越主小行星带飞越探测小行星的轨道设计.最后,给出2023年发射完整的结合引力辅助与小行星多次飞越的木星探测轨道设计算例.     

基于历史TLE的空间目标轨道预报误差演化规律研究

北美防空司令部(North American Aerospace Defense Command, NORAD)发布的双行根数(Two Line Element, TLE)是广大航天工作者最常用的轨道根数,与其对应的轨道模型是SGP4/SDP4 (Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4)解析模型.由于TLE中并没有包含相应的轨道精度信息,编目轨道的应用范围受到很大的限制.基于Space-Track网站发布的历史TLE数据和配套的SGP4/SDP4动力学模型,采用定轨标预报的方法统计并生成了大量目标轨道的预报误差,通过对预报轨道的时间区间划分给出了每个目标的预报误差随预报时间变化的拟合系数,并进一步对不同类型轨道预报误差的演化规律和特征进行了分类讨论,给出了4种轨道类型目标的轨道预报误差随时间演化的平均解析模型,为拓展双行根数的应用提供有价值的参考.     

OJ287双黑洞轨道计算:3.5阶后牛顿近似

大质量双黑洞OJ287是一个强引力辐射源.为了探测其引力波信号,需要知道波形,而这主要是由轨道运动所决定.为此,从广义相对论3.5阶后牛顿近似的运动方程出发对OJ287的轨道进行仔细研究,取大黑洞位置固定作为近似,给出了后牛顿近似下3.5阶的次黑洞轨道解,比他人2.5阶的工作高了一阶.次黑洞撞击吸积盘面到光学爆发存在时间延迟,这对于确定轨道参数有很大影响.利用径向距离与爆发时间关系的线性模型,对最近7次爆发时刻的观测值拟合,给出了更精确的OJ287双黑洞的轨道参数及其运动轨道.分析了计算结果,研究运动特征,并且发现了两个新性质:次黑洞进动在初期增加,在晚期接近并和时,进动达到最大值,然后减小并越过0而趋于负值.尚不能确定晚期的这个行为是否由3.5阶近似不够准确所造成.运动方程中耗散性的辐射项,后牛顿2.5阶和3.5阶的系数具有相反的符号.这意味着3.5阶项反而是从外界吸收能量.但2.5阶与3.5阶之和仍然是向外辐射引力波的,体系能量变化率为负.这个工作的计算结果可以用来更精确地计算OJ287的引力辐射.     

月球探测中的无动力返回轨道

首先在平面圆型限制性三体问题模型下给出了白道面内4种类型的对称无动力返回轨道,之后针对其中较实用的一种,考虑了其在白道面内的非对称情形,并探讨了其三维情形及近月、近地的轨道倾角限制.最后给出了地-月系真实引力模型下无动力返回轨道的设计方法和相应算例.     

卫星轨道确定模型误差的深度加权核估计方法

卫星动力学模型误差是客观存在的事实,动力学模型误差传递到轨道确定算法中构成部分形式未知的模型误差,并且与测量系统自身的系统误差和随机误差耦合在一起形成定轨模型误差,严重影响轨道确定精度.详细推导了存在动力学模型误差的轨道改进方程,对模型中能准确描述的部分建立了参数化模型,对不能准确描述的误差部分,建立了非参数模型.构建了部分线性轨道改进模型,利用二阶段估计法和核函数估计法对模型误差进行拟合估计,并在轨道改进中予以补偿.根据数据深度理论,建立了非参数模型误差的深度加权核估计方法,提高了模型误差估计的抗差性.最后结合天基空间目标监视系统进行了轨道确定仿真实验.实验结果表明,模型误差是影响轨道确定精度的重要因素,核函数估计法可以有效估计定轨中的模型误差,窗宽是提高模型估计精度的重要变量,通过深度加权处理可以明显提高核函数估计的抗差性,提高轨道确定精度.     

卫星跟踪卫星模式中轨道参数需求分析

首次基于半解析法利用GRACE(Gravity Recovery and Climate Experiment)双星K波段星间速度误差、GPS接收机轨道误差和加速度计非保守力误差影响累计大地水准面精度的联合模型开展了卫星跟踪卫星模式中轨道参数的需求分析.建议我国将来首颗重力卫星的平均轨道高度设计为400 km和平均星间距离设计为220 km较优.此研究不仅为我国将来卫星重力测量计划中轨道参数的优化选取以及全球重力场精度的有效和快速估计提供了理论基础和计算保证,同时对将来国际GRACE Follow-On地球重力测量计划和GRAIL(Gravity Recovery and Interior Laboratory)月球重力探测计划的发展方向具有一定的指导意义.     

修正的极大似然法拟合幂律频数分布

针对包含饱和样本数据的频数幂律分布拟合,提出一个新的幂律分布指数的极大似然估计方法的修正公式.对比研究显示,修正公式适用于剔除异常饱和值的幂律频数拟合.如果不剔除饱和值,幂律指数的估计只能使用修正前的公式,其误差随幂律指数变化,指数较小时误差较大.由此建议,对于包含饱和样本的频数分布拟合,首先剔除异常的饱和值,然后对剩余不含饱和值的子集使用修正公式进行参数估计.     

Substructure recovery by three-dimensional discrete wavelet transforms

We present and discuss a method to identify substructures in combined angular-redshift samples of galaxies within clusters. The method relies on the use of the discrete wavelet transform (hereafter DWT) and has already been applied to the analysis of the Coma cluster. The main new ingredient of our method with respect to previous studies lies in the fact that we make use of a 3D data set rather than a 2D one. We test the method on mock cluster catalogues with spatially localized substructures and on a N -body simulation. Our main conclusion is that our method is able to identify the existing substructures provided that: (a) the subclumps are detached in part or all of the phase space, (b) one has a statistically significant number of redshifts, increasing as the distance decreases due to redshift distortions; (c) one knows a priori the scale on which substructures are to be expected. We have found that to allow an accurate recovery we must have both a significant number of galaxies (≈200 for clusters at z ≥0.4 or about 800 at z ≤0.4) and a limiting magnitude for completeness m _B =16.
The only true limitation to our method seems to be the necessity of knowing a priori the scale on which the substructure is to be found. This is an intrinsic drawback of the method and no improvement in numerical codes based on this technique could make up for it.     

Cosmological systematics beyond nuisance parameters: form-filling functions

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalizing over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article, we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors.
As an alternative we present a functional form-filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown, we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model, we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalizing over a systematic, but that in contrast the functional form-filling approach is independent of the choice of basis set.
We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of  | m ( z )| ≲ 10⁻³ (1 + z )^0.7  is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to per cent accuracy.
A module associated with the work in this paper is available through the open source icosmo code available at http://www.icosmo.org .     

Accurate estimators of power spectra in N-body simulations

A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of fast Fourier transforms (FFTs), which is controlled by the order N of the expansion and by the dimension D of the system. In three dimensions, for the practical value   N = 3  , the number of FFTs required is 20.
We apply the method to the measurement of the power spectrum of a periodic point distribution that is a local Poisson realization of an underlying stationary field. We derive an explicit analytic expression for the spectrum, which allows us to quantify – and correct for – the biases induced by discreteness and by the truncation of the Taylor expansion, and to bound the unknown effects of aliasing of the power spectrum. We show that these aliasing effects decrease rapidly with the order N . For   N = 3  , they are expected to be, respectively, smaller than  ∼10⁻⁴  and 0.02 at half the Nyquist frequency and at the Nyquist frequency of the grid used to perform the FFTs. The only remaining significant source of errors is reduced to the unavoidable cosmic/sample variance due to the finite size of the sample.
The analytical calculations are successfully checked against a cosmological N -body experiment. We also consider the initial conditions of this simulation, which correspond to a perturbed grid. This allows us to test a case where the local Poisson assumption is incorrect. Even in that extreme situation, the third-order Fourier–Taylor estimator behaves well, with aliasing effects restrained to at most the per cent level at half the Nyquist frequency.
We also show how to reach arbitrarily large dynamic range in Fourier space (i.e. high wavenumber), while keeping statistical errors in control, by appropriately 'folding' the particle distribution.     

Detrending time series for astronomical variability surveys

We present a detrending algorithm for the removal of trends in time series. Trends in time series could be caused by various systematic and random noise sources such as cloud passages, changes of airmass, telescope vibration, CCD noise or defects of photometry. Those trends undermine the intrinsic signals of stars and should be removed. We determine the trends from subsets of stars that are highly correlated among themselves. These subsets are selected based on a hierarchical tree clustering algorithm. A bottom-up merging algorithm based on the departure from normal distribution in the correlation is developed to identify subsets, which we call clusters. After identification of clusters, we determine a trend per cluster by weighted sum of normalized light curves. We then use quadratic programming to detrend all individual light curves based on these determined trends. Experimental results with synthetic light curves containing artificial trends and events are presented. Results from other detrending methods are also compared. The developed algorithm can be applied to time series for trend removal in both narrow and wide field astronomy.     

The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations

The theory of low-order linear stochastic differential equations is reviewed. Solutions to these equations give the continuous time analogues of discrete time autoregressive time-series. Explicit forms for the power spectra and covariance functions of first- and second-order forms are given. A conceptually simple method is described for fitting continuous time autoregressive models to data. Formulae giving the standard errors of the parameter estimates are derived. Simulated data are used to verify the performance of the methods. Irregularly spaced observations of the two hydrogen-deficient stars FQ Aqr and NO Ser are analysed. In the case of FQ Aqr the best-fitting model is of second order, and describes a quasi-periodicity of about 20 d with an e-folding time of 3.7 d. The NO Ser data are best fitted by a first-order model with an e-folding time of 7.2 d.