Increased accuracy of computations in the main satellite problem through linearization methods

The set of canonical redundant variables previously introduced by the first author is derived from Cartesian coordinates in a simplified form which allows the reduction of the Kepler problem to four harmonic oscillators with unit frequency. The coordinates are defined to be the direction cosines of the position of the particle along with the inverse of its distance. True anomaly is the new independent variable. The behavior of this new transformation is studied when applied to the numerical integrations of the main problem in satellite theory. In particular, computation time and accuracy of orbits in the new variables are compared with those in K-S and Cartesian variables. It is noteworthy that for high eccentricities the new variables require the least computation time for comparable accuracy, regardless of the integration scheme.     

Multiple resonance in one problem of the stability of the motion of a satellite relative to the center of mass

We investigate the stability of the periodic motion of a satellite, a rigid body, relative to the center of mass in a central Newtonian gravitational field in an elliptical orbit. The orbital eccentricity is assumed to be low. In a circular orbit, this periodic motion transforms into the well-known motion called hyperboloidal precession (the symmetry axis of the satellite occupies a fixed position in the plane perpendicular to the radius vector of the center of mass relative to the attractive center and describes a hyperboloidal surface in absolute space, with the satellite rotating around the symmetry axis at a constant angular velocity). We consider the case where the parameters of the problem are close to their values at which a multiple parametric resonance takes place (the frequencies of the small oscillations of the satellite’s symmetry axis are related by several second-order resonance relations). We have found the instability and stability regions in the first (linear) approximation at low eccentricities.     

用于人卫激光测距仪的跟踪控制和数据处理系统

介绍一种用于人卫激光测距仪的望远镜转台跟踪控制和数据处理系统。该系统具有卫星轨道计算、跟踪控制测量、数据采集和跟踪误差可实时修正以及跟踪状态在计算机屏幕实时显示等多种功能，使我国ＳＬＲ网的观测水平跃上一个新的台阶。     

Additions to the Theory of the Rotation of Europa

In a previous paper (The Rotation of Europa, Henrard, Celest. Mech. Dyn. Astr., 91, 131–149, 2005) we have developed a semi-analytical theory of Europa, one of the Galilean satellites of Jupiter. It is based on a synthetic theory of the orbit of Europa and is developed in the framework of Hamiltonian formalism. It was assumed that Europa is a rigid body and Jupiter a point mass. Several additional effects should be investigated in order to complete the theory. The present contribution considers the effect of the shape of Jupiter and of the gravitational pull of Io. The sensitivity of the main theory to a change in the values of the moments of inertia of Europa is also considered.     

The impact of the new Earth gravity models on the measurement of the Lense–Thirring effect with a new satellite

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense–Thirring effect with a new Earth’s artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally prosed LARES mission (same semimajor axis a = 12,270 km of the existing LAGEOS and inclination i = 70°) by inserting the new spacecraft in a relatively low, and cheaper, orbit (a = 7500–8000 km, i  70°) and suitably combining its node Ω with those of LAGEOS and LAGEOS II in order to cancel out the first two even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential J₂, J₄ along with their temporal variations , . The total systematic error due to the mismodelling in the remaining even zonal harmonics would amount to 1% and would be insensitive to departures of the inclination from the originally proposed value of many degrees. No semisecular long-period perturbations would be introduced because the period of the node, which is also the period of the solar K₁ tidal perturbation, would amount to 10² days. Since the coefficient of the node of the new satellite would be smaller than 0.1 for such low altitudes, the impact of the non-gravitational perturbations of it on the proposed combination would be negligible. Then, a particular financial and technological effort for suitably building the satellite in order to minimize the non-conservative accelerations would be unnecessary.     

GPM卫星反演降水产品在江苏地区的适用性

以江苏省70个地面雨量站分钟观测数据为基准,对比分析了一个完整年周期GPM卫星搭载的双频降水雷达(DPR)反演降水产品精度。结果表明DPR常规模式(NS)、匹配模式(MS)和高灵敏度模式(HS)扫描产品反演降水与地面雨量计观测数据均在过境后几分钟内达到最佳匹配效果。以NS产品为例,全年反演降水均方根误差大致为2mm/h,相关系数在0.5以上,相对偏差为-20%左右。并且降水产品在夏季反演精度最高。对反演误差进行初步分析发现,卫星反演降水率算法精度对校正因子ε有非常强的敏感性,并且选择ε值的算法约束不足会导致最终计算求解模块SLV的路径积分衰减PIA值异常,引起极端降水反演的误差。     

非静力AREM模式设计及其数值模拟I:非静力框架设计

AREM（Advanced Regional Eta-coordinate Model）对中国暴雨、台风等中尺度天气系统的模拟、预报能力突出。但是伴随模式分辨率的提高,制约该模式发展的一个问题日渐突出,即"静力平衡近似"的约束。本文通过对原静力平衡系统进行修正,引入高阶订正参数定义第三运动方程来构建该模式的非静力动力框架。我们基于Euler原始方程组,有效结合原静力平衡模式的标准层结扣除及IAP（Institute of Atmospheric Physics）变换方法,推导出了球面余纬坐标下的非静力框架,并在E网格和η坐标下进行了时空离散。采用时间两部分离技术进行积分运算以提高计算效率,并通过"追赶法"结合迭代法计算声波。此框架可方便地继承静力平衡框架的特点,最大限度地保留静力平衡框架的优势。理论推导和数值试验表明,当非静力框架退化为静力平衡框架后,方程形式及其模拟结果一致。在文章第二部分将通过理想和实例试验检验非静力模式性能。     

GPM卫星双频测雨雷达探测降水结构的个例特征分析

全球测雨卫星（GPM）携带首部Ka和Ku波段测雨雷达于2014年2月发射升空,继热带测雨卫星（TRMM）的单频测雨雷达探测后,实现双频测雨雷达（DPR）探测。本文基于DPR不同波段及不同方式探测反演给出的四种降水产品[Ka波段高精度探测（KaHS）、Ku波段探测（KuPR）、Ka匹配方式探测（KaMS）和Ka及Ku双频联合探测反演产品（DPR_MS）],对2014年的四个降水个例的降水结构特征进行了分析,并就DPR探测波段、扫描方式及反演算法所引起的降水产品中降水结构特征差异进行了比较与讨论。结果表明,所选四个个例分别位于中国东部、西北太平洋区域、风暴轴区域以及美国本土,四者发生背景及降水特征差异显著,但表现出了较为一致的产品差异特征。KaHS的回波顶高度最高,比KuPR高约0.1 km,其对弱降水（小于0.5 mm h-1）的观测性能好,但对10 mm h-1以上的强降水存在严重低估。KuPR继承了TRMM测雨雷达（PR）对强降水的观测性能,但受频率限制对0.5 mm h-1以下的弱降水观测能力有限。KaMS的整体降水强度分布与KaHS类似,但受高回波阈值限制,KaMS漏掉了大量弱降水样本,对强弱降水的观测性能均有限,且其平均回波顶高度比KuPR可低约1 km,常将融化层误判为回波顶高度,故不适宜单独使用。DPR_MS的降水反演算法具有独立性,对强降水和弱降水的反演能力都较强,而其回波顶高度主要继承于KuPR的回波顶高度。此外,DPR_MS双频反演的粒子谱最为合理,揭示了西北太平洋区域台风个例两侧眼壁粒子谱的不均匀性。