Kepler Equation solver

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10¹⁸, exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.     

Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

New Definition of Discovery for Solar System Objects

We propose a new formal definition of discovery for a Solar System object. It is based on an objective and mathematically rigorous algorithm to assess when a set of observations is enough to constitute a discovery. When this definition is satisfied, in almost all cases the orbit is defined well enough to establish the nature of the object discovered (Main Belt vs. Near Earth Asteroid, Trans-Neptunian vs. long period comet). The frequency of occurrence of exceptions is estimated by a set of numerical experiments. The availability of a non-subjective definition of discovery allows some rules to be adopted for the assignment of discovery credit with a minimum risk of dispute. Such rules should be fair, encourage good practice by the observers and acknowledge the contribution of the orbit computers providing the identifications and the orbits, as well as the one of all the contributing observers.     

基于重力卫星几何轨道线性化的地球重力场反演方法

传统动力学法的观测方程以6个初始轨道参数和先验力模型为初值进行线性化,其线性化误差随积分弧长拉长而增大.本文直接以重力卫星的几何观测轨道为初值进行线性化,其线性化误差与轨道弧长无关,且不需要初始重力场模型和初始轨道参数.导出了基于卫星轨道观测值反演重力场模型的相关公式,利用JPL公布的RL02版本2008年全年的GRACE双星轨道数据和加速度计数据解算了90阶次的地球重力场模型TJGRACE01S,并以EGM2008模型为基准与其他模型进行了比较分析,结果表明:TJGRACE01S模型直到90阶次的大地水准面累积误差为17.6 cm,优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型,前27阶位系数整体精度优于EIGEN-GRACE01S,前15阶位系数整体精度与EIGEN-GRACE02S模型精度大致相当.利用美国8221个GPS水准点数据的分析结果也表明,本文模型也优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型.     

利用GEOSAT／ERM卫星测高数据计算中国近海海平面

本文利用一年（１９８６年１１月８日～１９８７年１１月１７日）２２个ＥＲＭ周期的ＧＥＯＳＡＴ卫星测高数据计算出中国近海海域（１０５°～１３５°Ｅ，０°～４０°Ｎ）相对于ＧＲＳ８０参考椭球面的１°×１°年平均海平面。该海平面我们称之为ＩＧＧＭＳＳ９５平均海平面。在数据处理过程中，由于采用了混合轨道误差模型及交叠平差技术，极大地消除了在误差中占主要成分的径向轨道误差影响，使得ＩＧＧＭＳＳ９５平均海平面的总体精度达到±２０～３０ｃｍ（ＲＭＳ）水平。与ＯＳＵ９１Ａ重力大地水准面模型相比较可以发现两者具有惊人的一致性。     

融合多尺度视网膜图像增强的动态云检测

云检测是气象卫星各类定量遥感产品的基础,无论是以云图为基础的天气分析还是以去云为前提的各类大气和地表参数反演、沙尘火情等灾害检测,都需要对遥感影像中的云进行准确识别,尤其是薄云和云边缘等细节识别。针对静止气象卫星(以Himawari-8为例)精细化云检测,本文提出了一种基于多尺度视网膜图像增强的动态云检测算法。该算法基于云层与背景信息辐射特征不同的原理,构建可见光和红外波段的晴空辐射背景场,通过多尺度图像增强和最大类间差方法对辐射差值进行云细节信息的增强和提取。利用2021-2022年的75景MODIS云检测产品作为验证数据进行算法精度验证,整体上算法精度达到91.13%,召回率为94.02%,精确率为86.71%,有较强的适用性和稳健性,且已经较好地支撑了近两年的定量遥感产品业务化应用。     

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多尺度相关性分析的机载双极化InSAR轨道误差校正方法

在高分辨率机载干涉SAR成像处理过程中,由于载机飞行过程中偏离理想轨迹,需要高精度的惯导系统和GPS系统记录载机的运动轨迹并进行运动补偿.然而,由于目前传感器导航精度的限制,在完成运动补偿处理后仍然存在轨道误差,从而影响干涉相位的精度,本文提出了一种机载双极化InSAR轨道误差去除方法.该方法利用小波多尺度分析对不同极...     

Automated design of gravity-assist trajectories to Mars and the outer planets

In this paper, a new approach to planetary mission design is described which automates the search for gravity-assist trajectories. This method finds all conic solutions given a range of launch dates, a range of launch energies and a set of target planets. The new design tool is applied to the problems of finding multiple encounter trajectories to the outer planets and Venus gravity-assist trajectories to Mars. The last four-planet grand tour opportunity (until the year 2153) is identified. It requires an Earth launch in 1996 and encounters Jupiter, Uranus, Neptune, and Pluto. Venus gravity-assist trajectories to Mars for the 30 year period 1995–2024 are examined. It is shown that in many cases these trajectories require less launch energy to reach Mars than direct ballistic trajectories.Assistant Professor, School of Aeronautics and AstronauticsGraduate Student, School of Aeronautics and Astronautics     

Fog Detection over China’s Adjacent Sea Area by using the MTSAT Geostationary Satellite Data

A fog threshold method for the detection of sea fog from Multi-function Transport Satellite (MTSAT1R) infrared (IR) channel data is presented.This method uses principle component analysis (PCA),texture analysis,and threshold detection to extract sea fog information.A heavy sea fog episode that occurred over China’s adjacent sea area during 7 8 April 2008 was detected,indicating that the fog threshold method can effectively detect sea fog areas nearly 24 hours a day.MTSAT-1R data from March 2006,June 2007,and April 2008 were processed using the fog threshold method,and sea fog coverage information was compared with the meteorological observation report data from ships.The hit rate,miss rate,and false alarm rate of sea fog detection were 66.1%,27.3%,and 33.9%,respectively.The results show that the fog threshold method can detect the formation,evolution,and dissipation of sea fog events over period of time and that the method has superior temporal and spatial resolution relative to conventional ship observations.In addition,through MTSAT-1R data processing and a statistical analysis of sea fog coverage information for the period from 2006 to 2009,the monthly mean sea fog day frequency,spatial distribution and seasonal variation characteristics of sea fog over China’s adjacent sea area were obtained.