古本今本《竹书纪年》的天象记载和纪年

对《竹书纪年》记载的天象和纪年进行了初步的分析研究,结果表明,今本《竹书纪年》中新增的天象如日食等,并非汲冢出土佚书的原有内容,而为宋元以后学者所加.     

两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.     

中国历代荧惑守列宿与四星聚、五星聚考查

利用授时历法和现代天文计算方法,对中国历代天文志记录的荧惑(火星)守列宿、四星聚、五星聚进行分析研究,结果表明:65条荧惑守列宿,正误率分别为49%和51%.如果把荧惑留、留守、在某宿等运动形态也考虑为守的范围,共有95条,其正误率分别为56%和44%.12条四星聚正误率各占一半,即50%.11条五星聚正误率分别为82%和18%(其中含五星并见).并对错误记录的原因做了初步探讨.     

Adiabatic chaos in the Prometheus–Pandora system

The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical–experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.     

Homogeneous and Heterogeneous Observational Data Weighting Method of Combined Orbit Determination of Near-earth Satellites of Bi-satellite Positioning System and its Applications

In the light of the problem of amalgamation and processing of multisource observational data in the combined orbit determination of near-earth satellites of the bi-satellite positioning system, the optimal weighting method of the improved variance component estimation of the two-step systematic error correction of homogeneous observational data is proposed. Analyses show that the multi-source amalgamation measurement model of the heterogeneous observational data essentially is a multi-structure, multi-parameter non-linear regression model, and the optimal weighting method of the combination of model structure characteristic analysis and variance component estimation of the heterogeneous observational data is established. The realization algorithms of the optimal weighting and the combined orbit determination parameter estimation of the two sorts of observational data are designed, and the simulation experiments of the combined orbit determination are carried out by taking the distances among the two satellites and the backup satellite and the homogeneous observational data and the distance between the two satellites and the heterogeneous observational data of satellite sensor angle measurements as the examples. The results of theoretical analysis and simulation calculation show that for the combined orbit determination of homogeneous observational data, the accuracy of orbit determination obtained by adopting the variance component estimation method of the two-step systematic error correction can be more superior than that obtained by means of the traditional empirical weighting method. For the combined orbit determination of heterogeneous observational data, through the introduction of the weighting factor by which the model structure is characterized the accuracies of the combined orbit determination of the near-earth satellite and geostationary satellite are both improved to a certain extent in comparison with the mean weighting mode.