太阳质量损失对地球轨道改变的长期影响的估计

研究了太阳质量损失对地球轨道２的长期影响。太阳质量损失包括太阳因光于辐射和太阳风流失两方面产生的质量损失。利用二体问题的中心体变质量的Ｊｅａｎｓ理论估计了太阳目前在主序阶段和将来后主序（红巨星＿阶段由于上述两种机制造成的质量损失对地球轨道改变的长期效应。计算结果表明：太阳质量损失在主序阶段对地球轨道改变的影响较小,但在后主序阶段对地球轨道改变的影响甚大,且此估计只是一种理论预测。     

太阳质量损失对流星群轨道改变的长期影响

将作者在变质量天体力学所得理论结果应用于太阳质量损失对流星群轨道根数变化的长期效应上。太阳质量损失包括光子辐射和太阳风造成的质量损失。利用G—M型变质量天体轨道根数变化方程的一阶和二阶解对15个流星群轨道半长轴、近日点距离、轨道周期和近日点经度因太阳质量损失造成的每世纪的长期改变效应做了数值计算,并得出计算结果。其计算结果表明,太阳质量损失使流星群轨道半长轴每世纪的改变效应较明显,它们同太阳距离的扩大影响值得关注,但对轨道周期的拉长每世纪的影响甚小,对近日点经度只有量级变化小到可以略而不计。     

太阳质量损失对高阶行星轨道的长期影响

在文[1]研究的基础上给出了太阳质量损失对三阶行星轨道的影响解，并计算了二、三阶解的长期效应的数值结果。理论结果表明，在三阶解中对于质量变化模型κ=3的情形，太阳质量损失对轨道半长轴继续产生长期项、混合项和周期项，但对轨道偏心率和近点角距只产生周期项，三阶解的效应值虽小，但有定性意义。     

太阳质量损失对高阶行星轨道的长期影响

在文[1]研究的基础上给出了太阳质量损失对三阶行星轨道的影响解,并计算了二、三阶解的长期效应的数值结果。理论结果表明,在三阶解中对于质量变化模型k=3的情形,太阳质量损失对轨道半长轴继续产生长期项、混合项和周期项,但对轨道偏心率和近点角距只产生周期项,三阶解的效应值虽小,但有定性意义。     

太阳质量变化对小行星轨道根数的影响

利用变质量天体力学方法研究了太阳质量变化对小行星轨道根数的影响,质量变化包括因光子辐射和太阳造成的质量损失以及因太阳吸积周围星际物质造成的质量增加两个联合因素,利用Gylden-Meshcherskii(G-M)型变质量天体轨道根数变化方程的一阶和二阶解对7颗小行星轨根数的长期和周期性的影响作了数值计算,在一阶解中太阳质量流失对小行星轨道半长轴,轨道偏心率和近点辐角的变化率产生增大作用,而质量吸积起减小作用,在二阶解中两者起到增大作用,不过质量流失不大于质量吸积的作用,故总的趋势是使半长轴,偏心率和近点辐角的变化率增大。     

太阳多方模型对行星轨道要素变化的长期摄动影响

本文利用天体力学中的摄动理论和天体物理学中的气体星多方模型理论研究了太阳多方模型对行星轨道要素变化的长期摄动影响。文中给出了太阳日多方指数ｎ＝３的模型由于自转、扁度和内部密度分布等因素对行星轨道要素变化的长期摄动效应的理论结果。研究结果表明：行星轨道要素除长轴、偏心率和轨道倾角不受长期摄动外升交点经度、近日点经度以及平近点角均受长期摄动的影响。最后利用理论结果对行星轨道要素的长期投动效应做了数值计算，数值结果在表１中给出。     

北斗三号卫星精密定轨中的光压模型研究

对于在轨运行的BDS (BeiDou Navigation Satellite System)卫星, 太阳光压是作用在卫星上主要的非引力摄动. 受多种因素的影响, 太阳光压摄动力难以精确建模, 是BDS卫星精密定轨和轨道预报过程中重要的误差来源. 由于ECOMC (Empirical CODE Orbit Model 1 and 2 Combined)模型兼顾了ECOM1 (Empirical CODE Orbit Model 1)和ECOM2 (Empirical CODE Orbit Model 2)模型的特点, 在模型中引入了较多的待估参数, 使得参数之间存在强相关性. 针对ECOMC模型的这一缺陷, 文中收集了2019年1月至2022年4月武汉大学分析中心提供的BDS-3卫星精密星历, 采用动力学轨道拟合方法得到了ECOMC模型的13个光压参数. 通过对该模型的光压参数进行时间序列分析, 分别给出了BDS-3 IGSO (Inclined Geosynchronous Orbit)和MEO (Medium Earth Orbit)卫星光压模型的参数选择策略. 并利用轨道拟合和轨道预报试验, 验证了光压模型参数选择策略的合理性. 结果表明, 采用改进型ECOMC模型进行BDS-3 IGSO和MEO卫星轨道拟合的效果最佳, 同时, 也能够提升BDS-3 IGSO和MEO卫星中长期轨道预报的精度.     

Solar Sail Halo Orbits at the Sun–Earth Artificial L 1 Point

Halo orbits for solar sails at artificial Sun–Earth L₁ points are investigated by a third order approximate solution. Two families of halo orbits are explored as defined by the sail attitude. Case I: the sail normal is directed along the Sun-sail line. Case II: the sail normal is directed along the Sun–Earth line. In both cases the minimum amplitude of a halo orbit increases as the lightness number of the solar sail increases. The effect of the z-direction amplitude on x- or y-direction amplitude is also investigated and the results show that the effect is relatively small. In case I, the orbit period increases as the sail lightness number increases, while in case II, as the lightness number increases, the orbit period increases first and then decreases after the lightness number exceeds ~0.01.     

稳健估计在轨道改进中的应用

通过对20颗卫星的模拟计算，研究了人造卫星光学观测的轨道改进方法，给出了资料预处理(观测精度σ0=5″)的剔除门限，使野值的比例在大多数情况下小于10％；在轨道改进中，先用Huber估计迭代2次，再用Hampel估计迭代到收敛，保证了轨道改进的精度；重点研究了Hampel估计的权函数参数(C0，C1，C2)的取值，得出结论：对于大于或等于6σ0的野值，C0可取为2．2，C1可取为3．6，C2的取值和野值大小有关．     

Estimation of Distribution Algorithm for Initial Orbit Determination of Too-short-arc Based on Kernel Density Estimation

A new approach of the initial orbit determination for too-short-arc with angular measurements is implemented by building the probabilistic model in the solution space with the estimation of distribution algorithm. Without any assumption about distribution, the non-parametric kernel density estimation is employed in the model building. The method, unlike other evolutionary algorithms, such as the genetic algorithm and particle swarm optimization, considers the fitness as well as the characteristics of the solution space. Numerical experiments with real observations indicate that without any constraints, the proposed technique has a good performance for the observations of usual accuracy.     

The Data Depth-weight-kernel Estimation of the Model Error of Satellite Orbit Determination

It is an objective fact that there exists error in the satellite dynamic model and it will be transferred to satellite orbit determination algorithm, forming a part of the connotative model error. Mixed with the systematic error and random error of the measurements, they form the unitive model error and badly restrict the precision of the orbit determination. We deduce in detail the equations of orbit improvement for a system with dynamic model error, construct the parametric model for the explicit part of the model and nonparametric model for the error that can not be explicitly described. We also construct the partially linear orbit determination model, estimate and fit the model error using a two-stage estimation and a kernel function estimation, and finally make the corresponding compensation in the orbit determination. Beginning from the data depth theory, a data depth weight kernel estimator for model error is proposed for the sake of promoting the steadiness of model error estimation. Simulation experiments of SBSS are performed. The results show clearly that the model error is one of the most important effects that will influence the precision of the orbit determination. The kernel function method can effectively estimate the model error, with the window width as a major restrict parameter. A data depth-weight-kernel estimation, however, can improve largely the robustness of the kernel function and therefore improve the precision of orbit determination.     

考虑地球扁率摄动影响的初轨计算方法

在二体问题意义下的短弧定轨,Laplace型方法是最主要最典型的一种初轨计算方法。若测角资料达到10^-4-10^-5精度(相当于2″—20″之间),那么要使定轨精度达到与其相应的程度,地球非球形引力位中的扁率项摄动应该考虑,在此前提下,同样可以采用相应的Laplace型定轨方法。即给出这种严格包含扁率摄动的初轨计算方法的原理和具体计算过程以及计算实例,除采用多资料定轨方法外,这种方法也是提高初轨计算精度的一种途径,它同样可用于多资料的情况,这种方法对于大扁率主天体(即中心天体)的卫星定轨将更有实用价值。     

抗差估计在星载GPS卫星非差运动学定轨中的应用

针对星载GPS卫星非差运动学定轨的特点,提出将抗差估计应用于星载GPS卫星运动学定轨,一方面尽量保留来自每颗GPS卫星的观测值,保持较强的卫星几何强度,避免轨道求解出现奇异;另一方面,采用等价权思想,有效地降低质量较差的观测值对定轨结果的影响,保证定轨精度．还采用CHAMP卫星的实测GPS数据验证了新方案的可行性和有效性．     

Influence of Solar Activity on Precise Orbit Prediction of LEO Satellites

The perturbations of low earth orbit(LEO) satellites operating in the orbit of 300～2000 km are complicated.In particular,the atmospheric drag force and solar radiation pressure force change rapidly over a short period of time due to solar activities.Using spaceborne global positioning system(GPS) data of the CHAMP,GRACE and SWARM satellites from 2002 to 2020,this paper studies in depth the influence of solar activity on LEO satellites’ precise orbit prediction by performing a series of orbit pre...