近地小行星的巡天项目不断涌现,得到了海量的观测数据.而巡天观测方式使获得的数据弧段过短,传统方法在定轨和识别上存在极大困难,加之短弧定轨问题本身的病态性,如何有效利用这些短弧数据对于发现、监测和评估小行星的威胁具有重要意义...近地小行星的巡天项目不断涌现,得到了海量的观测数据.而巡天观测方式使获得的数据弧段过短,传统方法在定轨和识别上存在极大困难,加之短弧定轨问题本身的病态性,如何有效利用这些短弧数据对于发现、监测和评估小行星的威胁具有重要意义.在进化算法下构建极短弧定轨的计算框架,选用三变量的(a, e, M)优选法,保持维数较低的同时,使优化结果不再依赖观测量.采用参数较少、操作简便的差分进化算法,利用不同偏心率小行星的轨道模拟数据进行试验,对获得的最优解及其分布聚集区域进行分析,大偏心率轨道由于其本身的复杂性,会对算法搜索的灵敏度产生影响,需缩小搜索空间以提高搜索能力.结果表明算法在小偏心率问题中表现较好,可以得到有效结果为后续工作提供参考信息,大偏心率问题在传统方法失效的情况下,虽然最优解在整体分布中并不明显,但分布仍包含真实解,可结合分布密度和适值大小进行分析.未来需要对大偏心率问题作进一步研究,考虑其观测位置和观测时刻对算法产生的影响,分类计算.展开更多
This paper investigates a simplified model for describing the gravitational fields of non- axisymmetric elongated asteroids. The connection between the simplified model and the target aster-oid is built by considering...This paper investigates a simplified model for describing the gravitational fields of non- axisymmetric elongated asteroids. The connection between the simplified model and the target aster-oid is built by considering the positions of equilibrium points. To improve the performance of po-sition matching for the equilibrium points associated with these non-axisymmetric asteroids, a non-axisymmetric triple-particle-linkage model is proposed based on two existing axisymmetric particle- linkage models. The unknown parameters of the simplified model are determined by minimizing the matching error using the nonlinear optimization method. The proposed simplified model is applied for three realistic elongated asteroids, 243 Ida, 433 Eros and （8567） 1996 HW1. The simulation re-sults verify that the current particle-linkage model has better matching accuracy than the two existing particle-linkage models. The comparison, between the simplified model and the polyhedral model, on the topological cases of the equilibrium points and the distribution of gravitational potential further validate the rationality and accuracy of the simplified model.展开更多
There are plentiful asteroids moving periodically around their central primaries, such as the Sun. Due to the perturbation of the central primary, the gravitational force of the perturbed asteroid system varies period...There are plentiful asteroids moving periodically around their central primaries, such as the Sun. Due to the perturbation of the central primary, the gravitational force of the perturbed asteroid system varies periodically. In this paper, based on the idea of integrating the solar gravitational force as a part of the system instead of treating it as perturbation, the parametric resonance response is investigated. A novel type of stable parametric resonance orbits has been detected. It is found that the steady-state motion amplitude of parametric resonance orbit is determined by the frequency-response equation. The stability of the novel orbits has also been demonstrated. The new type of orbits may contribute to possible asteroid exploration missions.展开更多
文摘近地小行星的巡天项目不断涌现,得到了海量的观测数据.而巡天观测方式使获得的数据弧段过短,传统方法在定轨和识别上存在极大困难,加之短弧定轨问题本身的病态性,如何有效利用这些短弧数据对于发现、监测和评估小行星的威胁具有重要意义.在进化算法下构建极短弧定轨的计算框架,选用三变量的(a, e, M)优选法,保持维数较低的同时,使优化结果不再依赖观测量.采用参数较少、操作简便的差分进化算法,利用不同偏心率小行星的轨道模拟数据进行试验,对获得的最优解及其分布聚集区域进行分析,大偏心率轨道由于其本身的复杂性,会对算法搜索的灵敏度产生影响,需缩小搜索空间以提高搜索能力.结果表明算法在小偏心率问题中表现较好,可以得到有效结果为后续工作提供参考信息,大偏心率问题在传统方法失效的情况下,虽然最优解在整体分布中并不明显,但分布仍包含真实解,可结合分布密度和适值大小进行分析.未来需要对大偏心率问题作进一步研究,考虑其观测位置和观测时刻对算法产生的影响,分类计算.
基金supported by the National Natural Science Foundation of China (Grant No.11672126)the Innovation Funded Project of Shanghai Aerospace Science and Technology (Grant Nos.SAST2017032 and SAST2015036)the Scientific Research Foundation for New Staffs of Nanjing University of Aeronautics and Astronautics (Grant No.1011-YAH17071)
文摘This paper investigates a simplified model for describing the gravitational fields of non- axisymmetric elongated asteroids. The connection between the simplified model and the target aster-oid is built by considering the positions of equilibrium points. To improve the performance of po-sition matching for the equilibrium points associated with these non-axisymmetric asteroids, a non-axisymmetric triple-particle-linkage model is proposed based on two existing axisymmetric particle- linkage models. The unknown parameters of the simplified model are determined by minimizing the matching error using the nonlinear optimization method. The proposed simplified model is applied for three realistic elongated asteroids, 243 Ida, 433 Eros and （8567） 1996 HW1. The simulation re-sults verify that the current particle-linkage model has better matching accuracy than the two existing particle-linkage models. The comparison, between the simplified model and the polyhedral model, on the topological cases of the equilibrium points and the distribution of gravitational potential further validate the rationality and accuracy of the simplified model.
基金supported in part by the National Natural Science Foundation of China(Project Nos.11772009,11972007 and 11832002)the Beijing Municipal Natural Science Foundation(Project No.1192002)the International Research Cooperation Seed Fund of Beijing University of Technology(No.2018B15)。
文摘There are plentiful asteroids moving periodically around their central primaries, such as the Sun. Due to the perturbation of the central primary, the gravitational force of the perturbed asteroid system varies periodically. In this paper, based on the idea of integrating the solar gravitational force as a part of the system instead of treating it as perturbation, the parametric resonance response is investigated. A novel type of stable parametric resonance orbits has been detected. It is found that the steady-state motion amplitude of parametric resonance orbit is determined by the frequency-response equation. The stability of the novel orbits has also been demonstrated. The new type of orbits may contribute to possible asteroid exploration missions.
