激光干涉仪空间天线(laser interferometer space antenna,LISA)是欧洲太空局和美国航天局合作用于探测从0.1mHz到1Hz低频引力波的航天项目,引力波的探测将通过在空间中的3个探测器之间使用激光干涉仪的高精度测距来实现.3个探测器计划于2018年前后发射,并于一年后进入引力波探测实验的绕日轨道.为了引力波探测的成功,保持3个探测器所组成星座的高度稳定性是至关重要的.我们在以前2015年实验轨道优化设计的基础上,选取2019年3月1日为起始历元做了实验轨道的优化设计,介绍了任意起始时刻下确定轨道优化起始点的规则和轨道优化的算法;并给出了从地球停泊轨道进入引力波探测实验轨道的发射段和分离段的轨道设计,讨论了所需飞行时间与发射能量之间的关系,给出了设计实例.
In deriving the physical properties of asteroids from their photometric data, the scattering law plays an important role, although the shape variations of asteroids result in the main variations in lightcurves. By following the physical behaviors of light reflections, Hapke et al. deduced complex functions to represent the scattering process, however, it is very hard to accurately simulate the surface scattering law in reality. For simplicity, other numerical scattering models are presented for efficiently calculating the physical properties of asteroids, such as the Lommel-Seeliger （LS） model. In this article, these two models are compared numerically. It is found that in some numerical applications the LS model in simple form with four parameters can be exploited to replace the Hapke model in complex form with five parameters. Furthermore, the generated synthetic lightcurves by the Cellinoid shape model also show that the LS model can perform as well as the Hapke model in the inversion process. Finally, by applying the Principal Component Analysis （PCA） technique to the parameters of the LS model, we present an efficient method to classify C and S type asteroids, instead of the conventional method using the parameters of the Hapke model.
Based on large quantities of co-orbital phenomena in the motion of natural bodies and spacecraft, a model of the co-orbital restricted three-body problem is put forward. The fundamental results for the planar co-orbital circular restricted three-body problem are given, which include the selection of variables and equations of motion, a set of approximation formulas, and an approximate semi-analytical solution. They are applied to the motion of the barycenter of the planned gravitational observatory LISA constellation, which agrees very well with the solution of precise numerical integration.
Research about asteroids has recently attracted more and more attention, especially focusing on their physical structures, such as their spin axis, rotation period and shape. The long distance between observers on Earth and asteroids makes it impossible to directly calculate the shape and other parameters of asteroids, with the exception of Near Earth Asteroids and others that have passed by some spacecrafts. Photometric measurements are still generally the main way to obtain research data on asteroids, i.e. the lightcurves recording the brightness and positions of asteroids. Supposing that the shape of the asteroid is a triaxial ellipsoid with a stable spin, a new method is presented in this article to reconstruct the shape models of asteroids from the lightcurves, together with other physical parameters. By applying a special curvature function, the method calculates the brightness integration on a unit sphere and Lebedev quadrature is employed for the discretization. Finally, the method searches for the optimal solution by the Levenberg-Marquardt algorithm to minimize the residual of the brightness. By adopting this method, not only can related physical parameters of asteroids be obtained at a reasonable accuracy, but also a simple shape model of an ellipsoid can be generated for reconstructing a more sophisticated shape model.
