二体积分定轨。II
Orbit Determination with the two-body Integrals. II
摘要：
开普勒问题的第一积分用于计算从天体的两个短观测弧开始的初步轨道，这可以通过光学或雷达观测获得。我们为这个问题写多项式方程，我们可以使用计算代数的强大工具来解决。提出了一种判定两个短弧的连接是否成功的算法，即它们是否属于同一个观测体，并进行了数值试验。在本文中，我们继续在[Gronchi，Dimare，Milani，'Orbit determination with the two-body integrals'，CMDA（2010）107/3，299-318]中开始的研究，其中使用角动量和能量积分。一个合适的分量的拉普拉斯-伦茨矢量的地方的能量原来是方便的，事实上，所得到的系统的程度减少到不到一半。
英文摘要：
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for this problem, that we can solve using the powerful tools of computational Algebra. An algorithm to decide if the linkage of two short arcs is successful, i.e. if they belong to the same observed body, is proposed and tested numerically. In this paper we continue the research started in [Gronchi, Dimare, Milani, 'Orbit determination with the two-body intergrals', CMDA (2010) 107/3, 299-318], where the angular momentum and the energy integrals were used. A suitable component of the Laplace-Lenz vector in place of the energy turns out to be convenient, in fact the degree of the resulting system is reduced to less than half.
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