二体积分定轨法
Orbit Determination with the two-body Integrals
摘要：
本文研究了利用开普勒问题的第一积分来计算太阳系天体初始轨道的一个有限集的方法。这种方法被认为是应用于现代天文测量观测，其中包含的信息往往只允许计算，通过插值，两个角位置的观察机构和他们的时间导数在一个给定的时期，我们称这组数据可归因。给定同一物体在两个不同时期的两个属性，我们可以使用两体问题的能量和角动量积分来写出两个时期的拓扑中心距离和径向速度的多项式方程组。我们定义了两种不同的算法的解决方案的计算，基于不同的方式来执行消除变量，并获得一元多项式。此外，我们还利用数据的冗余性来检验两个属性属于同一个身体的假设（连锁问题）。还可以计算协方差矩阵，描述由观测误差统计产生的初始轨道的不确定性。该方法的性能进行了研究，通过使用大量的模拟观测的泛STARRS项目。
英文摘要：
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results from the observation error statistics. The performance of this method has been investigated by using a large set of simulated observations of the Pan-STARRS project.
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