From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs
From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs
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DOI：
10.1007/s10569-005-3314-7
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发表时间：
2005-04
影响因子：
1.6
通讯作者：
A. Milani;Z. Knežević
中科院分区：
文献类型：
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作者：
A. Milani;Z. Knežević
当代调查提供了大量对太阳系小型天体（主要是小行星）的探测结果。通常，报告的天体测量不足以计算轨道和/或对已发现的物体进行识别。初步轨道确定的经典方法在这种情况下会失败：需要一种新方法。当观测结果不足以计算轨道时，我们用属性（两个角度及其时间导数）来表示数据。未定变量的范围和范围变化率跨越太阳系轨道的允许区域，该区域可以通过通过最佳三角测量选择的一组虚拟小行星（VA）来采样。归因结果来自拟合，并具有由协方差矩阵表示的不确定性，因此未来观测的预测可以通过准乘积结构（允许区域乘以置信椭圆体）来描述，该结构可以通过每个节点被置信椭圆体包围的三角测量来近似。识别两个独立的观测短弧的问题已经解决。对于第一条弧允许区域中的每个 VA，我们考虑第二条弧时的预测和相应的协方差矩阵，并将它们与第二条弧及其自身协方差的归因进行比较。通过使用惩罚（增加平方和，如识别算法中的那样），我们选择可以将两条弧拟合在一起并计算初步轨道的 VA。即使两个属性也可能不足以使用收敛微分校正算法计算轨道。初步轨道用作约束微分校正的初步猜测，提供沿变化线（LOV）的解，该解可用作第二代VA以进一步预测第三弧时的观测结果。一般来说，第三条弧的识别将确保最小二乘轨道，不确定性由协方差矩阵描述。
Contemporary surveys provide a huge number of detections of small solar system bodies, mostly asteroids. Typically, the reported astrometry is not enough to compute an orbit and/or perform an identification with an already discovered object. The classical methods for preliminary orbit determination fail in such cases: a new approach is necessary. When the observations are not enough to compute an orbit we represent the data with an attributable (two angles and their time derivatives). The undetermined variables range and range rate span anadmissible regionof solar system orbits, which can be sampled by a set ofVirtual Asteroids(VAs) selected by an optimal triangulation. The attributable results from a fit and has an uncertainty represented by a covariance matrix, thus the predictions of future observations can be described by a quasi-product structure (admissible region times confidence ellipsoid), which can be approximated by a triangulation with each node surrounded by a confidence ellipsoid. The problem of identifying two independent short arcs of observations has been solved. For each VA in the admissible region of the first arc we consider prediction at the time of the second arc and the corresponding covariance matrix, and we compare them with the attributable of the second arc with its own covariance. By using the penalty (increase in the sum of squares, as in the algorithms for identification) we select the VAs which can fit together both arcs and compute a preliminary orbit. Even two attributables may not be enough to compute an orbit with a convergent differential corrections algorithm. The preliminary orbits are used as first guess for constrained differential corrections, providing solutions along theLine Of Variations(LOV) which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a least squares orbit, with uncertainty described by the covariance matrix.