An efficient integrator that uses Gauss-Radau spacings
An efficient integrator that uses Gauss-Radau spacings
复制标题
使用 Gauss-Radau 间距的高效积分器
DOI：
10.1007/978-94-009-5400-7_17
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
E. Everhart
中科院分区：
文献类型：
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作者：
E. Everhart
彗星轨道数值积分的问题之一是其数值稳定性问题。对于那些与巨行星发生近距离碰撞的天体来说，这个问题有一个特殊的特点。除了数学意义上的积分的数值不稳定性之外，还有一个不稳定性的来源是由于初始数据的不准确性，即轨道要素。本文通过对P/Shajn-Schaldach彗星在368.4年的时间间隔内的运动进行数值积分，给出了这种情况的一个例子，在此期间发生了6次与木星的近距离相遇。这颗彗星的起始轨道要素的不准确性是通过中央轨道每个要素的最后一位数字的变化来模拟的，由最佳轨道要素集确定。在积分过程中，八个模型轨道经历相对于中心轨道的微分摄动。数值上的不稳定性，由起始轨道要素的不准确性引起，表现为这些轨道的色散，往往会在每次与木星相遇后突然增加。它表明，与密切的元素表示的意见，一个或两个办法内1 Au从木星可以使轨道完全不确定的可达到的精度。
One of the problems of the numerical integrations of cometary orbits is that of their numerical stability. For those bodies which undergo close encounters with the giant planets the problem has a specific feature. Apart from the numerical instability of integrations in the mathematical sense, there is an additional source of instability due to the inaccuracy of initial data, i.e. the orbital elements. An example of this case is presented in this paper by the numerical integration of the motion of comet P/Shajn-Schaldach over an interval of 368.4 years, within which six close encounters with Jupiter occurred. The inaccuracy of the starting orbital elements of this comet is modelled by changes in the last digit of each element of the central orbit, determined by the set of the best orbital elements. In the process of integration, eight model orbits experience differential perturbations with respect to the central orbit. The numerical instability, caused by the inaccuracy of starting orbital elements and represented by the dispersion of these orbits, tends to increase abruptly beyond each encounter with Jupiter. It is shown that, with the attainable accuracy of the osculating elements representing the observations, one or two approaches to within 1 AU from Jupiter can make the orbit entirely indeterminate.