An Algebraic Method to Compute the Critical Points of the Distance Function Between Two Keplerian Orbits
An Algebraic Method to Compute the Critical Points of the Distance Function Between Two Keplerian Orbits
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DOI：
10.1007/s10569-005-1623-5
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发表时间：
2005-09
影响因子：
1.6
通讯作者：
G. Gronchi
中科院分区：
文献类型：
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作者：
G. Gronchi
我们描述了一种有效的算法来计算具有共同焦点的两个开普勒轨道（有界或无界）之间距离函数的所有临界点。这个函数的临界值对于不同的目的都很重要，例如评估小行星或彗星与太阳系行星碰撞的风险。我们的算法基于代数消元理论：通过计算两个二元多项式的结果，我们找到了一个16次一元多项式，它的实数根给出了临界点的一个分量。我们还讨论了一些简并的情况，并给出了几个例子，包括已知的小行星和彗星的轨道。
We describe an efficient algorithm to compute all the critical points of the distance function between two Keplerian orbits (either bounded or unbounded) with a common focus. The critical values of this function are important for different purposes, for example to evaluate the risk of collisions of asteroids or comets with the Solar system planets. Our algorithm is based on the algebraic elimination theory: through the computation of the resultant of two bivariate polynomials, we find a 16th degree univariate polynomial whose real roots give us one component of the critical points. We discuss also some degenerate cases and show several examples, involving the orbits of the known asteroids and comets.