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Uncertainty propagation in the N-body problem using Dromo elements

机译:使用Dromo元素在N体问题中的不确定性传播

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Reliable and efficient uncertainty propagation is crucial for the task of monitoring possible impacts of Near Earth Asteroids with our planet. It is well known that a switch of the primary body can greatly reduce the numerical truncation error in the case of planetary flybys. In the present work, the advantages of performing a primary body switch in the uncertainty propagation problem are explored. For this purpose, first we present the linear uncertainty propagation using Dromo formulation, which has been shown in previous works to have a satisfactory performance when propagating the orbit uncertainty of Near Earth Asteroids. Next, we introduce the concept of primary body switch for the uncertainty propagation problem. The algorithm is based on the following procedure. We sample the initial orbit uncertainty distribution and linearly propagate the samples, considering the N-body gravitational influence. A primary body switch, which is a nonlinear mapping, is performed for all the samples at a threshold distance from the approaching planet, the Earth. The orbit of the samples is then linearly propagated with respect to the Earth using the Dromo formulation until the threshold distance is reached again. Finally, the propagation center is changed back to the heliocentric frame and the linear propagation continues. We apply the proposed method to an extensive set of asteroids that approach the Earth. Results suggest that the average error of the linear propagation can be reduced up to a factor of 30 when compared to a purely heliocentric linear propagation using Dromo elements.
机译:可靠而有效的不确定性传播对于监视近地小行星对我们星球的可能影响至关重要。众所周知,在行星飞越的情况下,切换主体可以大大减少数值截断误差。在当前的工作中,探索了在不确定性传播问题中执行初级开关的优势。为此,我们首先介绍使用Dromo公式的线性不确定性传播,在先前的研究中已经表明,该线性不确定性传播在传播近地小行星的轨道不确定性方面具有令人满意的性能。接下来,我们介绍用于不确定性传播问题的主体开关的概念。该算法基于以下过程。考虑到N体重力影响,我们对初始轨道不确定性分布进行采样并线性传播样本。对于所有样本,在距接近的行星地球的阈值距离处执行一次非线性映射的主体开关。然后,使用Dromo公式将样本的轨道相对于地球线性传播,直到再次达到阈值距离。最后,传播中心变回日心框架,并且线性传播继续进行。我们将拟议的方法应用于接近地球的大量小行星。结果表明,与使用Dromo元件的纯日心中心线性传播相比,线性传播的平均误差最多可以降低30倍。

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