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首页> 外文期刊>Journal of Guidance, Control, and Dynamics >Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects
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Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects

机译：近地物体最佳低推力挠度的半解析解

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摘要

This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action,ninversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of thenasteroid at the minimum orbit interception distance from the Earth’s orbit is computed through proximal motionnequations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived toncompute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give thensecular variation of the elements, and their periodic components are approximated through a trigonometricnexpansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented alongnwith their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analyticalnapproach provides a significant savings in computational time while maintaining a good accuracy. Finally, somenexamples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular,nthe semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set ofnPareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizingnthe orbital deviation.
机译：当小推力作用在小行星上时，本文提出了半解析问题的解决方案，该推力与太阳的距离的平方成反比。距距地球轨道最小轨道拦截距离处的小行星类卫星的位移是根据近端运动方程计算的，这是轨道元素变化的函数。然后导出一组半解析公式，以计算元素的变化：高斯行星方程在一个轨道公转中求平均值，得到元素的长期变化，并且它们的周期分量通过三角函数展开近似。给出了半解析公式的两个公式，即纬度和时间公式，以及它们对高斯方程的完整数值积分的准确性。结果表明，半解析方法可在节省计算时间的同时保持良好的准确性。最后，提出了偏差任务的一些例子，作为所提出的半分析理论的应用。特别是，半解析公式与多目标优化算法结合使用，以找到一组帕累托最优任务选项，这些选项可以使小行星警告时间和航天器质量最小化，同时使轨道偏离最大化。

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