Analytical theory of the spin-orbit state of a binary asteroid deflected by a kinetic impactor

Michalis Gaitanas, Christos Efthymiopoulos, Ioannis Gkolias, George Voyatzis, Kleomenis Tsiganis
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Abstract

We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system’s evolution after deflection by a kinetic impactor. To this end, both linear and nonlinear (canonical) theories are developed. We make the simplifying approximations (to be relaxed in a forthcoming paper) of planar binary orbit and axisymmetric shape of the primary body. To study the effect of a DART-like hit on the secondary body, the momentum transfer enhancement parameter \(\beta \) is introduced and retained as a symbolic variable throughout all formulas derived, either by linear or nonlinear theory. Our approach can be of use in the context of the analysis of the post-impact data from kinetic impactor missions, by providing a precise modeling of the impactor’s effect on the seconadry’s librational state as a function of \(\beta \).

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动能撞击器偏转双小行星自旋轨道状态的解析理论
我们研究了一颗双小行星从同步到扰动的自由状态,以全双刚体问题(F2RBP)为模型,主要重点是推导出描述该系统在受到动能撞击器偏转后的演变的分析公式。为此,我们开发了线性和非线性(典型)理论。我们对平面双轨道和主天体的轴对称形状做了简化近似(将在即将发表的论文中放宽)。为了研究类似DART的撞击对副天体的影响,引入了动量传递增强参数\(\beta \),并将其作为一个符号变量保留在线性或非线性理论推导的所有公式中。我们的方法可用于分析动能撞击器任务的撞击后数据,提供撞击器对次级天体自由状态影响的精确模型,作为\(\beta \)的函数。
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