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Third-Body Perturbation Using a Single Averaged Model: Application in Nonsingular Variables

机译：使用单个平均模型的第三体摄动：在非奇异变量中的应用

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摘要

The Lagrange's planetary equations written in terms of the classical orbital elements have the disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical model used and do not have physical reasons. In this paper, we studied the third-body perturbation using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the inclination.
机译：用经典轨道元素表示的拉格朗日行星方程具有偏心率和倾角奇异的缺点。这些奇异性是由于使用的数学模型引起的，没有物理原因。在本文中，我们使用非奇异变量的单个平均模型研究了第三体摄动。目标是使用单一平均模型消除由航天器的运动引起的短周期项，从而对由第三物体在航天器中引起的扰动进行半分析研究。如果月亮或太阳不发生共振，则此方法有效。一些图显示了赤道和圆形轨道的开普勒元素的时间历史，这是奇异的情况。在本文中，扩展仅限于偏心率的二阶和摄动体和被摄动体的半长轴之比，而对于倾角则限于四阶。

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