An analysis of the orbital motion of artificial satellites around Mercury is presented taking into account its non-sphericity (J₂, J₃, C₂₂) and the perturbation of the third body. The disturbing potential due to the third body is developed in circular and inclined orbit. The double-averaged method should be used with caution in some situations where the averaging is applied at different timescales. In this work, a study is presented considering this observation for orbits around Mercury. When the mean anomaly of the Sun is eliminated, the idea is that all effects whose periods below 88 days are neglected. As the rotation of Mercury is about 58.6 days, this means that the perturbation due to the C₂₂ term must also be neglected. However, since the C₂₂ term is important and should be taken into account, then terms longer than 58.6 days should also be preserved. In other words, keeping the C₂₂ term with a period of 58.6 days means that the solar terms with the longest period (88 days) will be maintained here. The single-averaged method is applied to eliminate only the mean anomaly of the spacecraft. A comparison between the single and double averaged models is presented. We found that for the case of Mercury the two models are in agreement, but the single-averaged model is more realistic because it keeps more terms in the disturbing potential. Several types of resonances can be analyzed starting of the single-averaged potential. Considering our single-averaged disturbing potential, the terms due to Lidov–Kozai resonance were isolated to make a qualitative analysis considering the libration and circulation regions in the diagram, eccentricity versus argument of the pericenter.

中文翻译：

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使用单平均和双平均方法以及Lidov-Kozai机制的半分析方法

考虑到水星的非球形度（J ₂，J ₃，C ₂₂）和第三体的扰动，对水星周围人造卫星的轨道运动进行了分析。第三体产生的扰动势在圆形和倾斜轨道上产生。在某些情况下，在不同的时间范围应用平均时，应谨慎使用双平均法。在这项工作中，提出了一项研究，该研究考虑了对水星周围轨道的观测。当消除了太阳的平均异常时，其想法是忽略所有低于88天的影响。由于水星的自转大约是58.6天，这意味着由于C引起的扰动也必须忽略_22个任期。但是，由于C ₂₂术语很重要且应予以考虑，因此，应保留超过58.6天的术语。换句话说，保持C ₂₂期限为58.6天的期限表示将保留最长期限（88天）的日照期限。采用单平均方法仅消除航天器的平均异常。提出了单平均模型和双平均模型之间的比较。我们发现，对于Mercury而言，这两个模型是一致的，但是单一平均模型更为实际，因为它在干扰可能性中保留了更多的术语。可以从单平均电势开始分析几种类型的共振。考虑到我们的单平均扰动电位，考虑了图中的自由和循环区域，偏心率与中心点的论点，对李多夫-科扎共振产生的项进行了定性分析。