Abstract An integral index is used in this manuscript to search for the least gravitationally perturbed orbits around an oblate spheroid. Although there are missions where perturbations are desired, such as Sun-synchronous orbits, near Keplerian orbits can be useful in some cases during the whole mission or partially, helping to keep the oscillations of the orbital parameters in the minimum possible level, which can be interesting to observe celestial bodies. These orbits are also good candidates to require a lower number of station-keeping maneuvers, helping to simplify the logistic of the mission. The index used is available in the literature and it is based on the integration of the accelerations suffered by a spacecraft over time. An oblate spheroid is used to represent the approximate shape of non-spherical bodies because it has a closed equation for the potential, which makes it ideal for the analysis proposed, and because it is a shape similar to what is found for several objects in the small bodies population. The Lagrange planetary equations are also used to map orbits that have a minimum rate of variation in their orbital elements, and compared with the results obtained with the integral index. The results show a very good agreement between the index and the variations of the orbital elements of the spacecraft, in particular in terms of locating the least perturbed orbits to place the spacecraft.

中文翻译：

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使用积分索引搜索扁球体周围的轨道

摘要 本手稿中使用积分指数来搜索扁球体周围引力扰动最小的轨道。虽然有些任务需要扰动，例如太阳同步轨道，但在整个任务期间或部分情况下，开普勒附近的轨道在某些情况下可能很有用，有助于将轨道参数的振荡保持在尽可能低的水平，这可以是观察天体很有趣。这些轨道也是需要较少数量的站保持机动的良好候选者，有助于简化任务的后勤工作。所使用的指数可在文献中找到，它基于航天器随时间遭受的加速度的积分。扁球体用于表示非球体的近似形状，因为它具有一个封闭的势方程，这使得它非常适合所提出的分析，并且因为它的形状类似于在数个物体中发现的形状小体人口。拉格朗日行星方程还用于绘制轨道元素变化率最小的轨道，并与使用积分指数获得的结果进行比较。结果表明，该指数与航天器轨道要素的变化之间具有很好的一致性，特别是在定位最小扰动轨道以放置航天器方面。拉格朗日行星方程还用于绘制轨道元素变化率最小的轨道，并与使用积分指数获得的结果进行比较。结果表明，该指数与航天器轨道要素的变化之间具有很好的一致性，特别是在定位最小扰动轨道以放置航天器方面。拉格朗日行星方程还用于绘制轨道元素变化率最小的轨道，并与使用积分指数获得的结果进行比较。结果表明，该指数与航天器轨道要素的变化之间具有很好的一致性，特别是在定位最小扰动轨道以放置航天器方面。