Spacecraft and natural objects orbiting an active comet are perturbed by gas drag from the coma. These gases expand radially at about 0.5 km/s, much faster than orbital velocities that are on the order of meters per second. The coma has complex gas distributions and is difficult to model. Accelerations from gas drag can be on the same order of gravity and are currently poorly understood. Semi-analytical solutions for the evolution of the Keplerian orbital elements of a spacecraft orbiting a comet using simplified drag and coma models are derived using a Fourier series expansion in the argument of latitude. It is found that the mean element evolution is only dependent on the zeroth- and first-order terms of the Fourier series expansion. For an arbitrary, inverse-square, radial, perturbing force, there are no frozen orbits; however, the argument of pericenter has a stable equilibrium and an unstable equilibrium and the angular momentum vector of the orbit is constant. Furthermore, the radius of the orbit at two specific angles relative to the ascending node is preserved. The evolution of the orbit is governed by the argument of pericenter, resulting in orientations that raise and lower the radius of pericenter and implying safe and unsafe orbit orientations for spacecraft operations.

中文翻译：

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任意彗发彗星的轨道演化

围绕活跃彗星运行的航天器和自然物体会受到彗发产生的气体阻力的干扰。这些气体以大约 0.5 公里/秒的速度径向膨胀，比每秒米数量级的轨道速度快得多。彗发具有复杂的气体分布并且难以建模。气体阻力产生的加速度可能与重力相同，目前了解甚少。使用简化的阻力和彗发模型的航天器围绕彗星运行的开普勒轨道元素演化的半解析解是在纬度参数中使用傅立叶级数展开推导出来的。发现平均元素演化仅依赖于傅立叶级数展开的零阶和一阶项。对于任意的、平方反比、径向、扰动力，没有冻结轨道；然而，中心点的自变量有一个稳定平衡点和一个不稳定平衡点，轨道的角动量矢量是常数。此外，相对于升交点的两个特定角度的轨道半径被保留。轨道的演变由周心的参数控制，导致提高和降低周心半径的方向，并暗示航天器运行的安全和不安全轨道方向。