This paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

本文介绍了可用于长期受低推力加速度和轨道扰动影响的航天器运动的长期传播的分析公式。本文考虑了由于以下原因而产生的加速度：遵循平方反比定律的低推力剖面，由于中心体重力场而引起的重力扰动和第三体重力扰动。分析公式以非奇异的等分元素表示。第三体重力扰动的公式已从文献中已经存在的第三体势方程开始获得。但是，等当量轨道元素变化的最终分析公式是一种新颖的推导。对于不同的轨道状态，结果得到了验证，