This paper presents analytical solutions for the estimation of the \(\Delta V\) cost of the transfer of a spacecraft subject to a low-thrust action. The equations represent an extension of solutions already available in the literature. Moreover, the paper presents novel analytical solutions for low-thrust transfers under the effect of the second-order zonal harmonics of the Earth’s gravitational potential. In particular, the paper is divided into two parts. The first part presents analytical expressions for the \(\Delta V\) cost of transfers. All analytical equations were validated through numerical integration of the dynamics of the spacecraft. The second part of the paper introduces new analytical equations for low-thrust transfers between circular inclined orbits with different values of the right ascension of the ascending node, under the effect of the second-order zonal harmonic of the Earth’s gravitational potential. Both in the first and second parts, analytic solutions for the variation with time of the orbital elements during the transfer are presented. The proposed equations are applicable to low-thrust transfer realised through a long spiral trajectory.

本文提出了估计受低推力作用的航天器转移的\(\Delta V\)成本的解析解。这些方程代表了文献中已有解决方案的扩展。此外，本文提出了在地球引力势的二阶纬向谐波影响下的低推力传递的新解析解。特别是，本文分为两部分。第一部分给出了\(\Delta V\) 的解析表达式转移成本。所有分析方程都通过航天器动力学的数值积分得到验证。论文的第二部分介绍了在地球引力势的二阶纬向谐波作用下，具有不同升交点赤经值的圆形倾斜轨道之间低推力转移的新解析方程。第一部分和第二部分都给出了轨道元素在转移过程中随时间变化的解析解。所提出的方程适用于通过长螺旋轨迹实现的低推力传递。