There has been a growing interest in spacecraft formation flying for space science applications. Such missions will require an accurate and efficient dynamics model, on-board the flight computer, to calculate and control the desired relative motion. Hence, an analytical dynamics model which can be applied to eccentric orbits and includes perturbations can provide an increase in accuracy and efficiency. This paper develops an accurate analytical solution of relative motion between two spacecraft using classical orbital elements. The analytical solution is obtained by propagating the orbital elements forward in time, while taking into account gravitational field up to the fifth harmonic, third-body and drag secular and periodic perturbations, and calculating the relative motion in the local-vertical-local-horizontal reference frame at each time-step. The analytical solution was observed to accurately describe the relative motion when compared with a numerical simulator, yielding errors on the order of meters for separation distances on the order of hundreds of meters.

对于用于空间科学应用的航天器编队飞行，人们越来越感兴趣。这样的任务将需要在飞行计算机上的准确而有效的动力学模型，以计算和控制所需的相对运动。因此，可以应用于偏心轨道并包括扰动的分析动力学模型可以提高准确性和效率。本文利用经典的轨道要素，开发出了两种航天器之间相对运动的精确解析解。通过将轨道元素在时间上向前传播，同时考虑到五次谐波的引力场，第三体和长期惯性和周期扰动，并计算局部-垂直-局部-水平方向的相对运动，从而获得了解析解。每个时间步的参考帧。