J_2摄动情况下编队飞行卫星相对运动精确解析模型研究

Precision Analytical Equation to Relative Motion of Formation Flying Satellites for J_2 Perturbation

给出了一种描述J2摄动情况下编队飞行卫星相对运动的精确解析模型.在近圆轨道情况下引入无奇点变量,得到了参考星相对运动坐标系中从星运动的一般形式,进一步推导了J2摄动影响下初始时刻无奇点平均/瞬时轨道要素偏差表示的任意时刻编队飞行卫星相对动力学解析方程.仿真结果表明,编队飞行相对运动解析模型的相对位置误差在运行14圈内可以达到m级,为经典Hill方程对应误差的1%左右,能够精确预报编队队形的变化规律,为提出有效队形控制策略提供了理论基础.同时计算量小,适合于编队卫星星上自主运算和自主方案规划.

A precision analytical equation to relative motion of formation flying satellites for ,J2 perturbation is presented. Introduced non-singular variable, mean elements analytical orbit theory for J2 perturbation is described. General equation for relative motion of formation satellites is obtained by first-order Taylor series expansion about chief satellite. On the basis of J2 analytical orbit theory, relative motion analytical equation for the J2 perturbed near-circular reference orbit is derived by using initial relative non-singularity mean elements or osculating elements, and the state transition matrixes, from the relative mean to the relative osculating non- singular elements and from the initial relative mean to random time relative mean non-singular elements and from the true argument of latitude to the mean argument of latitude, are prescribed. Simulation indicated that the relative error precision of analytical equation is less than or equal to meter level, and max-relative position errors are less than by far its of Hill equation. The method preserves advantage of precision long-time prediction for formation configuration ,low computational costs and autonomous control and maneuver scheme planning of formation satellites.