Relative Orbit Geometry Through Classical Orbit Element Differences
Relative Orbit Geometry Through Classical Orbit Element Differences
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DOI：
10.2514/1.12595
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发表时间：
2004-09
影响因子：
2.6
通讯作者：
H. Schaub
中科院分区：
文献类型：
--
作者：
H. Schaub
航天器编队的相对轨道几何形状可以用相对于共同主轨道的一组轨道要素差来描述。对于无摄动轨道运动，如果异常差用平均异常表示，并且所有半长轴相等，则这些轨道要素差保持不变。给出了圆主参考轨道和椭圆主参考轨道线性化相对轨道几何的一般估计方法。相对轨道是纯粹通过相对轨道根数差来描述的，而不是通过使用笛卡尔初始条件的经典方法。给出了以真异常角表示的相对运动的解析解。当这个角度从0到2π扫描时，估计沿轨道、平面外和轨道的径向尺寸是微不足道的。基于轨道元素的相对运动预测对密切元素空间和平均元素空间都是有效的。线性化中的主要假设是相对轨道半径小于相对于地球的惯性轨道半径。由此产生的线性化相对运动解可用于帮助选择轨道要素差异，从而产生自然的所需相对轨道几何形状。线性化的解析解，显示什么长期漂移是由具有非零的半长轴差，或什么影响的J 2引力摄动的平均相对运动。
The relative orbit geometry of a spacecraft formation can be elegantly described in terms of a set of orbit element differences relative to a common chief orbit. For the nonperturbed orbit motion, these orbit element differences remain constant if the anomaly difference is expressed in terms of the mean anomaly and all semimajor axes are equal. A general method is presented to estimate the linearized relative orbit geometry for both circular and elliptic chief reference orbits. The relative orbit is described purely through relative orbit element differences, not through the classical method of using Cartesian initial conditions. Analytical solutions of the relative motion are provided in terms of the true anomaly angle. When this angle is swept from 0 to 2π, it is trivial to estimate the along-track, out-of-plane, and orbit radial dimensions. The orbit element-based relative motion predictions are valid for both the osculating element space and the mean element space. The main assumption being made in the linearization is that the relative orbit radius is small compared to the inertial orbit radius relative to Earth. The resulting linearized relative motion solution can be used to assist in selecting the orbit element differences that yield a natural desired relative orbit geometry. Linearized analytical solutions are provided that show what secular drift is caused by having a nonzero semimajor axis difference, or what influence the J 2 gravitational perturbation will have on the mean relative motion.