The reachable domain of ground track under a single upper-bounded impulse for a given initial orbit is solved based on the Gauss's variational equations. Considering the linear J2 perturbation, the reachable domain problem is transformed into solving the ranges of longitude difference between the maneuvering and reference orbits at all feasible latitudes. For the coplanar impulse, the longitude difference is a monotonically decreasing function only of the transfer-time difference, and then the extreme values of the transfer-time difference are obtained by the Newton-Raphson iterations. For the noncoplanar impulse, the reachable domain is related to both the orbital plane change and the transfer-time difference, and then the extreme values of the longitude difference are solved by the sequence quadratic programming algorithm. Finally, the envelopes of the reachable domain are obtained by comparing the extreme values and the boundary values of the longitude difference. Several numerical examples with coplanar and noncoplanar impulses are provided to verify the effectiveness of the proposed method for solving the envelopes of the reachable domain.

中文翻译：

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单次脉冲的地面轨迹可达域


基于高斯变分方程求解给定初始轨道的单个上界脉冲下的地面轨道可达域。考虑线性J2扰动，将可达域问题转化为求解所有可行纬度上机动轨道与参考轨道之间的经度差范围。对于共面脉冲，经度差仅是传递时间差的单调递减函数，然后通过Newton-Raphson迭代获得传递时间差的极值。对于非共面脉冲，可达域与轨道平面变化和传递时间差有关，然后通过序列二次规划算法求解经度差的极值。最后，通过比较经度差的极值和边界值，得到可达域的包络线。提供了几个共面和非共面脉冲的数值例子来验证所提出的方法求解可达域包络的有效性。