J_2 invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth＇s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.

Short-Term Orbit Prediction with J₂and Mean Orbital Elements

An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in all the orbital elements with the present theory over second-order theory. The theory is used for computing the mean orbital elements, which are found to be more accurate than provided by Bhatnagar and taqvi’s theory (up to second power in eccentricity). Mean elements have a large number of practical applications.

考虑J_2项摄动的卫星编队飞行

针对参考卫星运行于圆轨道的编队飞行 ,分析了J2 项摄动的影响。在此基础上提出了一种方法 ,通过调整环绕卫星的半长轴 ,大大减小了J2 项摄动对编队飞行的破坏作用。此外 ,基于冲量假设估计了编队保持的代价。数值结果表明 ,调整长半轴的卫星编队可以长期保持 ,节省了大量的控制燃料。

The J_2 invariant relative configuration of spaceborne SAR interferometer for digital elevation measurement

A 3-craft formation configuration is proposed to perform the digital elevation model （DEM） for the distributed spacebome interferometric synthetic aperture radar （InSAR）, and it is optimized by the modified ant colony algorithm to have the best compatibility with J2 invariant orbits created by differential correction algorithm. The configuration has succeeded in assigning the across-track baseline to vary periodically and with its mean value equal to the optimal baseline determined by the relative height measurement accuracy. The required relationship between crafts＇ magnitudes and phases is formulated for the general case of interferometry measure from non-orthographic and non-lateral view. The J2 invariant configurations created by differential correction algorithm are employed to investigate their compatibility with the required configuration. The colony algorithm is applied to search the optimal configuration holding the near-constant across-track baseline under the J2 perturbation, and the absolute height measurement accuracy is preferable as expected.

J_2摄动对编队飞行卫星相对轨道构形的影响

利用相对轨道根数法研究J2摄动对卫星编队飞行的相对轨道构形的影响,并利用高精度的算法进行数值仿真。结果表明:摄动可以使相对轨道构形发生转动与漂移两种变化。摄动引起相对轨道构形变化的形式,取决于参加编队卫星的轨道根数。当主、从星的轨道参数中只有升交点赤径不相同时,摄动对相对轨道构形几乎没有影响;当主、从星偏心率不相同时,摄动将引起相对轨道构形的转动;而当主、从星之间轨道倾角、近地点幅角和近地点时刻各不相同时,摄动将引起相对轨道构形的漂移。

编队飞行卫星相对运动的零J_2摄动条件

地球形状摄动对卫星编队飞行的相对运动有很大影响,会使卫星的相对轨道发生转动或漂移。该文推导了主、从星沿小偏心率轨道运行情况下的相对轨道的零J2摄动条件。如果编队卫星的交点周期和节线的进动速率相等,那么J2摄动对相对运动没有影响,卫星可长期保持编队飞行。在选取的主、从星轨道根数之差为小量的前提下,给出了零J2摄动的一阶近似条件的解析表达式。仿真结果表明,当编队卫星的相对运动满足零J2摄动的一阶近似条件时,卫星相对运动轨道构形的漂移明显减少。

利用DORIS相位数据的Jason-2卫星精密定轨

主要研究了DORIS系统RINEX观测值模型的建立及其主要误差——星载接收机钟差的改正方法,在此基础上实现了基于DORIS系统RINEX相位观测值数据的Jason-2卫星精密轨道确定。研究表明,利用拟合接收机钟差和利用RINEX频偏数据这两种钟差改正方法,基于RINEX相位观测值的Jason-2卫星精密定轨均能达到径向1cm量级的精度;而拟合接收机钟差改正能同时削弱接收机钟的高阶振荡误差,可以获得更高的定轨精度。

Planning for space station long-duration orbital mission under multi-constraints

An integrated nonlinear planning(NLP) model is built for space station long-duration orbital missions considering both the vehicle visiting schedules and the interaction effects between target phasing,vehicle return adjusting and Earth observation aiming.A two-level optimization approach is proposed to solve this complicated problem.The up-level problem employs the launch times of visiting vehicles as design variables,considers the constraints of crew rotations,resource resupplies and rendezvous launch windows,and is solved by a genetic algorithm.The low-level problems employ the maneuver impulses and burn times within each orbital mission as design variables,and a high-efficient shooting iteration method is proposed based on an analytical equation for the phase angle correction considering the J 2 perturbation.The results indicate that the integrated NLP model for space station long-duration orbital missions is effective,and the proposed optimization approach can obtain the optimal solutions that satisfy the multiple constraints and reduce the total propellant consumption.