Optimal periodic relative orbit and rectilinear relative orbits with eccentric reference orbits

作者：Zhang Gang^*; Zhou Di; Sun Zhaowei; Cao Xibin

来源：Celestial Mechanics and Dynamical Astronomy, 2013, 117(2): 137-148.

DOI：10.1007/s10569-013-9499-2

• Periodic relative orbit
• Eccentric reference orbit
• Initial coasting time
• Minimum fuel
• Rectilinear relative orbit
• Formation flying
• Fly-around trajectory

The problem of two-body linearized periodic relative orbits with eccentric reference orbits is studied in this paper. The periodic relative orbit in the target-orbital coordinate system can be used in fly-around and formation-flying orbit design. Based on the closed-form solutions to the Tschauner-Hempel equations, the initial condition for periodic relative orbits is obtained. Then the minimum-fuel periodic-orbit condition with a single impulse is analytically derived for given initial position and velocity vectors. When considering the initial coasting time, the impulse position of the global minimum-fuel periodic orbit is proved to be near to the perigee of the target and can be obtained by numerical optimization algorithms. Moreover, the condition for a special periodic orbit, i.e., the rectilinear relative orbit in the target-orbital frame, is obtained. Numerical simulations are used to demonstrate the efficacy of the method, and show the geometry of the periodic relative orbit and the rectilinear relative orbit.

• 出版日期2013-10
• 单位哈尔滨工业大学