A second-order solution to the two-point boundary value problem for rendezvous in eccentric orbits

作者：Zhang Gang^*; Zhou Di

来源：Celestial Mechanics and Dynamical Astronomy, 2010, 107(3): 319-336.

DOI：10.1007/s10569-010-9269-3

• Relative motion
• State transition
• Eccentric orbit
• J2 perturbations
• Rendezvous

A new second-order solution to the two-point boundary value problem for relative motion about orbital rendezvous in one orbit period is proposed. First, nonlinear differential equations to describe the relative motion between a chaser and a target are presented considering the second-order terms in the gravity. Then, by regarding the second-order terms as external accelerations, we establish second-order state transition equations. Moreover, the J2 perturbations effects can also be considered in the state transition equations. Last, the initial relative velocity to fulfill a rendezvous is determined by solving the state transition equations. Numerical simulations show that the new second-order state transition equations are accurate. The second-order solution to the two-point boundary value problem on eccentric orbits is valid even if the relative range is farther than 500 km.

• 出版日期2010-7
• 单位哈尔滨工业大学