An approximate analytical method for short-range impulsive orbit rendezvous using relative Lambert solutions

作者：Zhang Gang^*; Zhou Di; Mortari Daniele

来源：Acta Astronautica, 2012, 81: 318-324.

DOI：10.1016/j.actaastro.2012.05.037

• Orbit rendezvous
• Relative Lambert'
• s problem
• Multiple revolution
• Singularity points

A new approximate analytical method for the two-body impulsive orbit rendezvous problem with short range is presented. The classical analytical approach derives the initial relative velocity from the state transition matrix of linear relative motion equations. This paper proposes a different analytical approach based on the relative Lambert solutions. An approximate expression for the transfer time is obtained as a function of chaser';s and target';s semi-major axes difference. This results in first and second order estimates of the chaser';s semi-major axis. Singularity points of rendezvous time for the classical and proposed new methods are both analyzed. As compared with the classical method, the new solution is simpler, more accurate, and has fewer singularity points. Moreover, the proposed method can be easily expanded to higher order solutions. A numerical example quantifies the accuracy gain for multiple-revolution cases.

• 出版日期2012-12
• 单位哈尔滨工业大学