The Journal of the Astronautical Sciences

, Volume 66, Issue 4, pp 446–459 | Cite as

Adaptive LEO-Phase Free-Return Orbit Design Method for Manned Lunar Mission Based on LEO Rendezvous

  • Bo-yong HeEmail author
  • Heng-nian Li
  • Ai-wu Zheng


To design a free-return orbit for manned lunar mission based on low earth orbit (LEO) rendezvous, an adaptive LEO-phase free-return orbit design method based on high-precision dynamics model is proposed. First, the radius of perilune and the absolute value of perilune velocity are decoupled using a coordinate system rotation, which is derived from moon-centric local vertical and local horizontal instantaneous coordinate system at the time of perilune. The two Euler rotation angles and the absolute value of perilune velocity are used as independent design variables because their initial values are easy to guess. Next, a two-segment numerical integration strategy is proposed to calculate orbital elements at the moments of trans-lunar injection and free-return vacuum perigee. Subsequently, an optimization algorithm software package for solving large-scale nonlinear sequential quadratic programming problems (SQP_snopt) is employed to search the objective free-return orbit with a fixed trans-lunar injection inclination and the other two constraints on radiuses of perigee at the times of trans-lunar injection and vacuum perigee. After that, an iteration algorithm is devised to adjust trans-lunar injection window for adaptive LEO-phase. Finally, numerical results show a fast and accurate performance of the direct optimization method, which can provide valuable references to manned lunar missions based on LEO rendezvous.


Manned lunar mission Free-return orbit Adaptive LEO-phase Orbit design High-precision dynamics model 



This work was supported by the National Natural Science Foundation of China (Grant No. 11702330) and National Defense Science and Technology Innovation Special Zone Project.


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Copyright information

© American Astronautical Society 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Astronautic Dynamics (ADL)Xi’an Satellite Control CenterXi’anChina
  2. 2.Beijing Aerospace Flight and Control CenterBeijingChina

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