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Analysis of direct transfer trajectories from LL2 halo orbits to LLOs

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Abstract

A convenient procedure for designing the direct transfer trajectory from lunar L2 point (LL2) halo orbit to a low lunar orbit (LLO) is presented in this paper. The trajectory characteristics are analyzed to support the manned lunar missions design aimed at lunar surface global access. The concise procedure is established based on the circular restricted three-body problem (CR3BP) model. An analytical algorithm is employed to estimate an initial maneuver vector for approaching the Moon in its close vicinity. An iteration process is adopted to generate favorable trajectory that satisfies the constraints at perilune. By introducing a number of intermediate coordinate frames, an algorithm to compute the arriving LLO inclination and right ascension of ascending node (RAAN) is proposed. The orbital inclination and RAAN in this paper are defined and established in the J2000 frame rather than in the synodical frame. Numerical results show that, regardless of value of out-of-plane amplitude (\(Az\)) of the halo orbit, the overall maneuver cost of the trajectory largely depends on departure position, and it has two minima around 0.65 km/s. Further study shows that the values of the arriving LLO inclination and RAAN largely depend on the choices of the departure time and the value of \(Az\). The periodicity, due to the natural motion of the Moon, is discovered to play a role in this time dependency. It is concluded that the fuel optimal trajectory permits access to almost any final lunar orbit, including a polar orbit, by means of varying the departure time and \(Az\) value.

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Acknowledgement

This work is supported by the National Natural Science Foundation of China under Grant No. 11372345.

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  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Pengfei Cao, Boyong He & Haiyang Li

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  1. Pengfei Cao
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  2. Boyong He
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Correspondence to Haiyang Li.

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Cao, P., He, B. & Li, H. Analysis of direct transfer trajectories from LL2 halo orbits to LLOs. Astrophys Space Sci 362, 153 (2017). https://doi.org/10.1007/s10509-017-3124-x

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