logo

SCIENCE CHINA Information Sciences, Volume 60, Issue 11: 112301(2017) https://doi.org/10.1007/s11432-016-9069-9

Effect of orbital shadow at an Earth-Moon Lagrange point on relay communication mission

More info
  • ReceivedNov 16, 2016
  • AcceptedFeb 9, 2017
  • PublishedSep 19, 2017

Abstract

The shadow effect is an important constraint to be considered during the implementation of exploration missions. In this paper, for the Earth-Moon Lagrange point L2 relay communication mission, shadow effect issues on a periodic orbit about L2 are investigated. A systematic analysis based on the time domain and phase space is performed including the distribution, duration, and frequency of shadows. First, the Lindstedt-Poincare and second-order differential correction methods are used in conjunction with the DE421 planetary ephemeris to achieve a mission trajectory family in a high-precision ephemeris model. Next, on the basis of a conical shadow model, the influence of different orbital phases and amplitudes on the shadow is analyzed. The distribution of the shadow is investigated as well. Finally, the configuration of the shadow and its characteristics are studied. This study provides an important reference and basis for mission orbit design and shadow avoidance for relay satellites at an Earth-Moon Lagrange point.


Acknowledgment

This work was supported by National Science and Technology Major Project of the Ministry of Science and Technology of China (Lunar Exploration Program), National Natural Science Foundation of China (Grant No. 11572038), and Chang Jiang Scholars Program.


References

[1] Farquhar R W. Lunar Communications with Libration-Point Satellites. J Spacecraft Rockets, 1967, 4: 1383-1384 CrossRef ADS Google Scholar

[2] Ming X, Shijie X. Trajectory and Correction Maneuver During the Transfer from Earth to Halo Orbit. Chin J Aeronautics, 2008, 21: 200-206 CrossRef Google Scholar

[3] Mingtao L, Jianhua Z. Impulsive lunar Halo transfers using the stable manifolds and lunar flybys. Acta Astronaut, 2010, 66: 1481-1492 CrossRef ADS Google Scholar

[4] Canalias E, Masdemont J J. Computing natural transfers between Sun Earth and Earth Moon Lissajous libration point orbits. Acta Astronaut, 2008, 63: 238-248 CrossRef ADS Google Scholar

[5] Parker J S. Families of low-energy lunar halo transfers. In: Proceedings of AAS/AIAA Spaceflight Dynamics Conference, Tampa, 2006. 06-132. Google Scholar

[6] Kulkami J, Campbell M. Asymptotic stabilization of motion about an unstable orbit: application to spacecraft flight in halo orbit. In: Proceeding of the 2004 American Control Conference, Boston, 2004. 1025--1030. Google Scholar

[7] Xu M, Zhou N, Wang J L. Robust adaptive strategy for station keeping of halo orbit. In: Proceedings of the 24th Chinese Control and Decision Conference, Taiyuan, 2012. 3086--3091. Google Scholar

[8] Keeter T M. Station-keeping strategies for libration point orbit: target point and floquet mode approaches. Dissertation for Master's Degree. Indiana: Purdue University, West Lafayette, 1994. 145--148. Google Scholar

[9] Liu L, Cao J F, Hu S J, et al. Maintenance of relay orbit about the Earth-Moon collinear libration points. J Deep Space Explor, 2015, 2: 318--324. Google Scholar

[10] Dong G, Xu D, Li H. Initial result of the Chinese Deep Space Stations' coordinates from Chinese domestic VLBI experiments. Sci China Inf Sci, 2017, 60: 012203 CrossRef Google Scholar

[11] Jorba , Masdemont J. Dynamics in the center manifold of the collinear points of the restricted three body problem. Physica D-NOnlinear Phenomena, 1999, 132: 189-213 CrossRef ADS Google Scholar

[12] Li M T. Low energy trajectory design and optimization for collinear libration points missions. Dissertation for Ph.D. Degree. Beijing: Center for Space Science and Applied Research Chinese Academy of Sciences, 2010. 46--49. Google Scholar

[13] Montenbruck O, Gill E. Satellite Orbits: Models, Methods and Application. 2nd ed. Berlin: Springer, 2001. 80--81. Google Scholar

  • Figure 1

    (Color online) Southern family of halo orbit in the Earth-Moon three-body system.

  • Figure 2

    Geometrical relations of the shadow effect.

  • Figure 3

    (Color online) Distribution of orbital shadow in time-phase space.

  • Figure 4

    (Color online) Distribution of total shadow time for different orbital phases.

  • Figure 5

    Maximum single shadow time of spacecraft.

  • Figure 6

    (Color online) Distribution of orbital shadow for 9000 km amplitude.

  • Figure 8

    (Color online) Different shadow configurations.

  • Table 1   Extreme values of orbital shadow duration and frequency
    Phase ($^{\circ}$) Shadow duration (h) Phase ($^{\circ}$) Number of shadow
    96.72 97 98.19 21
    115.6 112 114.4 21
    244.2 111 244.2 20
    262.5 96 264.4 19
  • Table 2   Maximum shadow time of mission orbits and spacecraft for different orbital amplitudes
    Amplitude (km) Maximum total shadow duration for orbits (h) Maximum single shadow time for spacecraft (h)
    Upper bound Lower bound
    9000 115 19.5 4.0
    11000 113 14.0 3.5
    12000 112 12.5 3.5
    13000 110 11.5 3.5
    15000 108 10.0 3.0
  • Table 3   Distribution of shadow configurations in Earth shadow
    Configuration Frequency Range of phase ($^{\circ}$) Maximum single shadow time (h)
    a Twice(only in the first year) 61–137 5.0
    Twice (only in the first year) 225–294
    b Every half year 110–261 4.0
    (the second and third years)
    c Every half year $-$116–116 5.5
    (the second and third years)
  • Table 4   Distribution of shadow configurations in Moon shadow
    Configuration Frequency Range of phase ($^{\circ}$) Maximum single shadow time (h)
    b Five times a year 230–251 5.5
    Five times a year 107–127
    c Five times a year 86–106 11.0
    Five times a year 254–273
    d Twice a year 249–258 7.0
    Twice a year 101–112

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号