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

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


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.


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.


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  • 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

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