Skip to main content
SpringerLink
Log in

The precise positioning of lunar farside lander using a four-way lander-orbiter relay tracking mode

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

China is planning to land a spacecraft on the farside of the Moon, a premiere, by 2018. In essence, the traditional tracking modes, based on direct visibility, cannot operate for the lunar farside lander tracking, and therefore a relay satellite, visible at the same time by both the lander and the Earth, will be required, operating in the so-called four-way mode (Earth-relay satellite-lander-relay satellite-Earth). In this paper, we firstly give the mathematical formulation of the four-way relay tracking mode and of its partial derivatives with respect to the relevant parameters, implemented in our POD software WUDOGS (Wuhan University Deep-space Orbit determination and Gravity recovery System). In a second step, in simulation mode, we apply this relay mode to determining lander coordinates, which are absolutely needed for a sample return mission, or to add constraints on rotation models of the Moon. The results show that with Doppler measurements at a 0.1 mm/s error level, the positioning of the farside lander could be done at centimeters level (1-\(\delta\)) in the case of a circumlunar relay satellite; and at a 5 meters level (1-\(\delta\)) in the case of a Lagrange point (L2) Halo relay satellite.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Archinal, B.A., A’Hearn, M.F., Bowell, E., et al.: Report of the IAU working group on cartographic coordinates and rotational elements: 2009. Celest. Mech. Dyn. Astron. 109(2), 101–135 (2011). https://doi.org/10.1007/s10569-010-9320-4

    Article  ADS  MATH  Google Scholar 

  • Burns, J.O., Kring, D.A., Hopkins, J.B., et al.: A lunar L2-farside exploration and science mission concept with the Orion Multi-Purpose Crew Vehicle and a teleoperated lander/rover. Adv. Space Res. 52(2), 306–320 (2013). https://doi.org/10.1016/j.asr.2012.11.016

    Article  ADS  Google Scholar 

  • Cao, J.F., Zhang, Y., Hu, S.J., et al.: An analysis of precise positioning and accuracy of the CE-3 lunarlander soft landing. Geomat. Inf. Sci. Wuhan Univ. 41(2), 274–278 (2016). https://doi.org/10.13203/j.whugis20140123

    Article  Google Scholar 

  • Crawford, I.A., Joy, K.H.: Lunar exploration: opening a window into the history and evolution of the inner solar system. Philos. Trans. R. Soc. A 372, 20130315 (2014). https://doi.org/10.1098/rsta.2013.0315

    Article  ADS  Google Scholar 

  • Dong, G.L., Xu, D.Z., Li, H.T., et al.: Initial result of the Chinese Deep Space Stations’ coordinates from Chinese domestic VLBI experiments. Sci. China Inf. Sci. 60, 012203 (2017). https://doi.org/10.1007/s11432-016-0195-9

    Article  Google Scholar 

  • Folkner, W.M., Williams, J.G., Boggs, D.H., et al.: The planetary and lunar ephemerides DE430 and DE431. IPN Prog. Rep. 196, 1–81 (2014)

    Google Scholar 

  • Goossens, S., Matsumoto, K., Rowlands, D.D., et al.: Orbit determination of the SELENE satellites using multi-satellite data types and evaluation of SELENE gravity field models. J. Geod. 85, 487–504 (2011)

    Article  ADS  Google Scholar 

  • Haas, R., Halsig, S., Han, S., Iddink, A., Jaron, F., La Porta, L., Lovell, J., Neidhardt, A., Nothnagel, A., Plötz, Ch., Tang, G., Zhang, Z.: Observing the Chang’E-3 lander with VLBI (OCEL). In: First International Workshop on VLBI Observations of Near-field Targets, Bonn, Germany, October 5–6, 2016 (2016)

    Google Scholar 

  • Huang, Y., Hu, X.G., Li, P.J., et al.: Precise positioning of the Chang’E-3 lunar lander using a kinematic statistical method. Chin. Sci. Bull. 57, 2686–2692 (2012). https://doi.org/10.1007/s11434-012-5484-5

    Article  Google Scholar 

  • Huang, Y., Chang, S.Q., Li, P.J., et al.: Orbit determination of Chang’E-3 and positioning of the lander and the rover. Chin. Sci. Bull. 59(23), 2268–2277 (2014). https://doi.org/10.1007/s11434-014-0542-9

    Article  Google Scholar 

  • Jia, Y., Zou, Y., Ping, J., et al.: The scientific objectives and payloads of Chang’E-4 mission. Planet. Space Sci. (2018). https://doi.org/10.1016/j.pss.2018.02.011

    Article  Google Scholar 

  • Klopotek, G., Hobiger, T., Haas, R.: Geodetic VLBI with an artificial radio source on the Moon: a simulation study. J. Geod. 92, 457 (2018)

    Article  ADS  Google Scholar 

  • Konopliv, A.S., Park, R.S., Yuan, D.N., et al.: The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL primary mission. J. Geophys. Res., Planets 118(7), 1415–1434 (2013)

    Article  ADS  Google Scholar 

  • Kring, D.A., Durda, D.D.: A global lunar landing site study to provide the scientific context for exploration of the Moon. LPI Contrib. 1694, 688 (2012)

    Google Scholar 

  • Lemoine, F.G., Goossens, S., Sabaka, T.J., et al.: High-degree gravity models from GRAIL primary mission data. J. Geophys. Res., Planets 118(8), 1676–1698 (2013). https://doi.org/10.1002/jgre.20118

    Article  ADS  Google Scholar 

  • Li, F., Ye, M., Yan, J., et al.: A simulation of the four-way lunar lander-orbiter tracking mode for the Chang’E-5 mission. Adv. Space Res. 57(11), 2376–2384 (2016). https://doi.org/10.1016/j.asr.2016.03.007

    Article  ADS  Google Scholar 

  • Mathews, P.M., Dehant, V., Gipson, J.M.: Tidal station displacements. J. Geophys. Res., Solid Earth 102(B9), 20469–20477 (1997)

    Article  Google Scholar 

  • Mazarico, E., Rowlands, D.D., Neumann, G.A., et al.: Orbit determination of the Lunar Reconnaissance Orbiter. J. Geod. 86, 193–207 (2012)

    Article  ADS  Google Scholar 

  • Mazarico, E., Neumann, G.A., Barker, M.K., Goossens, S., Smith, D.E., Zuber, M.T.: Orbit determination of the Lunar Reconnaissance Orbiter: status after seven years. Planet. Space Sci. (2017). https://doi.org/10.1016/j.pss.2017.10.004

    Article  Google Scholar 

  • Mimoun, D., Wieczorek, M.A., Alkalai, L., et al.: Farside explorer: unique science from a mission to the farside of the Moon. Exp. Astron. 33(2–3), 529–585 (2012). https://doi.org/10.1007/s10686-011-9252-3

    Article  ADS  Google Scholar 

  • Montenbruck, O., Eberhard, G.: Satellite Orbits: Models, Methods, and Applications. Springer, Berlin (2000)

    Book  Google Scholar 

  • Moyer, T.D.: Mathematical formulation of the double precision orbit determination program. Technical Report, Jet Propulsion Laboratory, Pasadena, California, 32–1527 (1971)

  • Moyer, T.D.: Formulation for Observed and Computed Values of Deep Space Network Data Tyes for Navigation. John Wiley & Sons, Inc., Hoboken (2003)

    Book  Google Scholar 

  • Oleson, S.R., McGuire, M.L.: COMPASS final report: Lunar Relay Satellite (LRS). NASA/TM-217140 (2012)

  • Paulikas, G.A., et al.: The Scientific Context for Exploration of the Moon: Final Report. National Research Council, Washington (2007). 120 pp. https://doi.org/10.17226/11954

    Book  Google Scholar 

  • Petit, G., Luzum, B.: IERS conventions (2010), Bureau International des Poids et Mesures Sevres (France) (2010)

  • Rambaux, N., Williams, J.G.: The Moon’s physical librations and determination of their free modes. Celest. Mech. Dyn. Astron. 109(1), 85–100 (2011)

    Article  ADS  Google Scholar 

  • Smith, D.E., Zuber, M.T., Neumann, G.A., et al.: Summary of the results from the lunar orbiter laser altimeter after seven years in lunar orbit. Icarus 283, 70–91 (2017). https://doi.org/10.1016/j.icarus.2016.06.006

    Article  ADS  Google Scholar 

  • Tang, G., Nothnagel, A., Haas, R., Neidhardt, A., et al.: Research and analysis of lunar radio measurements of the Chang’E-3 lander. In: Proceedings of the First International Workshop on VLBI Observations of Near-field Targets, Bonn, Germany, October 5–6, 2016, pp. 35–40 (2016)

    Google Scholar 

  • Tapley, B.D., Schutz, B.E., Born, G.H.: Statistical Orbit Determination. Elsevier Academic Press, Burlington (2004)

    Google Scholar 

  • Tommei, G., Milani, A., Vokrouhlický, D.: Light-time computations for the BepiColombo radio science experiment. Celest. Mech. Dyn. Astron. 107(1–2), 285–298 (2010). https://doi.org/10.1007/s10569-010-9273-7

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Tong, F.X., Zheng, W.M., Shu, F.C.: Accurate relative positioning of Yutu lunar rover using VLBI phase-referencing mapping technology. Chin. Sci. Bull. 59, 3362–3369 (2014) (in Chinese). https://doi.org/10.1360/N972014-00578

    Article  Google Scholar 

  • Vasilyev, M.V., Shuygina, N.V., Ygudina, E.I.: Expected impact of the lunar lander VLBI observations on the lunar ephemeris accuracy. In: The 13th EVN Symposium & Users Meeting Proceedings, St. Petersburg, Russia, September 20–23, 2016 (2016)

    Google Scholar 

  • Wang, Q., Liu, J.Z.: A Chang’E-4 mission concept and vision of future Chinese lunar exploration activities. Acta Astronaut. (2016). https://doi.org/10.1016/j.actaastro.2016.06.024

    Article  Google Scholar 

  • Wei, Y., Yao, Z., Wan, W.: China’s roadmap for planetary exploration. Nat. Astron. 2, 346–348 (2018). https://doi.org/10.1038/s41550-018-0456-6

    Article  ADS  Google Scholar 

  • Wieczorek, M.A.: FARSIDE A mission to the farside of the Moon, call for a Medium-size mission opportunity in ESA’s science programme for a launch in 2025 (M4) (2014)

  • Williams, J.G., Boggs, D.H., Folkner, W.M.: DE430 lunar orbit, physical librations, and surface coordinates. JPL Memorandum IOM 335-JW, DB, WF-20130722-016, July 14 (2013)

  • Woodard, M., Cosgrove, D., Morinelli, P., et al.: Orbit determination of spacecraft in Earth-Moon L1 and L2 libration point orbits. In: AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska (2011)

    Google Scholar 

  • Wu, W.R., Wang, Q., Tang, Y.H., et al.: Design of Chang’E-4 lunar farside soft-landing mission. J. Deep Space Explor. 4(2), 111–117 (2017)

    Google Scholar 

  • Xiao, L., Qiao, L., Xiao, Z.Y., et al.: Major scientific objectives and candidate landing sites suggested for future lunar explorations. Sci. Sin. Phys. Mech. Astron. 46, 029602 (2016) (in Chinese). https://doi.org/10.1360/SSPMA2015-00507

    Article  Google Scholar 

  • Yan, J.G., Yang, X., Ye, M., Li, F., Jin, W.T., Barriot, J.P.: Independent Mars spacecraft precise orbit determination software development and its applications. Astrophys. Space Sci. 362(7), 123 (2017)

    Article  ADS  Google Scholar 

  • Ye, M.: Development of lunar spacecraft precision orbit determination software system and research on a four-way relay tracking measurement mode. Ph.D. Dissertation, Wuhan University, Wuhan (2016)

  • Ye, M., Yan, J.G., Li, F., et al.: Preliminary results of LUGREAS and its CVT with GEODYN-II. In: International Symposium on Lunar and Planetary Science, ISLPS, Wuhan (2016)

    Google Scholar 

  • Ye, M., Li, F., Yan, J.G., et al.: Wuhan university deep-space orbit determination and gravity recovery system (WUDOGS) and its application analysis. Acta Geod. Cartogr. Sin. 46(3), 288–296 (2017). https://doi.org/10.11947/j.AGCS.2017.20160525

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by National Scientific Foundation of China (Grant Nos. 41604004,41804025,41874010), Innovation Group of Natural Fund of Hubei Province (Grant Nos. 2015CFA011 and 2018CFA087), the Opening Project of Shanghai Key Laboratory of Space Navigation and Positioning Techniques (No. KFKT_201703), and China Postdoctoral Science Foundation (Grant No. 2016M602360). Jean-Pierre Barriot is founded by the French Space Agency (CNES), through a Decision d’aide à la Recherche. The anonymous reviewers are highly acknowledged for their constructive comments which improved the quality of this paper.

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 129 Luoyu Road, Wuhan, 430070, China

    Mao Ye, Fei Li, Jianguo Yan, Weitong Jin & Xuan Yang

  2. Shanghai Key Laboratory of Space Navigation and Positioning Techniques, Chinese Academy of Sciences, 80 Nandan Road, Shanghai, 200030, China

    Mao Ye

  3. Observatoire Géodésique de Tahiti, University of French Polynesia, BP 6570, 98702, Faa’a, Tahiti, French Polynesia

    Mao Ye & Jean-Pierre Barriot

  4. Chinese Antarctic Center of Surveying and Mapping, Wuhan University, 129 Luoyu Road, Wuhan, 430079, China

    Fei Li & Weifeng Hao

Authors
  1. Mao Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianguo Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jean-Pierre Barriot
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Weifeng Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Weitong Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Xuan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ye, M., Li, F., Yan, J. et al. The precise positioning of lunar farside lander using a four-way lander-orbiter relay tracking mode. Astrophys Space Sci 363, 236 (2018). https://doi.org/10.1007/s10509-018-3421-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10509-018-3421-z

Keywords

Search

Navigation