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Studying sequences of resonant orbits to perform successive close approaches with the Moon

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Abstract

This research shows a study of the dynamical behavior of a spacecraft that performs a series of close approaches with the Moon. This maneuver is also known in the literature as Gravity-Assisted Maneuver. It is a technique to reduce the fuel expenditure in interplanetary missions by replacing maneuvers based on engines by passages near a massive body. The spacecraft moves under the gravitational attraction of the two bodies that dominate the system, the Earth and the Moon in the present study, and has a negligible mass. The main assumption to study this problem is that the motions are planar everywhere. In particular, we are looking for geometries that allow multiple close approaches without any major correction maneuvers. It means that the only maneuvers allowed are the negligible ones made to force the spacecraft to pass by the Moon with a specified distance from its surface. So, resonant orbits are required to obtain the series of close approaches. Analytical equations are derived to obtain the values of the parameters required to get this sequence of close approaches. The main motivation for this study is the existence of several studies for missions that has the goal of studying the space around the Earth–Moon system using multiple close approaches to make the spacecraft to cover a larger portion of the space without any major maneuver. After obtaining the trajectories, the criterion of Tisserand is used to validate the trajectories found. Then, a verification of the accuracy of the “patched-conics” method for the Earth–Moon system is made.

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Acknowledgments

The authors wish to express their appreciation for the support provided by Grants # 473387/2012-3 and 304700/2009-6, from the National Council for Scientific and Technological Development (CNPq); grants # 2011/08171-3, 2011/13101-4, 2014/06688-7 and 2012/21023-6, from São Paulo Research Foundation (FAPESP) and the financial support from the National Council for the Improvement of Higher Education (CAPES).

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Authors and Affiliations

  1. National Institute for Space Research - INPE, Av dos Astronautas 1758, São José dos Campos, SP, Brazil

    Jorge Kennety S. Formiga & Antonio F. B. A. Prado

  2. College of Technology, FATEC-SJC, São José dos Campos, SP, Brazil

    Jorge Kennety S. Formiga

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  1. Jorge Kennety S. Formiga
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  2. Antonio F. B. A. Prado
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Correspondence to Antonio F. B. A. Prado.

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Technical Editor: Fernando Alves Rochinha.

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Formiga, J.K.S., Prado, A.F.B.A. Studying sequences of resonant orbits to perform successive close approaches with the Moon. J Braz. Soc. Mech. Sci. Eng. 37, 1391–1404 (2015). https://doi.org/10.1007/s40430-014-0254-8

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  • DOI: https://doi.org/10.1007/s40430-014-0254-8

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