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Close approach of a cloud of particles around an oblate planet

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Abstract

The goal of the present paper is to study close approaches of a cloud of particles with an oblate planet, which means that there is a \(J_{2}\) term in the gravitational potential of the planet. This cloud of particles is assumed to be created during the passage of a spacecraft by the periapsis of its orbit, by an explosion or any other disruptive event. The system is formed by two large bodies (Sun and planet), assumed to be in circular orbits around the center of mass of the system, and the cloud of particles. The particles that belong to the cloud make a close approach to the flat planet and then they are dispersed by the gravitational force of the planet. The motion is governed by the equations of motion given by the planar restricted circular three-body problem plus the effects of the oblateness of the planet. Jupiter is used for numerical simulations. The results show the differences between the behavior of the cloud after the passage, considering or not the effects of the oblateness of the planet. The results show that the oblateness of the planet is equivalent to an increase in the mass of the planet.

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Acknowledgments

The authors wish to express their appreciation for the support provided by Grants # 473387/2012-3, 304700/2009-6 and 473164/2013-2 from the National Council for Scientific and Technological Development (CNPq); Grants # 2011/08171-3, 2011/13101-4, 2014/06688-7, 2012/21023-6 and 2014/22295-5 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. State University of São Paulo, FEG/UNESP, Guaratinguetá, Brazil

    Vivian M. Gomes

  2. Federal Center for Technological Education of Minas Gerais, DELCOM/CEFET-MG, Contagem, Brazil

    Geraldo M. C. Oliveira

  3. National Institute for Space Research, DMC/INPE, São José dos Campos, Brazil

    Geraldo M. C. Oliveira, Antonio F. B. A. Prado & Diogo M. Sanchez

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  1. Vivian M. Gomes
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  2. Geraldo M. C. Oliveira
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  3. Antonio F. B. A. Prado
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  4. Diogo M. Sanchez
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Corresponding author

Correspondence to Diogo M. Sanchez.

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Communicated by Elbert E. N. Macau, Antônio Fernando Bertachini de Almeida Prado and Cristiano Fiorilo de Melo.

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Gomes, V.M., Oliveira, G.M.C., Prado, A.F.B.A. et al. Close approach of a cloud of particles around an oblate planet. Comp. Appl. Math. 35, 663–673 (2016). https://doi.org/10.1007/s40314-015-0264-x

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  • DOI: https://doi.org/10.1007/s40314-015-0264-x

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