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Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 133–143 | Cite as

Orbital effects in a cloud of space debris making a close approach with the earth

  • Jorge Kennety S. FormigaEmail author
  • Vivian Martins Gomes
  • Rodolpho Vilhena de Moraes
Article
  • 93 Downloads

Abstract

The present paper has the goal of studying the changes of the orbital parameters of each individual element of a cloud of particles that makes a close approach with the Earth. Clouds of particles are formed when natural or man-made bodies explode for some reason. After an explosion like that, the center of mass of the cloud follows the same orbit of the body that generated the explosion, but the individual particles have different trajectories. The cloud is specified by a distribution of semi-major axis and eccentricity of their particles. This cloud is assumed to pass close to the Earth, making a close approach that modifies the trajectory of every particle that belongs to the cloud. The present paper makes simulations based in the “Patched-Conics” model to obtain the new trajectories of each particle. Then, it is possible to map the new distribution of the Keplerian elements of the particles that constituted the cloud, using the previous distribution as initial conditions. These information are important when planning satellite missions having a spacecraft passing close to a cloud of this type, because it is possible to obtain values for the density and amplitude of the cloud, so finding the risks of collision and the possible maneuvers that need to be made in the spacecraft to avoid the collisions.

Keywords

Orbital Maneuver Close approach Restricted three-body problem Space trajectories 

Mathematics Subject Classification

70F05 70F07 70F15 

Notes

Acknowledgements

The authors wish to express their appreciation for the support provided by Grants #2016/15675-1, 2011/13101-4, 2011/08171-3 from São Paulo Research Foundation (FAPESP); Grants # 473164/2013-2 and 309106/2015-0, 308823/2015-0 from the National Council for Scientific and Technological Development (CNPq) and Institute of Science and Technology, UNESP-São Paulo State University.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • Jorge Kennety S. Formiga
    • 1
    Email author
  • Vivian Martins Gomes
    • 2
  • Rodolpho Vilhena de Moraes
    • 3
  1. 1.Instituto de Ciência e TecnologiaUNESP, Universidade Estadual PaulistaSão PauloBrazil
  2. 2.Grupo de Dinâmica Orbital e PlanetologiaUNESP, Universidade Estadual PaulistaSão PauloBrazil
  3. 3.Universidade Federal de São Paulo/ICTSão PauloBrazil

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